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21.NONLINEAR ELEMENTS Earthquake Resistant Structures Should Have a Limited Number of Nonlinear Elements that can be Easily Inspectedand Replaced after a Major Earthquake.21.1 INTRODUCTION{ XE "Energy:Energy Dissipation Elements" }{ XE "Nonlinear Elements" }Many different types of practical nonlinear elements can be used in conjunction with the application of the Fast Nonlinear Analysis method. The FNA method is very effective for the design or retrofit of structures to resist earthquake motions because it is designed to be computationally efficient for structures with a limited number of predefined nonlinear or energy dissipating elements. This is consistent with the modern philosophy of earthquake engineering that energy dissipating elements should be able to be inspected and replaced after a major earthquake.Base isolators are one of the most common types of predefined nonlinear elements used in earthquake resistant designs. In addition, isolators, mechanical dampers, friction devices and plastic hinges are other types of common nonlinear elements. Also, gap elements are required to model contact between structural components and uplifting of structures. A special type of gap element with the ability to crush and dissipate energy is useful to model concrete and soil types of materials. Cables that can take tension only and dissipate energy in yielding are necessary to capture the behavior of many bridge type structures. In this chapter the behavior of several of those elements will be presented and detailed solution algorithms will be summarized.。
关于中国古代科学家的口头报告英语作文全文共3篇示例，供读者参考篇1Ancient Chinese Scientists: Pioneers of Discovery and InnovationHey everyone, today I'll be giving an oral report on some of the most important scientists and innovators from ancient China. China has an incredibly rich history of scientific exploration and groundbreaking discoveries dating back thousands of years. These brilliant minds laid the foundations for many fields we still study and benefit from today.Let's start by going way back to the 3rd century BC during the Qin Dynasty. This is when an extraordinary polymath named Zhang Heng lived. Zhang made major contributions to fields like astronomy, mathematics, geography, optics, and even invented one of the first seismometers to detect earthquakes. How crazy is that for technology from over 2,000 years ago?In astronomy, Zhang precisely calculated the radius of the sun and moon as well as the distances between the earth, sun and moon with remarkable accuracy given the limited toolsavailable at the time. He studied eclipses and created a atlas of over 300 stars and constellations. Zhang also designed an intricate water-powered armillary sphere that tracked the movements of celestial bodies.His seismometer was an incredibly ingenious device that used a complex system of enclosed brass balls and levers to detect the exact cardinal direction of an earthquake's origin. It's mind-blowing that he conceived of something so technically advanced back in ancient times.Moving ahead a few centuries to the Han Dynasty around 100 AD, we encounter the brilliant mathematician, inventor and mechanic Zhang Heng. This Zhang pioneered many developments in cartography and created the first model of the rotational movement of celestial bodies. To symbolize this groundbreaking concept, he designed an ingenious sphere powered by a water wheel that rotated around its axis.Another Han dynasty standout was the philosopher, writer and all-around polymath Zhang Zhongjing, considered the greatest clinician of his era. Zhang essentially founded the science of acupuncture therapy and published the seminal medical text "Treatise on Cold Damage Disorders" that was usedas the leading diagnostic and treatment reference work for over a millennium.Fast forwarding to the 3rd century AD during the Jin Dynasty, we have the legendary mathematician and astronomer Liu Hui. Liu made tremendous strides in geometry, pioneering the systematic study of spheres. He derived the volumes of complex three-dimensional shapes like prisms and pyramids as well as developing algorithms to calculate pi with incredible precision.Liu authored the pivotal mathematical text "Sea Island Mathematical Manual" that proved and elaborated upon principles from ancient Greek geometry texts like Euclid's "Elements." He became the first person to successfully calculate the volume and surface area of a three-dimensional sphere. Pretty amazing stuff considering this knowledge wouldn't reach Europe until over a millennium later.Skipping ahead to the Sui Dynasty in the 6th century AD,let's discuss the brilliant inventor, mathematician and engineer Xindu Faxian. This guy made major advancements in fields ranging from mechanical engineering to hydraulics andclock-making. Xindu invented China's first mechanical clock powered by water - the things we take for granted like accurate timekeeping would be impossible without pioneers like him.He also engineered an odometer that measured distance traveled which was attached to a rotating figure that rang a bell to record each distance increment. You can see how his distance measuring inventions laid the groundwork for the modern day pedometer.During the Tang Dynasty in the 7th century, we have the mathematician and astronomer Yi Xing whose work was instrumental in the development of trigonometry and spherical geometry. Yi made history by inventing the first torque spherical trigonometry, computing precise sine values and compiling comprehensive astronomical charts and records of solar eclipses.His book the "Condensed Treatise on Calculation" included ingenious methods for measuring the height of mountains and depths of pools using trigonometric functions before solving for the unknown side or angle. Yi Xing basically pioneered the use of sine function plane trigonometry in China.There are so many more innovators I could spotlight like the philosophers and mathematicians Shao Yong and Shen Kuo in the 11th century or the astronomer Guo Shoujing in the 13th century. But I'll leave you with one of the last greatscientists/inventors of ancient China - Zhu Shijie in the late 13th century during the Yuan Dynasty.Zhu was a true Renaissance man who made breakthroughs in fields like astronomy, anatomy, archeology, geology, optics, mathematics, and more. He was the first to describe the concept of conventional current by noting that the magnetic needle in a compass is controlled by Earth's magnetic field. Zhu also identified the concept of "fossil" noting the petrified remains of shelled creatures in rocks.In mathematics, Zhu pioneered the use of vector notation and proved the Pythagorean theorem using similar triangles over a century before it was done in Europe. He invented an incredibly precise astronomical instrument called the Equatorial Sundial that could calculate several astronomical quantities and the ecliptic paths of the sun and moon.These are just a few examples of the countless ancient Chinese scientists and innovators who expanded the frontiers of human knowledge through meticulous observation, brilliant reasoning, and insatiable curiosity. While largely unknown in the West, their pioneering work became the foundation for everything from astronomy and mathematics to engineering, optics, and medicine as we know it today.I hope you've gained a new appreciation for some of these great Chinese minds who overcame technological limitations tomake immeasurable contributions to science and humanity as a whole. Their stories of perseverance, intellectual courage, and human ingenuity still inspire new generations of thinkers and innovators today. Thanks for listening, everyone!