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基于多物质ALE算法的TNT炸药爆炸数值模拟分析作者：蔡晓虹来源：《建筑科技与经济》2017年第04期摘要：基于ANSYS/LS-DYNA动力非线性有限元程序，利用任意拉格朗日-欧拉（ALE）方法，以及多物质流固耦合方法对土壤爆炸荷载作用下进行了数值模拟研究，最终得出以下结论：TNT炸药爆炸后，形成球形冲击波阵面，并向外扩散，冲击波压强逐渐降低。
由下至上土壤各点的速度是逐渐增加的。
关键词：多物质ALE算法；ANSYS/LS-DYNA程序；TNT炸药；数值模拟；Based on the ALE algorithm TNT explosive substance，Numerical simulation analysisCai Xiao-hong（ Xi'an Shenzhou Aerospace Architectural Design Institute， 710025 ）Abstract： Based on the ANSYS/LS-DYNA dynamic nonlinear finite element program， using arbitrary Lagrange Euler （ ALE ） method，As well as the substance of fluid-solid coupling method on soil under explosive loading are studied by numerical simulation， reached the following conclusions： TNT after the explosion， the formation of spherical shock front， and spread outwards， shock wave pressure is reduced gradually. From the bottom of the soil at various points in the speed is gradually increased.Key words： multiple substance ALE algorithm； ANSYS/LS-DYNA； TNT explosive；numerical simulation；1.引言爆炸是能量短期内急剧释放的过程，具有短时高速高压的特点，在矿山爆破、金属爆炸成型、水下爆破排淤等军事与民用领域有着极为广泛的应用，研究结构在爆炸荷载作用下的动力响应，对于我国防护工程、爆破工程的发展具有十分重要的意义[1]。
船舶英语中的一些缩写船舶英语中的一些缩写ABS (American Bureau of Standard)美国船级社ANG (Angle Bar)角钢BFE (Builder Furnish Equipment)建造商提供设备BG (Bulk Carrier)散货船BHD (Bulkhead)舱壁BHP (Break Horsepower)制动马力BL (Base Line)基线BM (Breadth Molded)型宽BV (Bureau Veritas)法国船级社CAD (Computer Aided Design)计算机辅助设计CAM (Computer Aided Manufacturing)计算机辅助制造CB (Center of Buoyancy)浮心CCS (China Classification Society)中国船级社CF (Center of Floatation)漂心CFE (Contractor Furnish Equipment)承包商提供设备CG (Center of Gravity)重心CH (Channel)槽钢爱我船舶网CM (Metacenter)稳心CPP (The Controllable Pitch Propeller)可调螺距桨CS (Carbon Steel)碳素钢DB (Double Bottom)双层底DK (Deck)甲板DM (Depth Molded)型深DNV (Det Norske Veritas)挪威船级社DWG (Drawing)图DWL (Design Waterline)设计水线DWT (Deadweight)载重量FAT (Factory Acceptance Test)工厂验收试验FB (Flat Bar)扁钢FEM (Finite Element Method)有限元法FPSO (Floating Production Storage Offloading) 浮（船）式生产储油卸油系统FSO (Floating Storage Offloading)浮（船）式储油卸油系统Fwd (Forward)向船艏GL (Germanischer Lloyd)德国船级社GM (Metacentric Height)初稳心高HP (Half Bulb Plate)球扁钢LBP (Length between Perpendiculars)垂线间长LCG (Longitudinal Center of Gravity)纵向重心LNG (Liquefied Natural Gas Vessel) 液化石油气船LOA (Overall Length)总长Long. (Longitudinal)纵骨LPG (Liquefied Petroleum Gas Vessel) 液化天然气船LR (Lloyd's Register)英国劳氏船级社MDK (Main Deck)主甲板MODU (Mobile Offshore Drilling Units)移动式近海钻井平台MS (Mild Steel)低碳钢MTO (Material Takeoff)材料估算NK (Nippon Kaiji Kyokai)日本海事协会OFE (Owner Furnished Equipment)船东提供设备OT (Oil Tight)油密PL (Plate)板RI (Register Italian)意大利船级社SB (Starboard)右舷Semi- (Semi-submersible Platform)半潜式钻井平台STLP (Suspended T ension Leg Platform)悬式张力腿平台TCG (Transverse Center of Gravity)横向重心TEU (Twenty-foot equivalent Unit)20英尺国际标准集装箱TLP (Tension Leg Platform)张力腿平台UCLL (Ultra Large Crude Carrier)超大型油船VCG (Vertical Center of Gravity)垂向重心VLCC (Very Large Crude Carrier)特大型油船WB (Web Bar)腹板WL (Waterline)水线WT (Water Tight)水密MECHANICAL & PIPING（轮机）：AHU (Air Handling Unit)通风装置BHP (Break Horsepower)制动马力A/C (Air Compressor)空气压缩机A/C (Air Conditioning)空调BB (Ball Bearing)滚珠轴承BRG (Bearing)轴承CAS NUT(Castle Nut)蝶型螺帽CCR (Central Control Room)中心控制室COW (Crude Oil Washing)原油洗舱DFO (Diesel Fuel Oil)柴油DPS (Dynamic Position System)动力定位系统DT (Double-Thread)双头螺纹FS (Forged Steel)锻钢FW (Fresh Water)淡水FO (Fuel Oil)燃油GRP (Glass-reinforced Plastic)玻璃钢HVAV (Heating Ventilation and Air-condition)暖通空调系统HPU (Hydraulic Power Unit)液压工作站LSA (Life Saving Apparatus)救生器具LCC (Local Control Console)机旁控制台LO (Lube Oil)滑油MDO (Marine Diesel Oil)船用柴油OS (Operation System)操作系统PLC (Programmable Logic Controller)逻辑控制单元PMS (Power Manage System)动力管理系统ELECTRICAL（电气）:AC (Alternative Current)交流电AVR (Automatic Voltage Regulation)自动电压调整计CCTV (Closed Circuit Television)闭路电视CMS (Cargo Monitoring System)货物监控系统DC (Direct Current)直流电DFT (Dry Film Thickness)干膜DG (Diesel Generator)柴油发电机DVD (Digital Video Disc) 数字化视频光盘EMSP (Emergency Shutter Panel)应急关断板ESS (Emergence Shutdown System)应急关闭系统GPS (Global Position System)全球定位系统HG (Harbor Generator)停泊发电机HT (High Temperature)高温JB (Junction Box)接线盒LED (Light Emitting Diode)发光二极管LT (Low Temperature)低温MCU (Main Control Unit)主控器箱MG (Main Generator)主发电机MUR (Manual Voltage Regulation)手动调压器NEMA (National Electrical Manufacturers Association)国际电气制造业协会PA (Public Address System)公共寻呼系统PWM (Pulse Width Modulation)脉宽调制ST (Starter)启动器SWBD (Switch Board)配电盘，配电板UPS (Uninterrupted Power Supply)不间断电源VCR (Video Cassette Recorder)录像机PAINTING（涂装）:ARD (Alkyd Resin Deck)醇酸树脂甲板漆ARF (Alkyd Resin Finish)醇酸树脂面漆ARP (Alkyd Resin Primer)醇酸树脂底漆A/C (Anti-corrosive Paint)防腐漆CAF (Compressed Asbestos Fiber)压缩石棉填料。
中文英文英文中文艾利应力函数Airy stress function Airy stress function艾利应力函数板plate anti-sysmetric tensor反对称张量板边bounday of plate applied elasticity应用弹性力学板的抗弯强度flexural rigidity of plate axisymmetry轴对称板的内力internal force of plate base vector基矢量板的中面middle plane of plate basic assumptions ofelasticity弹性力学基本假定贝尔特拉米-米歇尔方程Beltrami-Michellequationbasic equation for thebending of thin plate薄板弯曲的基本方程贝蒂互换定理Betti reciprocal theorem Beltrami consistencyequation贝尔特拉米相容方程变温temperature change Beltrami-Michellequation 贝尔特拉米-米歇尔方程表层波surface wave Betti reciprocal theorem贝蒂互换定理半逆解法semi-inverse method body force体力薄板thin plate boundary condition边界条件薄板弯曲的基本方程basic equation for thebending of thin platebounday of plate板边薄膜比拟membrage analogy Boussinesq problem布西内斯克问题布西内斯克问题Boussinesq problem Boussinesq solution布西内斯克解答布西内斯克解答Boussinesq solution Boussinesq solution布西内斯克解答布西内斯克-伽辽金通解Boussinesq-Galerkingeneral solutionBoussinesq-Galerkingeneral solution布西内斯克-伽辽金通解半空间体semi-infinite body bulk modulus体积模量半平面体semi-infinite plane Castigliano formula卡斯蒂利亚诺公式贝尔特拉米相容方程Beltrami consistencyequationCauchy equation柯西方程边界条件boundary condition Cerruti problem塞路蒂问题变分法（能量法）variationalmethod,energy method characteristic equationof stress state应力状态特征方程薄板内力internal forces of thinplate coefficient of lateralpressure侧压力系数薄板弹性曲面elatic