篇2Ancient Chinese Scientists: Pioneers of InnovationGreetings everyone! For my oral report today, I'd like to take you on a journey through the fascinating world of ancient Chinese scientists and their groundbreaking contributions to various fields of knowledge.China has a rich history of scientific exploration and innovation, dating back thousands of years. Despite facing numerous challenges and limitations, the inquisitive minds of these early scholars paved the way for remarkable discoveries that continue to shape our understanding of the world today.One of the most renowned figures in Chinese scientific history is Zhang Heng, who lived during the Eastern Han Dynasty (25-220 AD). Zhang Heng was a true polymath, excelling in astronomy, mathematics, geography, and even literary arts. His most celebrated invention was the world's first seismoscope, an ingenious device capable of detecting earthquakes anddetermining their approximate direction. This groundbreaking achievement predated modern seismological instruments by nearly 1,700 years!Another pioneering scientist was Shen Kuo, a brilliant mind of the Song Dynasty (960-1279 AD). Shen Kuo's contributions spanned various disciplines, including geography, geology, astronomy, mathematics, and physics. He was the first to accurately describe the natural process of soil formation and erosion, laying the foundation for modern soil science. Additionally, Shen Kuo's meticulous observations of planetary motions and his advocacy for the spherical Earth theory challenged the prevailing geocentric model of the universe.Moving on to the field of medicine, we encounter the legendary Hua Tuo, who lived during the Eastern Han Dynasty (141-208 AD). Hua Tuo was a pioneering physician and surgeon who introduced groundbreaking surgical techniques and anesthetic methods. He is credited with developing the world's first general anesthetic, a concoction known as "mafeisan," which allowed patients to undergo complex operations without experiencing excruciating pain. Hua Tuo's innovative approach to medical practices revolutionized the field and paved the way for safer and more effective surgical procedures.In the realm of mathematics, we cannot overlook the brilliance of Liu Hui, who lived during the Three Kingdoms period (265-313 AD). Liu Hui made significant contributions to geometry and is best known for his work on calculating the value of pi (π). Th rough intricate calculations and geometric proofs, he derived an approximation of pi that was accurate to seven decimal places – a remarkable achievement for his time. Liu Hui's work laid the foundation for subsequent advancements in mathematics and contributed to our understanding of the fundamental constants that govern the universe.Continuing our journey, we encounter the remarkable achievements of Zu Chongzhi, a mathematician and astronomer from the Northern and Southern Dynasties (429-501 AD). Zu Chongzhi is celebrated for his pioneering work in calculating the value of pi with unprecedented accuracy. By employing an ingenious algorithm and complex geometric calculations, he derived an approximation of pi that surpassed all previous estimates, achieving an astonishing level of precision for his era.Moving into the realm of engineering, we cannot overlook the contributions of the brilliant Zhang Heng, whom we discussed earlier. In addition to his groundbreaking seismoscope, Zhang Heng is also credited with developing the world's firstwater clock powered by a complex system of water wheels and escapement mechanisms. This ingenious device not only kept accurate time but also showcased the advanced engineering capabilities of ancient Chinese scholars.Another remarkable engineering feat was the invention of the world's first mechanical clock by Yi Xing and Liang Lingzan during the Tang Dynasty (618-907 AD). This remarkable timepiece, powered by an intricate system of gears and escapements, revolutionized timekeeping and demonstrated the ingenuity of Chinese engineering. The mechanical clock's design principles would later inspire and influence the development of clocks and timekeeping devices across the globe.As we delve deeper into the annals of Chinese scientific history, we encounter the groundbreaking work of Shen Kuo once again. In addition to his contributions to geology and astronomy, Shen Kuo made significant advancements in the field of optics. He was the first to accurately describe the principles of camera obscura, a precursor to modern photography, and conducted pioneering experiments on the properties of light and vision. Shen Kuo's insights into optics laid the foundation for future developments in fields such as microscopy and telescopy.Lastly, we cannot overlook the invaluable contributions of ancient Chinese alchemists and their pursuit of immortality and transmutation. While their quest for eternal life and the ability to turn base metals into gold may seem fantastical today, their experiments and observations paved the way for the development of modern chemistry. The alchemists' meticulous documentation of chemical processes, their exploration of various substances, and their relentless pursuit of knowledge laid the groundwork for the scientific method and the eventual emergence of modern chemistry as a discipline.As we reflect on the achievements of these ancient Chinese scientists, it becomes evident that their contributions transcended mere discoveries or inventions. Their inquisitive minds, unwavering dedication to knowledge, and willingness to challenge prevailing beliefs paved the way for scientific progress and laid the foundation for our modern understanding of the world.Despite facing numerous limitations and obstacles, these pioneers of science persevered, driven by an innate curiosity and a desire to unlock the mysteries of the universe. Their legacies serve as a testament to the human spirit of inquiry and theboundless potential of the mind to push the boundaries of knowledge.In conclusion, the ancient Chinese scientists we have discussed today were true visionaries, whose groundbreaking contributions continue to shape our understanding of the world and inspire generations of scientists and scholars to come. Their achievements stand as a reminder of the enduring power of human ingenuity and the profound impact that curiosity and perseverance can have on advancing our collective knowledge.Thank you for your attention, and let us all strive to emulate the inquisitive spirit of these ancient pioneers as we forge ahead in our own scientific pursuits.篇3Ancient Chinese Scientists: Pioneering Minds of the EastGood morning everyone. Today, I'll be giving an oral report on some of the most influential ancient Chinese scientists and their groundbreaking contributions to various fields of study. From astronomy to mathematics, medicine to technology, these brilliant minds laid the foundation for many modern scientific principles we know today.Let's start with one of the earliest renowned figures - Zhang Heng, an incredibly gifted polymath who lived during the Eastern Han Dynasty around 78-139 AD. Zhang made pioneering developments in several disciplines, but his work in astronomy truly stands out. He was the first to correctly theorize that the sun was much larger than the earth, disproving the long-held belief that they were similar in size. Even more impressively, around 132 AD, Zhang invented the world's first seismoscope - a device that could detect earthquakes from great distances away. This remarkable invention worked using an ingenious design of metallic balls that would drop to indicate the cardinal direction of an earthquake's location.Moving ahead a few centuries, we come to the Tang Dynasty mathematician Zu Chongzhi who made significant advancements in calculating the value of pi. In around 480 AD, Zu computed pi to what was then the world record of 7 decimal places, using an extremely laborious process of inscribing and circumscribing polygons with increasing numbers of sides. His mathematically derived value of 3.1415926 for pi was incredibly accurate for that era. Zu also helped develop assembled numerical notation and systematized the use of negative numbers - both critical developments in the evolution of mathematics.No discussion of ancient Chinese science is complete without mentioning the iconic medical scholar Hua Tuo, who revolutionized surgery and anesthesia techniques in the 2nd century AD. Among his most famous innovations was a general anesthetic formulated using a mixture of wine and herbal extracts. This allowed Hua to perform complex surgeries on internal organs like the brain and abdomen - procedures previously thought to be impossible due to the extreme pain and shock inflicted. Some of Hua's other medical breakthroughs included developing practiced techniques for relieving acute intestinal obstruction through surgery, and using stone needles to puncture abscess cavities to drain out fluid buildup.Shifting gears to the field of technology, I have to highlight the brilliant 5th century inventor, engineer and Buddhist monk Xuan Xiaowei. Among his long list of innovations, perhaps the most well-known was the world's first water-driven spinning wheel design powered by a horizontal waterfed wheel. This automated textile machinery eliminated the incrediblylabor-intensive manual process of spinning fibers into thread or yarn. Xuan's other inventions included an improvedsquare-pallet chain pump design for irrigation, and adouble-action rotary winnowing fan that greatly increased crop efficiency.The sheer breadth and impact of these ancient scientists' contributions is astounding. From celestial phenomena to ingenious machinery and medical marvels, their pioneering research and developments laid the bedrock for future generations to build upon. Zhang Heng's astronomical observations and mechanical marvels. Zu Chongzhi's pi calculations and mathematical notation systems. Hua Tuo's groundbreaking surgical procedures and anesthesia protocols. Xuan Xiaowei's automated industrial machinery designs. The list of landmark achievements goes on and on.What's most remarkable is that these scholars pursued knowledge and scientific inquiry in an era where resources and technological means were extremely limited compared to modern times. Their resourcefulness, intellectual curiosity and perseverance in the face of limitations led to pivotal discoveries across multiple fields - paving the way for the scientific and industrial revolutions centuries later.While their names may not be as universally recognized as Galileo, Newton or Einstein in the Western world, these ancient Chinese pioneers undoubtedly belong among the pantheon of history's greatest scientific luminaries. Their accumulated wisdom, empirical observations and innovative thinking laid thebrickwork for future breakthroughs in countless disciplines. Without their foundational research, the world of science would have followed a vastly different trajectory.So the next time you ponder the mysteries of the cosmos, solve an algebraic equation, go under anesthesia for surgery or power up a mechanical device, remember the ingenuity and brilliance of these unsung ancient Chinese scholars who dared to push the boundaries of human knowledge. Their tireless spirit of intellectual exploration opened portals into realms of science once thought implausible or impossible. For that enduring legacy, all of humanity remains forever indebted to these pioneering minds of the ancient East.Thank you for your attention. I'll be happy to take any questions you may have.。
高中英语世界著名科学家单选题50题1. Albert Einstein was born in ____.A. the United StatesB. GermanyC. FranceD. England答案：B。
解析：Albert Einstein（阿尔伯特·爱因斯坦）出生于德国。
本题主要考查对著名科学家爱因斯坦国籍相关的词汇知识。
在这几个选项中，the United States是美国，France是法国，England是英国，而爱因斯坦出生于德国，所以选B。
2. Isaac Newton is famous for his discovery of ____.A. electricityB. gravityC. radioactivityD. relativity答案：B。
解析：Isaac Newton 艾萨克·牛顿）以发现万有引力gravity）而闻名。
electricity是电，radioactivity是放射性，relativity 是相对论，这些都不是牛顿的主要发现，所以根据对牛顿主要成就的了解，选择B。
3. Marie Curie was the first woman to win ____ Nobel Prizes.A. oneB. twoC. threeD. four答案：B。
解析：Marie Curie 居里夫人）是第一位获得两项诺贝尔奖的女性。
这题主要考查数字相关的词汇以及对居里夫人成就的了解，她在放射性研究等方面的贡献使她两次获得诺贝尔奖，所以选B。
4. Thomas Edison is well - known for his invention of ____.A. the telephoneB. the light bulbC. the steam engineD. the computer答案：B。
解析：Thomas Edison（ 托马斯·爱迪生）以发明电灯（the light bulb）而闻名。
全身运动不安运动阶段质量评估对婴幼儿神经系统疾病预测价值的Meta分析门光国;王凤敏;崔英波【摘要】目的探讨婴幼儿早期(出生后20周内)全身运动(GMs)不安运动阶段质量评估对婴幼儿神经系统疾病的预测价值.方法利用数据库检索到2015年12月前发表的相关文献,共有16篇文献纳入研究并进行Meta分析.结果 16篇文献QUADAS评分≥10的有8篇,临床特征等信息差异均无统计学意义(P＞0.05).GMs 不安运动阶段质量评估对神经系统发育不良结局(包括脑性瘫痪)的预测分析显示,灵敏度、特异度、阳性似然比(PLR)、阴性似然比(NLR)和诊断比值比(DOR)分别为0.78、0.93、11.26、0.24和55.43;SROC曲线表明灵敏度和特异度最佳结合点的Q值为0.852 2,AUC值为0.919 0.GMs不安运动阶段质量评估对脑性瘫痪的预测分析显示,灵敏度、特异度、PLR、NLR和DOR分别为0.91、0.94、12.91、0.12和133.66,SROC曲线表明灵敏度和特异度最佳结合点的Q值为0.918 5,AUC值为0.969 2.结论 GMs不安运动阶段质量评估是预测婴幼儿神经系统疾病的一种有效方法,但不推荐单独使用.【期刊名称】《浙江医学》【年(卷),期】2016(038)014【总页数】5页(P1161-1165)【关键词】全身运动;不安运动阶段;婴幼儿;神经系统疾病;脑性瘫痪;Meta分析【作者】门光国;王凤敏;崔英波【作者单位】315012 宁波市妇女儿童医院新生儿科;315012 宁波市妇女儿童医院新生儿科;315012 宁波市妇女儿童医院新生儿科【正文语种】中文全身运动（general movements，GMs）是一种复杂的动作，包括头部、躯干、手臂和腿的运动，出现于胎儿早期并持续到出生后3～4个月。
近年来，GMs质量评估对婴幼儿脑性瘫痪（CP）等神经系统疾病的预测价值得到越来越多证据支持[1-2]。
【2017年整理】Abaqus Explicit 接触问题1. Abaqus/Explicit 中的接触形式双击Interactions，出现接触形式定义。
分为通用接触(General contact)、面面接触(Surface-to-Surface contact)和自接触(Self-contact)。
1. 通用接触 General contact通用接触用于为多组件，并具有复杂拓扑关系的模型建模。
General contact algorithm• The contact d omain spans multiple bodies (both rigid and deformable) • Default domain is defined automatically via an all-inclusive element-based surface • The method is geared toward models with multiple components and complex topology。
• Greater ease in defining con tact model2. Surface-to-Surface contactContact pair algorithm• Requires user-specified pairing of individual surfaces• Often results in more efficient analyses since contact surfaces are limited in scope3. 自接触(Self-contact)自接触应用于当部件发生变形时，可能导致自己的某两个或多个面发生接触的情况。
如弹簧的压缩变形，橡胶条的压缩。
• 容易使用• “自动接触”• 节省生成模型的时间• 通用接触算法一般比双面接触算法快机械约束形式• 运动依从 Kinematic contact method (只有接触对形式可用,General contact不可用)默认的运动接触公式达到的计算精度与接触条件相一致。
1. Abaqus/Explicit 中的接触形式双击Interactions，出现接触形式定义。
分为通用接触（General contact）、面面接触（Surface-to-Surface contact）和自接触（Self-contact）。
1. 通用接触 General contact通用接触用于为多组件，并具有复杂拓扑关系的模型建模。
General contact algorithm• The contact domain spans multiple bodies (both rigid and deformable)•Default domain is defined automatically via an all-inclusive element-based surface• The method is geared toward models with multiple components and complex topology。
• Greater ease in defining contact model2. Surface-to-Surface contactContact pair algorithm• Requires user-specified pairing of individual surfaces• Often results in more efficient analyses since contact surfaces arelimited in scope3. 自接触（Self-contact）自接触应用于当部件发生变形时，可能导致自己的某两个或多个面发生接触的情况。
如弹簧的压缩变形，橡胶条的压缩。
•容易使用•“自动接触”•节省生成模型的时间•通用接触算法一般比双面接触算法快机械约束形式•运动依从Kinematic contact method（只有接触对形式可用,General contact不可用）默认的运动接触公式达到的计算精度与接触条件相一致。
《Plant Physiology》（双语）教学教案任课教师：王晓峰教授单位：生命科学学院植物学系授课班级：生科丁颖班、农学丁颖班等Introduction计划学时：2 h一.教学目的了解植物生理学的对象、内容、产生和发展及发展趋势。
二.教学重点植物生理学的内容及发展趋势，植物生理学与分子生物学的关系。
三.教学难点植物生理学的发展趋势四.教学方法采用以多媒体教学法为主。
五.教学用具多媒体硬件支持。
六.教学过程●Introduction of my research work briefly (5 min)●Concept of plant physiology and main contents and chapters of this course (20 min) ●Tasks of plant physiology（20 min）Some examples: Photoperiod, Solution culture, Water culture, Senescence, Ethylene, Tissue culture, Plant growth substance, Photomorphogenesis, Etiolation.●Establishment and development of plant physiology（30 min）In ancient China and western countries→Experimentally/scientifically→J.von Liebig’s work→Modern plant physiology. Establishment and development of plant physiology in China.●Perspectives of plant physiology（10 min）Five problems of human beings : Food, Energy, Environment, Resources, Population ●Summary of the contents of introduction（5 min）Chapter 1 Water Metabolism教学章节：植物对水分的需要、植物细胞对水分的吸收、植物根系对水分的吸收、蒸腾作用、植物体内水分的运输、合理灌溉的生理基础计划学时：3 h一、教学目的通过本章学习，主要了解植物对水分吸收、运输及蒸腾作用的基本原理，认识维持植物水分平衡的重要性，为合理灌溉提供理论基础。
Generative Fluid Dynamics: Integration of Fast Fluid Dynamics and Genetic Algorithms for wind loading optimizationof a free form surfaceAngelos Chronis1, Alasdair Turner1 and Martha Tsigkari11University College London, Gower Street,London, UK, WC1E 6BTangelos.chronis.09@, a.turner@, mtsigkar@Keywords:Computational Fluid Dynamics (CFD), Fast Fluid Dynamics (FFD), Genetic Algorithms (GA), wind load, optimization.AbstractThe integration of simulation environments in generative, performance-driven form-finding methods is expected to enable an exploration into performative solutions of unprecedented complexity in architectural design problems. Computational fluid dynamics simulations have a wide range of applications in architecture, yet they are mainly applied at final design stages for evaluation and validation of design intentions, due to their computational and expertise requirements.This paper investigates the potential of a fast fluid dynamics simulation scheme in a generative optimization process, through the use of a genetic algorithm, for wind loading optimization of a free form surface. A problem-specific optimization environment has been developed for experimentation. The optimization process has provided valuable insight on both the performance objectives and the representation of the problem. The manipulation of the parametric description of the problem has enabled control over the solution space highlighting the relation of the representation to the performance outcome of the problem.1.INTRODUCTIONThe recent advancements of digital fabrication and the continuous development of computer aided design tools have not only liberated architecture from its geometrical constraints but they have also infused in it a computational realm of experimentation into form and function of unprecedented complexity. With parametric design systems being only the start point and computationally simulated dynamical systems of form finding the quintessence of this exploration, architecture has in part shifted from the design and drafting to the