surface of thinplate complex potential复位势薄板弹性曲面微分方程differential equation ofelastic surface of thinplatecondition of single-value displacement位移单值条件薄板弯曲刚度flexural rigidity of thinplateconsistency equation相容方程布西内斯克解答Boussinesq solution contact problem接触问题产熵entropy prodction continuity连续性沉陷settlement continuous hypothesis连续性假设侧压力系数coefficient of lateralpressure coordinate curves坐标曲线ELASTICITY(弹性力学)常用专业名词中英文对照差分法finite-differencemethord coordinate surface坐标曲面差分公式finite-differencefromulate coupling耦合重三角级数double triangle series curvilinear coordinates曲线坐标大挠度问题large deflection problem deflection挠度单位张量unit tensor deformation形变单元分析element analysis density of comlementarystrain energy应变余能密度单元刚度矩阵element stiffness matrix density of internalenergy 内能密度等容波equivoluminal wave diaplacement位移等容的位移场equivoluminaldisplacement field diaplacementcomponents位移分量叠加原理superposition principle diaplacement method位移解法度量张量metric tensor diaplacement method位移法对称张量symmetric tensor diaplacement shapefunction位移的形函数单连体simply connected body diaplacement variationalequation位移变分方程单三角级数解single triangle series differential equation ofelastic surface弹性曲面的微分方程单元节点载荷列阵elemental nodal loadmatrix differential equation ofelastic surface of thinplate薄板弹性曲面微分方程单元劲度矩阵elemental stiffnessmatrix differential equation ofequilibrium平衡微分方程多连体multiply connected body differential equation ofequilibrium in terms ofdisplacement 以位移表示的平衡微分方程二阶张量second order tensor dilatation wave膨胀波反对称张量anti-sysmetric tensor discretization离散化符拉芒解答Flamant soluton discretization structure离散化结构反射reflection displacement boundarycondition位移边界条件傅里叶变换Fourier transform displacement model位移模式傅里叶积分Fourier integral distrotion wave畸变波复位势complex potential double triangle series重三角级数格林公式Green formula dummy index哑指标各向同性假设isotropic hypothesis elastic body弹性体供熵entropy supply elastic constants弹性常数广义变分原理generanized variatianalprincipleelastic matrix弹性矩阵广义胡克定律generanized Hooke law elastic principledirection 弹性主方向刚体位移rigid body displacement elastic symmetric plane弹性对称面各向同性isotropy elastic wave弹性波哈密顿变分原理Hamiton varitionalprincipleelasticity弹性哈密顿作用量Hamiton action elasticity弹性力学赫林格-赖斯纳变分原理Hellinger-Reissnervariational principleelatic surface of thinplate薄板弹性曲面亥姆霍兹定理Helmholtz theorem element analysis单元分析横观各向同性弹性体transverse isotropicelastic bodyelement stiffness matrix单元刚度矩阵横波transverse wave elemental nodal loadmatrix单元节点载荷列阵厚板thick plate elemental stiffnessmatrix 单元劲度矩阵胡海昌-鹫津久一郎变分原理Hu Haichang-Washizuvariational principleenergy method能量法混合边值问题mixed boundary-valueproblementropy prodction产熵胡克定律Hooke law entropy supply供熵混合边界条件mixed boundarycondition equation of stresscompatibility应力协调方程畸变波distrotion wave equivalent shear forcetorsional moment扭矩等效剪力基尔霍夫假设Kirchhoff hypothesis equivoluminaldisplacement field等容的位移场基矢量base vector equivoluminal wave等容波几何方程geometrical equation Euler method欧拉法几何可能的位移geometrically possibledisplacementEuler strain components欧拉应变分量几何可能的应变geometrically possiblestriainexternal