creation of the generative systems from which the final form emerges (Kolarevic 2003). The architectural discourse has lately been rigorously engaged in embodying the potential of this achievable complexity not only in the aesthetic but also in the performative aspects of contemporary architecture.The integration of simulation environments in the architectural computational framework has been a key factor in this exploration, as they provide the test bed for experimentation with the various aspects of architectural performance. This has led to a substantial development of both the simulation algorithms and their interfacing tools as well as their applicability in the building industry, facilitated also through the increase of available computational resources but also significantly through novel computational approaches and paradigms (Malkawi 2004). Although it is expected that the incorporation of these simulation environments in computational generative processes will enable a critical and systemic thinking into performance driven architecture and shape innovative performative solutions, their integration in a streamlined computational framework throughout all stages of the design process remains a challenge (Shea et al 2005).One of the areas that are still largely unexplored, in terms of its integration into generative design approaches is that of computational fluid dynamics (CFD). CFD simulations have a vast variety of applications in architecture, ranging from wind load analysis on buildings to ventilation and energy performance, contamination dispersion or even acoustical analyses (Malkawi 2004). However due to the complexity of the simulated phenomenaand the consequent computational demand of the simulation algorithms available, their use is restricted to final design stages for evaluation and validation of design intentions. There is evidence though, as it will be argued here, that through the use of less accurate but also computationally less demanding approaches, CFD simulations may be able to be applied not only at earlier design stages to inform preliminary design decisions, but even more to be integrated in generative form finding processes. In our approach we aim to explore the potential of a real-time fluid dynamics simulation scheme in the optimization of the wind loading of a free form surface canopy, through the use of a genetic algorithm (GA). It has to be stated, that the aim of this approach is not to attempt to simulate the physical phenomena with the maximum possible accuracy, but rather to investigate the potential of a resource effective simulation scheme in a conceptual stage generative approach.2.BACKGROUNDThe phenomena of fluid dynamics are described by the Navier Stokes equations and are considered one of the most challenging engineering problems. Navier-Stokes are notoriously difficult to approach analytically and therefore numerical methods are used to approximate their solution. This approximation introduces an amount of error in the simulation, the tolerance of which depends on the application and the goals of the simulation (Lomax et al 1999). The computational approaches to the simulation of fluids have been continuously expanding the past decades and there is a great variety of available simulation algorithms today, ranging from particle to mesh based approaches and from lower to higher accuracy models. Despite their continuous development though, the available simulation tools have not yet reached the expectations of researchers in combining accuracy with speed (Chen 2009). The computational timeframe of the simulations ranges from hours and days to even weeks, when involved in optimization processes (Hanna et al 2010).The areas of application of CFD in architecture are numerous and include among many others the analysis of indoor climate (Hartog et al 2000), ventilation performance (Chen 2009) and heating, ventilation and air conditioning (HVAC) systems (Hien & Mahdavi 1999) as well as the analysis of urban scale conditions, such as street layout configurations (Xiaomin et al 2006) and airflow analysis in dense urban environments (Chung & Malone-Lee 2010). In a number of these studies (Chung & Malone-Lee 2010; Hartog et al 2000; Hien & Mahdavi 1999) it is highlighted that there is a need to incorporate CFD simulations at earlier design stages. More specifically, what is pointed out is the inconsistency between the synthetic and the analytic design stages and therefore it is suggested that optimization needs to be initiated at early design stages to be more effective. The suggestions include parametric design systems, hybrid simulation approaches and visualization schemes to approach the simulation data sets.In the field of wind engineering, the applications of CFD simulations are also numerous and span all scales of the urban environment, from high rise buildings (Huang et al 2007) to building roofs (Kumar & Stathopouloos 1997). Although in most cases the study of wind loads is validated through wind tunnel experiments, the CFD simulations are considered a fundamental tool in wind load analysis (Baker 2007). Again the integration of CFD simulations in earlier design stages is attempted through different approaches, such as the development of tools that streamline the pre and post processing of the simulation (Kerklaan and Coenders 2007) or the use of special effect visualization-oriented tools, similarly to the approach taken here, to dynamically sketch and assess the performance of design alternatives of tension membrane structures, before formally assessing them through wind tunnel tests (Mark 2007).2.1.Fast Fluid DynamicsThe numerical scheme used in our approach was developed for the computer graphics industry (Stam 1999) and therefore the visual aspect but most importantly the speed of the simulation are more crucial than the accuracy of the solver. Although the simulation scheme does not disregard the physics of the fluid mechanics, due to the lower order numerical solvers used to approximate the solution, the solver suffers from an amount of numerical dissipation. Indeed recent experiments with the specific fluid simulation scheme show that the solver cannot accurately predict turbulent flows by comparing the results to standard experimental data for a number of different cases, i.e. flow in a lid-driven cavity, fully developed channel flow, forced convective flow and natural convective flow in a room (Zuo and Chen 2007; 2009; 2010). The same studies however consider the solver’s accuracy as adequate for a number of cases and objectives, such as building emergency management, preliminary sustainable design and real-time indoor environment control. The results on the speed of the simulations, on the other hand, are outstanding,with a timeframe that ranges from 4 to 100 times faster than real time. Moreover, when implemented on a parallel computing scheme the fast fluid dynamics (FFD) simulation timeframe are reported to be 500 to 1500 times faster than a CFD simulation. It is not aimed to attempt a validation of these results, here, but on the contrary to explore the potential of the fluid solver in a generative preliminary design optimization process.2.2.GAs and CFDGenetic algorithms have been widely used for optimization in many engineering fields and lately they have been increasingly applied in architectural oriented optimization problems. Very briefly, a GA is mimicking the natural selection process through a population of candidates that represent a solution to the given problem by assessing their fitness and reproducing their genetic material. One significant advantage of GAs that makes them inherently useful in architectural context is their effectiveness in searching through very large and complex solution spaces, where deterministic methods cannot perform that well. The integration of CFD simulations and GA optimization techniques is also not a novelty in other engineering areas. In the automotive, aerospace and nautical industries, the use of CFD in optimization techniques is fully integrated and automated (Duvigneau & Visonneau 2003) and falls under the general category of shape optimization (Roy et al 2008).In architectural related research though, there are very few attempts to couple CFD and GAs. These are mainly limited in the analysis of indoor environments and more specifically the optimization of HVAC systems. Malkawi et al (Choudhary & Malkawi 2002; Malkawi et al 2003; Malkawi et al 2005) have combined GAs and CFD to study the performance of a mechanically ventilated room, through the integration of a parametric model and the partial automation of the optimization process, which is also assisted by the user. Although the intervention of the user in the optimization procedure in this case is significant in driving the optimization procedure towards the desired solution space, the use of a commercial fluid solver does not allow for the adaptation of the simulation environment. Other approaches include the use of GAs and CFD for the optimization of HVAC systems in office spaces (Lee 2007; Kim et al 2007) as well as other performance criteria, such as the optimization of window design problems (Suga et al 2010) and smoke-control systems in buildings (Huang et al 2009). Again with a few exceptions these approaches do not significantly adapt the simulation environment to the needs of each problem or attempt to optimize the computational framework of the simulation. Furthermore most of these studies are considered with orthogonal geometries, thus limiting their applicability in form finding methods.3.THE OPTIMIZATION FRAMEWORKAs already mentioned, the aim of this approach is to explore the potential of a faster but less accurate CFD simulation scheme in the optimization of the performance, in terms of wind loading of a free form surface. The computational efficiency of the process was overall an important driver in the development of the simulation framework and therefore certain simplifications and compromises had to be made to make the attempt feasible. The free form surface was deliberately vaguely defined, and material and site specific parameters were not considered, in order to reduce the complexity of the problem and shift the interest mostly towards the potential of the solver in providing valuable insight on a simple problem, through a generative design process.Moreover the study was constrained to one constant wind direction to further reduce the problem’s complexity, although the use of a range of wind directions is strongly considered as a further step. Finally the wind loading calculation is also restricted to the mean wind load on the surface for simplification, while at a further stage more complex wind loading functions could be taken into account.The fluid solver used here is based on a three dimensional implementation (Ash 2006) of Stam’s (1999) fluid solver. The main simulation routines of the solver are the advection, diffusion and projection routines (see also Stam 2003) and as they form the core of the simulation algorithm they have not been significantly changed. Other parts of the simulation scheme have been adapted and developed to suit the needs of the study. Stam’s fluid solver is a grid-based method, i.e. the solution is derived by resolving the equations for each cell in a grid over each time step. The solver is based on a fixed-size grid cell, which does not allow the adaptation of the mesh resolution in areas of interest, but facilitates the integration of other parts of the simulation scheme. The implementation of the fluid solver, as well as all other parts of the optimization framework were developed by the authors in the Processing open-source programming language (Figure 1).Figure 1 Fluid domain section - velocity field3.1. BoundariesOne important aspect of the CFD simulations is the handling of the domain boundaries. As the fluid solver was developed for visualization purposes, the external boundary routines of the solver had to be adjusted to simulate a continuous channel flow instead of the original bounding box domain. Again, more complex and sophisticated boundaries that would take into account site parameters, such as the ground surface roughness, would increase the complexity of the problem and therefore were avoided. The modeling of a more complex urban environment was indeed attempted but dropped due to computational resource requirements.The internal boundaries of the fluid domain are derived by the free form surface and are therefore more complex to handle as they need to be redefined for each instance of the GA population. For this reason a meshing algorithm had to be developed. To describe the internal boundary meshing algorithm a description of the free form surface needs to be given. The surface is defined as a B-Spline (URBS) surface, which is controlled by a set of 25 control points, arranged in a two dimensional grid of 5 control points in each direction. To impose some constructability on the scheme, the 4 corners of the control grid are fixed to the ground, as they could serve as anchor points for the structure. The remaining control points are freely movable by the optimization algorithm inside a certain range of height, width and length, depending on the degrees of freedom which have varied during each optimization scheme, as it will be described further on. The range of movement is also constrained by the adjacency of the points, to avoid folding and distortion of the surface. This configuration defines the parametric range of movement of the surface inside the fluid domain and consequently the range of the solution space (Figure 2).Figure 2 Free form surface configuration (a) and movement range forone (b) and three (c) degrees of freedom.To set up the internal boundaries of the domain, for each parametric instance of the surface, a meshing algorithm had to be developed. For internal boundaries, at least two cells of the fluid domain in each dimension have to be occupied to counteract the velocity and density fields of the fluid in both directions normal to the surface. The meshing algorithm runs for every (u , v ) position on the surface (at given intervals) and assigns a solid boolean for the corresponding pair of cells of the fluid domain in each dimension. This boolean is used inside the boundary routine of the solver to adjust the condition at the boundary cells at each time step of the simulation. The boundary cells are also used for the calculation of the wind loading of the surface which is implicitly calculated from the density and velocity fields (Figures 3, 4).Figure 3 Internal boundaries generated by the meshing algorithm for one instance of the surface.Figure 4 Wind loading calculation – three time steps.3.2. The genetic algorithmEach member of the GA population represents an instance of the parametric surface and corresponds to a set of genes which define its parameters. Three different encoding schemes for the GA genes were used in our experiments, each with different results. Two of these schemes were a direct encoding of the moving position of the control points of the surface, movable in one (z component only) and three dimensions (x,y,z) respectively.To reduce the searchable solution space and increase the convergence of the optimization process, a topological description of the surface was also introduced as an encoding scheme. In this scheme, the control points of the surface were derived from a sine function, whose parameters were encoded in the genes in order to preserve the topological relation between the control points (Figure 5).Figure 5 The genotype and phenotype correspondence in two encoding schemes .In the scope of this effort two different gene crossover methods were also used, i.e. a multiple point and a single point crossover method which is also helpful in preserving the topology of the surface. In the multiple point crossover method each new member of the population inherits the genes from each of its parents in random order, therefore loosing the topological relationship between adjacent control points of the surface. In the single point crossover method, on the other hand, each new member inherits a uniform portion of its parents’ chromosomes, preserving the topological relationship between adjacent points.The population size of the GA in our experiments ranged from 36 to 64 members and the number of offspring did not exceed the 1500 generations, due to computation time limitations. As it has already been mentioned, the time efficiency of the process was an important factor in the development process therefore the optimization process did not reach its full potential in many of the experiments as it was restricted by the timeframe which has reached up to 8 hours on a typical configurations computer. One thing worth mentioning is that although the GA is able to generate multiple instances of the surface in no time, each of them has to be evaluated individually, in a serial manner, throughthe CFD simulation engine, as the generation of multiple CFD domains to parallelize the optimization process would exceed the capabilities of any machine. However a further step could involve the distribution of the optimization process over a network.The steps of the optimization process were the following:1) An initial population of surfaces is randomlygenerated by the GA. 2) For each member of the initial population the CFDdomain is preprocessed and the internal boundaries are defined. 