force外力几何线性的假设geometrically linearhypothesisfinite element有限元伽辽金法Galerkin method finite element method有限单元法伽辽金矢量Galerkin vector finite-differencefromulate 差分公式结点node finite-differencemethord 差分法结点荷载nodal load first law ofthermodynamics热力学第一定律结点力nodal force first(second,third)kindboundary-value problemof elasticity 弹性力学的第一（第二、第三）类边值条件结点位移nodal displacement Flamant soluton符拉芒解答解的唯一性定理theorem of uniquenesssolutionflexural rigidity of plate板的抗弯强度静力可能的应力statically possible stress flexural rigidity of thinplate薄板弯曲刚度均匀性假设homogeneoushypothesis Fourier integral傅里叶积分局部编码local coding Fourier transform傅里叶变换基尔斯解答Kirsch solution free energy density自由能密度极小势能原理princile of minimumpotential energyfree index自由指标接触问题contact problem Galerkin method伽辽金法均匀性homogeneity Galerkin vector伽辽金矢量卡斯蒂利亚诺公式Castigliano formula generanized Hooke law广义胡克定律开尔文问题Kelvin problem generanized variatianalprinciple广义变分原理扭转刚度torsional rigidity geometrical equation几何方程柯西方程Cauchy equation geometrically linearhypothesis几何线性的假设克罗内克δ符号Kroneckerdelta symbol geometrically possibledisplacement几何可能的位移空间轴对称问题spatial axisymmetryproblem geometrically possiblestriain几何可能的应变孔口应力集中stress concentration ofholesglobal analysis整体分析拉梅解答Lame slution global analysis整体分析离散化结构discretization structure global coding总体编码理想弹性体perfect elastic body global equivalent nodalload vector整体等效结点荷载列阵连续性continuity global nodaldisplacement vector整体结点位移列阵拉格朗日法Lagrange method global stiffness matrix总刚度矩阵拉格朗日函数Lagrange function global stiffness matrix整体劲度矩阵拉格朗日应变函数Lagrange straincomponentsGreen formula格林公式拉梅常数Lamé constants Hamiton action哈密顿作用量拉梅系数Lamé coefficient Hamiton varitionalprinciple哈密顿变分原理拉梅方程Lamé equation heat-conductionequation 热传导方程拉梅应变势Lamé strain potential Hellinger-Reissnervariational principle 赫林格-赖斯纳变分原理莱维方程Lévy equation Helmholtz theorem亥姆霍兹定理勒夫应变函数Love strain function homogeneity均匀性离散化discretization homogeneoushypothesis 均匀性假设连续性假设continuous hypothesis Hooke law胡克定律梁的纯弯曲pure bending of beam Hooke's law of volume体应变胡克定律莱维解Lévy solution Hu Haichang-Washizuvariational principle 胡海昌-鹫津久一郎变分原理面力surface force infinitesimaldeformation hypothesis小变形假设膜板membrane plate internal force内力米歇尔相容方程Michell consistencyequationinternal force of plate板的内力挠度deflection internal forces of thinplate 薄板内力内力internal force inverse method逆解法能量法energy method irrotationaldisplacement field无旋的位移场逆解法inverse method irrotational wave无旋波扭矩等效剪力equivalent shear forcetorsional momentisotropic hypothesis各向同性假设扭转torsion isotropy各向同性纳维解Navier solution Kelvin problem开尔文问题内能密度density of internalenergy Kirchhoff hypothesis基尔霍夫假设纽勃-巴博考维奇通解Neuber-Papkovichgeneral solutionKirsch solution基尔斯解答欧拉法Euler method Kroneckerdelta symbol克罗内克δ符号欧拉应变分量Euler strain components Lagrange function拉格朗日函数耦合coupling Lagrange method拉格朗日法膨胀波dilatation wave Lagrange straincomponents拉格朗日应变函数平衡微分方程differential equation ofequilibriumLamé coefficient拉梅系数平面波plane wave Lamé constants拉梅常数平面应力问题plane stress problem Lamé equation拉梅方程平面应变问题plane