3) The simulation engine runs until it converges andthe fitness of the member is evaluated as the mean wind load on the surface in a given time period. 4) The fluid domain and the internal boundaries arereset. 5) When the whole of the initial population has beenevaluated and ranked, a new member is generated by the GA and steps 2 to 4 are repeated for each new member (Figure 6).Figure 6 The optimization flowchart.4. RESULTSThe results of the experiments with the first two (direct) encoding schemes were, as expected, similar, with a slight increase in the performance range achieved by the three degrees of freedom scheme. In both cases the optimization process was successful in optimizing the performance of the surface, steadily decreasing the wind loads, though not reaching its full potential, in the given timeframe. The optimum range of generated surfaces in both schemes presented significant uniformity in their form, characterizedby symmetry in the vertical to the wind direction as well as by a wave-like profile in the parallel direction leading to an overall aerodynamic shape. In both schemes however the optimum forms did not converge to a single trend, but were divided into two schemes, almost inverted from each other in form but both performing equally in the CFD domain. This lack of uniformity could be indicative of a possible preliminary convergence to local optima, also due to the computational demands of the process, or possibly of an under-constrained problem set up which leads to multiple solutions. Therefore it led to further experimentation in an effort to constrain the solution space through both a different crossover method and a different encoding scheme (Figures 7-12).Figures 7, 8 Three degrees of freedom - Optimization screenshot and 4fittest membersFigures 9, 10 Fitness plots for one and three degrees of freedom. Figures 11, 12 One degree of freedom - 4 fittest members of the twooptimization trendsThe single crossover method introduced was effective in reducing the time frame of the optimization, achieving a similar performance range in almost half the amount of generations, without though effectively converging to one uniform solution. The shape of the optimal surfaces followed again two distinct trends with two inverted shape patterns similar to the ones observed with the multiple crossover method (Figures 13, 14).On the contrary, through the topological description scheme, the optimization process converged to one single optimal trend throughout all the experiments, without though reaching the same performance range, indicating that the preservation of the surface topology was effective in the restriction of the solution space but also in the restriction of the achievable performance (Figures 15, 16).Figures 13, 14 Single crossover method - 4 fittest members and fitness graphFigures 15, 16 Topological description scheme- 4 fittest members and fitness graph5.DISCUSSIONThe incorporation of the FFD solver in the optimization process has been effective in providing an experimentation platform for generative techniques. Although the computational demand of the process remains high, it has been feasible not only to integrate the complex CFD simulations in a generative approach but furthermore to generate results, with regards to the objectives of this study, in a complex solution space. More importantly the implementation of the fluid solver in an object-oriented programming environment has enabled the adaptation of the simulation environment to the study’s objectives.In terms of the problem-specific generated results, the optimization process has provided valuable insight on the problem, through the identification of performance trends, in relation to the different encoding schemes. The manipulation of the problem’s representation has provided control over the generated solution space, highlightingtherelationship between the parametric definition range and the resulting performance range. This control though can by no means be regarded as a way to a deterministic solution to the studied problem, if not properly assessed in relation to more realistic design parameters. In the scope of this study, several inseparable parameters of what would constitute a realistic architectural problem are deliberately omitted, for simplification. Nevertheless the focus of the study was on the potential of the implementation of the solver in a preliminary design stage and thus it can be regarded as a starting point for further experimentation.It needs to be mentioned that for these results to be useful one essential further step is the formal assessment of their performance using standard simulation packages, or potentially physical tests, as the inaccuracy caused by the numerical dissipation of the solver could possibly be misleading. Moreover, the use of generic parameters, in both the simulation framework and the description of the problem, does not facilitate the assessment of the results in an architectural context. A more thorough modeling of the simulation environment as well as the incorporation of other important optimization constraints, such as pedestrian comfort or other types of loading, are important further steps as well. Further work in progress also includes the use of multi-objective GAs to incorporate other optimization constraints in the problem, the use of artificial neural networks, trained by the solution space to increase the time efficiency and achieve a two-step optimization process as well as the implementation of further developed versions of the fluid solver to produce more accurate results.6.CONCLUSIONIn this study we explored the potential of a fast fluid dynamics simulation scheme in a generative optimization process. The implementation of the fluid solver in a problem-specific optimization framework has been effective in providing informative insight on the representation of the problem. Although more complex representations and objectives as well as a formal validation of the generated results would be required to address real architectural problems, this implementation is considered as a proof of concept and further experimentation with the simulation framework is expected to yield more interesting results. ReferencesA SH,M.2006. 'Fluid Simulation for Dummies', [online] Available at: /pyblog/fluid-simulation-for-dummies.html [Accessed01 September 2010].B AKER,C.2007. 'Wind engineering-Past, present and future', in Journal of Wind Engineering and Industrial Aerodynamics 95(9-11), 843-870.C HEN,Q.2009. 'Ventilation performance prediction for buildings: A method overview and recent applications', in Building and Environment 44(4), 848-858.C HOUDHARY,R.,M ALKAWI,A.M.,2002. 'Integration of CFD and genetic algorithms', in Proceedings of the Eighth International Conference on Air Distribution in Rooms, Copenhagen, Denmark.C HUNG,D.H.J.AND L.C.M ALONE-L EE 2010. 'Computational Fluid Dynamics for Urban Design', in Proceedings of the 15th International Conference on Computer-Aided Architectural Design Research in Asia CAADRIA, April 2010, Hong Kong, China, 357–366.D UVIGNEAU,R.&V ISONNEAU,M.2003. 'Shape optimization strategies for complex applications in Computational Fluid Dynamics', in Proceedings 2nd International Conference on Computer Applications and Information Technology in the Maritime Industries, May 2003, Hamburg, Germany.H ANNA,S.,H ESSELGREN,L.,G ONZALEZ,V.&V ARGAS,I.2010. 'Beyond Simulation: Designing for Uncertainty and Robust Solutions', in Proceedings of the Symposium on Simulation for Architecture and Urban Design at the 2010 Spring Simulation Multiconference, April 2010, Orlando, USA.H ARTOG,J.P. D.,K OUTAMANIS, A.AND L USCUERE,P.G.2000. 'Possibilities and limitations of CFD simulation for indoor climate analysis', available from: Repository of Delft University of Technology.H IEN,W.N.&M AHDAVI,A.1999. 'Computational Air Flow Modeling for Integrative Building Design', in Proceedings of the 6th International Building Performance Simulation Association Conference –'Building Simulation 1999', September 1999, Kyoto, Japan.H UANG,S.,L I,Q.&X U,S.2007. 'Numerical evaluation of wind effects on a tall steel building by CFD', in Journal of Constructional Steel Research 63(5), 612-627.K ERKLAAN,R. A.G.&C OENDERS,J.2007. 'Geometrical modeling strategies for wind engineering', in Proceedings of the IASS Symposium on Shell and Spatial Structures –'Structural Architecture: Towards the future, looking to the past', Venice 2007, Italy, 81-82K IM,T.;S ONG,D.;K ATO,S.&M URAKAMI,S.2007. 'Two-step optimal design method using genetic algorithms and CFD-coupled simulation for indoor thermal environments', in Applied Thermal Engineering 27(1), 3-11.K OLAREVIC,B.2003. 'Computing the Performative in Architecture', in Proceedings of the 21st eCAADe Conference –'Digital Design', Graz 2003, Austria.。