strain problem Lame slution拉梅解答泊松比Poisson ratio Lamé strain potential拉梅应变势普朗特比拟Prandtl analogy large deflection problem大挠度问题普朗特应力函数Prandtl stress function Lévy equation莱维方程切变模量shear modulus Lévy solution莱维解切应变shear strain linear elasticity线性弹性力学切应力shear stress linear expansioncoefficient线膨胀系数切应力互等定理reciprocal theorem ofshear stresslinear thermal elasticity线性热弹性力学切应力线shear stress lines local coding局部编码求和约定summation convention longitudinal wave纵波球面波spherical wave Love strain function勒夫应变函数曲线坐标curvilinear coordinates mathematical elasticity数学弹性力学热力学第一定律first law ofthermodynamicsmembrage analogy薄膜比拟热力学第二定律second law ofthermodynamicsmembrane plate膜板热弹性应变势thermal elastic strainpotentialmetric tensor度量张量热应力thermal stress Michell consistencyequation米歇尔相容方程热传导方程heat-conductionequation middle plane of plate板的中面瑞利波Rayleigh wave mixed boundarycondition 混合边界条件瑞利-里茨法Rayleigh-Ritz method mixed boundary-valueproblem混合边值问题三阶张量third order tensor multiply connected body多连体塞路蒂问题Cerruti problem Navier solution纳维解圣维南扭转函数Saint-Venant torsionfunction Neuber-Papkovichgeneral solution纽勃-巴博考维奇通解圣维南方程Saint-Venant equation no initial stresshypothesis 无初始应力的假设圣维南原理Saint-Venant principle nodal displacement结点位移数学弹性力学mathematical elasticity nodal force结点力弹性elasticity nodal load结点荷载弹性波elastic wave node结点弹性常数elastic constants normal strain线应变弹性对称面elastic symmetric plane normal strain正应变弹性力学的平面问题plane problem ofelasticitynormal stress正应力弹性力学的第一（第二、第三）类边值条件first(second,third)kindboundary-value problemof elasticityorthotropic elastic body正交各向异性弹性体弹性曲面的微分方程differential equation ofelastic surfaceperfect elastic body理想弹性体弹性体elastic body perfect elasticity完全弹性弹性体的虚功原理principle of virtual workfor elastic solidperfectly elastic body完全弹性体弹性主方向elastic principledirection perfectly elastichypothesis完全弹性的假设弹性矩阵elastic matrix permulation tensor置换张量体力body force physical equation物理方程体应变胡克定律Hooke's law of volume physically linerhypothesis 物理线性的假设弹性力学elasticity plane problem ofelasticity 弹性力学的平面问题弹性力学基本假定basic assumptions ofelasticityplane strain problem平面应变问题体积模量bulk modulus plane stress problem平面应力问题体积应力volumetric strain plane wave平面波体应变volumetric strain plate板完全弹性的假设perfectly elastichypothesisPoisson ratio泊松比完全弹性体perfectly elastic body potential energy ofexternal force外力势能位移边界条件displacement boundarycondition potential functiondecomposition ofdisplacement field位移场的势函数分解式位移变分方程diaplacement variationalequationPrandtl analogy普朗特比拟位移场的势函数分解式potential functiondecomposition ofdisplacement fieldPrandtl stress function普朗特应力函数位移分量diaplacementcomponentspressure tunnel压力隧道位移解法diaplacement method princile of minimumpotential energy极小势能原理位移的形函数diaplacement shapefunctionprincipal plane主平面无初始应力的假设no initial stresshypothesisprincipal shear stress主切应力无旋波irrotational wave principal strain主应变无旋的位移场irrotationaldisplacement fieldprincipal stress主应力物理线性的假设physically linerhypothesis principle direction ofstrain应变主方向外力external force principle direction ofstress应力主方向外力功work of external force principle of least work最小功原理外力势能potential energy ofexternal force principle of minimum complementary energy最小余能原理完全弹性perfect elasticity principle of minimumpotential energy最小势能原理位移diaplacement principle of virtual workfor elastic solid弹性体的虚功原理位移单值条件condition of single-value displacementprinciple plane of stress应力主面位移法diaplacement method pure bending of beam梁的纯弯曲位移模式displacement model quadratic surface ofstrain 应变二次曲面物理方程physical equation quadratic surface ofstress 应力二次曲面线膨胀系数linear expansioncoefficientRayleigh wave瑞利波线性弹性力学linear elasticity Rayleigh-Ritz method瑞利-里茨法线性热弹性力学linear thermal elasticity reciprocal theorem ofshear stress切应力互等定理相对位移张量relative displacementtensorreflection反射小变形假设infinitesimaldeformation hypothesisrefraction折射小挠度问题small deflection matrix relative displacementtensor相对位移张量形函数矩阵shape function matrix rigid body displacement刚体位移虚位移virtual displacement rotation components转动分量虚位移方程virtual displacementequationrotation vector转动矢量虚应变virtual strain Saint-Venant equation圣维南方程虚应力virtual stress Saint-Venant principle圣维南原理虚应力方程virtual stress equation Saint-Venant torsionfunction圣维南扭转函数线应变normal strain second law ofthermodynamics热力学第二定律相容方程consistency equation second order tensor二阶张量形变deformation semi-infinite body半空间体形变势能strain erergy semi-infinite plane半平面体形函数shape function semi-inverse method半逆解法虚功方程virtual work equation settlement沉陷哑指标dummy index shape function形函数杨氏模量Young modulus shape function matrix形函数矩阵一点的应变状态state of strain at a point shear modulus切变模量一点的应力状态state of stress at a point shear strain切应变以位移表示的平衡微分方程differential equation ofequilibrium in terms ofdisplacementshear stress切应力应变二次曲面quadratic surface ofstrain shear stress lines切应力线应变分量strain components simply connected body单连体应变能密度strain energy density single triangle series单三角级数解应变矩阵strain matrix small deflection matrix小挠度问题应变协调方程strain compatibilityequation spatial axisymmetryproblem空间轴对称问题应变余能密度density of comlementarystrain energyspherical wave球面波应变张量strain tensor state of strain at a point一点的应变状态应变张量不变量strain tensor invariant state of stress at a point一点的应力状态应变主方向principle direction ofstrain statically possible stress静力可能的应力应力变分方程stress variationalequation strain compatibilityequation应变协调方程应力边界条件stress boundarycondition strain components应变分量应力二次曲面quadratic surface ofstress strain energy density应变能密度应力分量stress components strain erergy形变势能应力环量stress circulation strain matrix应变矩阵应力解法stress method strain tensor应变张量应力矩阵stress matrix strain tensor invariant应变张量不变量应力协调方程equation of stresscompatibility stress boundarycondition应力边界条件应力张量stress tensor stress circulation应力环量应力张量不变量stress tensor invariant stress components应力分量应力主方向principle direction ofstress stress concentration ofholes孔口应力集中应力状态特征方程characteristic equationof stress statestress matrix应力矩阵应用弹性力学applied elasticity stress method应力解法有限元finite element stress method应力法圆柱体扭转torsion of circular bar stress tensor应力张量压力隧道pressure tunnel stress tensor invariant应力张量不变量应力法stress