Efficient Shape Optimisation of an Aircraft Landing Gear Door Locking Mechanism by Coupling Abaqusto GENESISMark Arnold and Martin GamblingPenso Consulting LtdGRM Consulting LtdAbstract: The objective of this work was to minimize the mass of a mechanism for locking aircraft landing gear doors whilst ensuring stresses did not exceed the material allowable stress. A typical metallic locking mechanism comprises a frame attached to the aircraft structure and supporting a number of linkages through pivot pins. These linkages transfer translational motion of a hydraulic actuator into rotation of a hook, which engages with the door. The structure was modelled with Abaqus/Standard as a non-linear static analysis involving contact, but with no material or geometric non-linearity. Existing commercial optimisation codes are available to perform Topology and Shape optimisation with Abaqus, however these require a non-linear Abaqus simulation to be performed for each design iteration. To achieve an optimized design in a shorter duration, the non-linear Abaqus model was coupled with an equivalent linear VR&D GENESIS analysis model, representing only the frame, using an interface developed by GRM Consulting Ltd. Shape optimisation studies were performed using this coupled approach to derive the optimum geometry for the frame. Whilst optimizing within GENESIS the Abaqus interface periodically executed a non-linear Abaqus simulation with updated geometry to maintain correlation between the two solvers. In conclusion, this coupled optimisation allowed a detailed design to be achieved in a significantly reduced timescale due the efficient application of optimisation technology, using only the minimum number of time-consuming, non-linear iterations.Keywords: Aircraft, Coupled Analysis, Design Optimisation, Finite Element Analysis, Minimum-Weight Structures, Optimisation, Non-Linearity, Process Automation, Stress Analysis.2009 SIMULIA Customer Conference 11. IntroductionDue to the shortening of aerospace product development cycle times, aggressive cost and mass targets and the demand for increased fuel efficiency, there is increasing pressure upon aerospace engineers to create more efficient designs for aircraft structures and get these to market quicker. Because of these demands, optimisation techniques are becoming commonplace in aerospace engineering since they offer engineers the opportunity to develop minimum mass solutions in a reduced timescale.The objective of this work, which was performed for a UK aerospace company, was to minimize the mass of a typical aircraft landing gear door locking mechanism whilst ensuring it achieved certain structural targets. Penso would normally have optimized such a static structural problem using the Vanderplaats Research & Development, Inc (VR&D) GENESIS finite element analysis and design optimisation software, which can perform size, topometry, shape, topography and also topology optimisation. However, as this problem required the simulation of contact nonlinearity and GENESIS was restricted to linear static analysis, Abaqus/Standard was selected as the most appropriate finite element analysis software. Abaqus had limited design optimisation capabilities, so the ideal solution would be to link the non-linear analysis capabilities of Abaqus with the optimisation capabilities of Genesis. Fortunately, GRM Consulting Ltd, who distributes GENESIS in the UK, had recently developed software for performing a coupled optimisation between theLS-DYNA non-linear dynamic finite element analysis software and GENESIS and was keen to extend its capabilities to include Abaqus.2. Coupled Optimisation ApproachTo allow efficient design optimisation of the aircraft landing gear component and other such problems, a pioneering approach has been developed coupling the advanced simulation capabilities of Abaqus with VR&D GENESIS. GENESIS is a world leading integrated analysis and optimisation tool supporting topology, size and shape, topography and topometry optimisation methods for linear analysis problems.The objective of the approach is to allow Abaqus analysis problems considering loading regimes including contact, pre-loads, interference fits and material non-linearity to be efficiently optimised. Currently, methods such as Design of Experiments and Response Surface Approximations are available for problems such as shape optimisation, however, these methods are limited in the number of variables that can be considered and require many non-linear analysis to obtain the required design sensitivity information. For example, a 6 variable DoE problem would require approximately 40-50 Abaqus simulations.A method has therefore been developed to couple the non-linear analysis capabilities of Abaqus to the design optimisation toolset within GENESIS. The process works by automatically interpreting the non-linear loading in Abaqus into an approximate linear analysis problem within GENESIS. This analysis can then be efficiently optimised using gradient based methods before an updated Abaqus model is automatically generated and analysed to assess the non-linear performance. Due 2 2009 SIMULIA Customer Conference2009 SIMULIA Customer Conference 3to the approximation to a linear analysis load case some deviation will occur between Abaqus and GENESIS and therefore an iterative loop is defined between the solvers until convergence occurs. This process is demonstrated in Figure 1.Figure 1. Coupled Optimisation Workflow.By coupling to the solver within GENESIS sensitivity calculations are made via gradients in the linear solver and, therefore, there is little or no limitation on the number of design variables that can be considered. Whilst in this paper only shape optimisation is considered, methods such as Topology optimisation where tens or hundreds of thousands of variables are present can be considered. Typically, using this new coupling method Abaqus analysis problems can be optimised in anywhere from 2 to 10 non-linear analysis iterations.By coupling the advanced analysis capabilities of Abaqus to GENESIS it is possible to efficiently consider non-linear design optimisation problems of a size not currently possible using methods such as Design of Experiments and response surface approximations. Some of the key non-linear loading conditions that can be efficiently considered are:● Contact● Interference fits● Pre-loads● Plastic deformationsFigure 2 shows an example of how the process can be applied to perform topology optimisation on a component loaded via contact and considering interference fits.Figure 3. Topology Optimisation Considering Contact and Interference Fits. Bending LoadTorsion LoadTopologyOptimisation Results4 2009 SIMULIA Customer ConferenceThe coupling optimisation approach does, however, have some conditions which cannot currently be considered. Once such case is the controlling of plastic strains or non-linear stresses to a defined limit during the Abaqus non-linear loading. Developed to support such constraints is ongoing, however, it is not currently available.3. Application to aircraft landing gear door locking mechanism3.1 Description of Uplock MechanismTo validate this coupled optimisation approach, it was applied to the problem of reducing the mass of an aircraft landing gear door locking mechanism. A typical mechanism comprises a frame attached to the aircraft structure by a number of bolts, as shown in Figure 3. The frame supports a number of linkages through pivot pins, which rotate within bushes pressed into the frame. These linkages transfer translational motion of a hydraulic actuator, mounted to one side of the frame, into rotation of a hook. During extension of this actuator, the hook rotates into a locked position and engages with a roller mounted to the landing gear door as it closes. During retraction of this actuator, the hook rotates into an unlocked position and disengages with the roller, allowing it to open. An alternate actuator, acting through an additional ‘alternate’ linkage, was mounted to theopposite side of the frame to unlock the landing gear doors in case the primary actuator failed.Figure 3. Uplock Mechanism Model.3.2 Abaqus Input Model CreationThe uplock mechanism frame, linkages and hook were each machined from billets of steel having a number of different grades dependent upon the required yield stress and ultimate stress allowables. The bushes and pins were also manufactured from steel. Static loads applied to the uplock mechanism were classified as either a hook load applied by the roller to the hook, an actuator extension or retraction fatigue loads applied to the linkage, or a combination of these loads. The hook load was further classified as either a limit, ultimate or fatigue loading condition, whilst the actuator load was further classified as either a fatigue or system loading condition. These loads represented events such as tyre burst, flight manoeuvres and a frozen roller.An Abaqus/Standard model of the uplock mechanism structure was created using ANSA, a pre-processor suitable for use with a variety of finite element analysis software developed by BETA CAE Systems S.A. The uplock mechanism model comprised a mesh of first-order solid (continuum) hexahedral, wedge and tetrahedral elements, with modified second-order tetrahedral elements used to model a section of the aluminium aircraft structure supporting the frame. Distributing coupling constraints were defined on the hook surface to distribute the concentrated hook load over a narrow band of elements, whilst kinematic coupling constraints were used to transfer the single point constraint reaction forces into the aircraft structure and distribute the load generated by the actuator (not modeled) to its attachment pins.The steel and aluminium materials were modeled using linear elastic and isotropic properties, since previous analysis had shown that the stresses were below yield. As well as not modelling any material non-linearity, geometric non-linearity was also not considered since previous analysis had shown the displacements and rotations to be small. Since the bushes, pins and links were all modeled as unconnected components due to their complex interaction, contact between adjacent components was modeled with pairs of contact surfaces defined on the exterior (free) faces of the solid elements. Therefore, a non-linear static analysis would be required. Tied contacts were also used to constrain some of the nuts and washers to the pins. The finite-sliding, node-to-surface contact formulation was used throughout and friction was not included on the contact surface interaction properties. A number of spring elements were modeled to eliminate rigid body motion of some components, although contact stabilization (*CONTACT CONTROLS, STABILIZE) was also used in Abaqus to address this issue when contact was not fully established.Since most of the bushes were press fitted into the frame and links due to being an interference fit, preloads would exist in the frame, links and bushes. Since it was considered important to represent this pre-stress, the first load step of the analysis was to simulate the interference fit prior to applying any external loading. This was achieved in Abaqus by defining an automatic shrink fit to removes these initial ‘overclosures’ between the bushes and frame/link contact pairs over the step (*CONTACT INTERFERENCE, SHRINK). The second step of the analysis then involved applying the hook and/or actuator load as a concentrated nodal force. The boundary conditions for both steps consisted of zero displacement constraints at a number of nodes on the aircraft structure in translational and/or rotational DOF.2009 SIMULIA Customer Conference 56 2009 SIMULIA Customer Conference 3.3 Abaqus Baseline ResultsThe baseline model was analyses using Abaqus/Standard Version 6.7-5 and was subsequentlypostprocessed using µETA post-processor, also developed by BETA CAE Systems S.A. The nodal averaged, corner von mises stress in the frame for the ultimate hook load are shown in Figure 4. The peak stress occurred at the upper lugs, where the frame was mounted to the aircraft structure, with a slightly lower stress at the lower lug, about which the hook pivots. Although the peak stress exceeded the material ultimate allowable, this was as a result of the aircraft structure bushes being physically connected at the nodes, instead of using a contact, and so this stress was ignored. The mass of the baseline frame was 0.0609 lbf sec 2/in (a mass unit consistent with inch, sec, lbf).Figure 4. Von Mises Stress in Frame before Optimisation.3.4 Coupled Optimisation SetupSince the intension was only to optimize the frame, the first stage was to create an input model of the frame in GENESIS format, which is very similar to that of MSC NASTRAN. This was easily achieved by importing the Abaqus model into ANSA and then exporting just the frame nodes and elements in NASTRAN format. It was important that the numbering of the node and element ids was identical in the Abaqus and GENESIS models so the coupled optimisation software could correlate the results from both sets of analysis.The second stage was to import the NASTRAN input file of the frame into Design Studio, the pre- and post-processor for GENESIS. Since the frame would not have any single point constraints defined, inertia relief constraints had to be defined to restrain the model and eliminate rigid body motion. It was decided to optimize the thickness of the vertical and the inclined members connecting the lower lug to the two upper lugs, since the stress in these members was found to be low from the baseline analysis. Since the frame model comprised of solid elements, this would require a shape optimisation involving node perturbation to adjust the size of these members in the analysis model.Shape optimisation domains, three-dimensional hexahedral volumes, were defined following the feature lines of the frame and each containing the solid elements bounded by the volume (see Figure 6). Perturbation vectors were then applied to the corner points (nodes) of these domains to adjust the thickness of the two frame members within user-defined limits through the use of two design variables. The lower bound for the thickness was defined to be greater than the minimum member size for machining.The objective function for the optimisation was to minimise the mass of the frame . A constraint was defined on the nodal stresses with an upper limit of 155000 psi, which was the material ultimate stress allowable.Figure 5. Coupled Optimisation Workflow.2009 SIMULIA Customer Conference782009 SIMULIA Customer ConferenceFigure 6. Frame Shape Optimisation Domains.3.5 Coupled Optimisation ResultsThe nodal averaged, corner von mises stress in the frame for the ultimate hook load afteroptimisation are shown in Figure 7. The peak stress again occurred at the upper lugs, where the frame was mounted to the aircraft structure. As the objective of the optimisation was to minimise the component mass, whilst ensuring stresses remained within the limits, the stress in the two members connecting the lower lug to the upper lugs was noted to increase. They did, however, remain within the defined stress limit of 155000 psi. The mass of the optimised frame was 0.0582 lbf sec 2/in, showing a notable reduction on the baseline design. It is also important to note that the shape optimisation design variables, by definition, ensured that the manufacturing dimensional constraints were satisfied.2009 SIMULIA Customer Conference9Figure 7. Von mises stress in frame after optimisation.4. ConclusionsThe coupled optimisation was found to allow a mass optimized design to be achieved in minimum time and within defined design constraints due to a greatly reduced number of costly non-linear design iterations.The coupling of GENESIS' efficient linear optimisation to the advanced analysis capabilities of Abaqus has proved to be an extremely efficient method for design mass reduction. The coupling of methods such as Topology optimisation to Abaqus capabilities such as contact, pre-load and plasticity brings about a new advance in what can be achieved through design optimisation tools, saving both development time and cost through lighter solutions, brought more quickly to market. In conclusion, a power solution has been developed, which allows engineers to utilise the most appropriate analysis software for loading assessment (eg Abaqus, LS-DYNA, MARC, PAM) whilst still being able to make use of the well proven optimisation capabilities of GENESIS.5. References1.Abaqus Analysis User's Manual, Version 6.7-5, Simula, 20082.VR&D GENESIS Design Reference Manual, Vanderplaats R&D Inc, Version 10.0, 20083.GRM Abaqus Solver Coupling Interface, GRM Consulting Ltd, Version 1.3, 200910 2009 SIMULIA Customer Conference。