method stress variationalequation 应力变分方程应力主面principle plane of stress summation convention求和约定有限单元法finite element method superposition principle叠加原理折射refraction surface force面力整体等效结点荷载列阵global equivalent nodalload vectorsurface wave表层波整体结点位移列阵global nodaldisplacement vectorsymmetric tensor对称张量整体分析global analysis temperature change变温正应变normal strain theorem of uniquenesssolution解的唯一性定理正应力normal stress thermal elastic strainpotential热弹性应变势正交各向异性弹性体orthotropic elastic body thermal stress热应力置换张量permulation tensor thick plate厚板主应变principal strain thin plate薄板主应力principal stress third order tensor三阶张量主平面principal plane torsion扭转主切应力principal shear stress torsion of circular bar圆柱体扭转转动矢量rotation vector torsional rigidity扭转刚度转动分量rotation components total complementaryenergy总余能自由能密度free energy density total potential energy总势能自由指标free index transverse isotropicelastic body横观各向同性弹性体纵波longitudinal wave transverse wave横波总刚度矩阵global stiffness matrix unit tensor单位张量总势能total potential energy variationalmethod,energy method变分法（能量法）总余能total complementaryenergyvirtual displacement虚位移总体编码global coding virtual displacementequation虚位移方程最小功原理principle of least work virtual strain虚应变最小势能原理principle of minimumpotential energyvirtual stress虚应力最小余能原理principle of minimumcomplementary energyvirtual stress equation虚应力方程坐标曲面coordinate surface virtual work equation虚功方程坐标曲线coordinate curves volumetric strain体积应力整体分析global analysis volumetric strain体应变整体劲度矩阵global stiffness matrix work of external force外力功轴对称axisymmetry Young modulus杨氏模量。
金属切削理论大作业2017年04月1基于ANSYS金属切削过程的有限元仿真付振彪，2016201064天津大学机械工程专业2016级研究生机械一班摘要：本文基于材料变形的弹塑性理论，建立了材料的应变硬化模型，采用有限元仿真技术，利用有限元软件ANSYS，对二维正交金属切削过程中剪切层及切屑的形成进行仿真。
从计算结果中提取应力应变云图显示了工件及刀具的应力应变分布情况，以此对切削过程中应力应变的变化进行了分析。
关键词：有限元模型；切削力；数学模型；二维模型；ANSYS1 绪论1.1金属切削的有限元仿真简介在当今世界，以计算机技术为基础，对于实际的工程问题应用商业有限元分析软件进行模拟，已经成为了在工程技术领域的热门研究方向，这也是科学技术发展所导致的必然结果。
研究金属切削的核心是研究切屑的形成过程及其机理，有限元法就是通过对金属切屑的形成机理进行模拟仿真，从而达到优化切削过程的目的并且可用于对刀具的研发。
有限元法对切屑形成机理的研究与传统的方法相比，虽然都是对金属切削的模拟，但是用有限元法获得的结果是用计算机系统得到的，而不是使用仪器设备测得的。
有限元法模拟的是一种虚拟的加工过程，能够提高研究效率，并能节约大量的成本。
1.2研究背景及国内外现状最早研究金属切削机理的分析模型是由Merchant [1][2]，Piispanen[3]，Lee and Shaffer[4]等人提出的。
1945 年Merchant 建立了金属切削的剪切角模型，并确定了剪切角与前角之间的对应关系这是首次有成效地把切削过程放在解析基础上的研究，成功地用数学公式来表达切削模型，而且只用几何学和应力-应变条件来解析。
但是材料的变形实际上是在一定厚度剪切区发生的，而且它假设产生的是条形切屑，所以该理论的切削模型和实际相比具有很大的误差。
1951 年，Lee and Shaffer 利用滑移线场(Slip Line Field)的概念分析正交切削的问题。
沈阳建筑大学学报(自然科学版)Journal of Shenyang Jianzhu University (Natural Science)2 02 1年1月第37卷第1期Jan. 2021Vol. 37, No. 1文章编号：2095 -1922(2221)01 -0001 -08 doi ：10.11717/j. issn ：2095 -1922.2021.31.01钢-UHPC 组合桥面的疲劳性能研究顾萍，鲁凡，张志强，马家欢(同济大学土木工程学院，上海200092)摘 要目的研究钢-UHPC 组合桥面的疲劳裂纹类型和发展规律，分析疲劳裂纹对组合桥面板结构受力特性的影响，为钢-UHPC 组合桥面的设计提供理论依据。
方法 依据实桥主桥钢桥面的构造参数，设计制作了两个足尺试验构件，进行静载、疲劳试验，并与有限元计算结果进行对比分析。
结果有限元模型计算的各测点应力和位移 与实测值基本吻合；纵肋与横隔板连接焊缝处容易发生疲劳裂纹，所有试件均在此处发现了裂纹;纵肋腹板裂纹较小时，对钢桥面受力性能影响较小；随着纵肋腹板裂纹、UHPC 与钢桥面板脱层扩展，试件刚度显著下降，最大挠度增量达33%。
结论纵向 配筋不同的两个构件其受力特性和疲劳性能差异不大，建议UHPC 层中纵向钢筋可按直径10 mm 密配筋布置。
关键词正交异性组合桥面板;疲劳试验;裂纹;脱层;刚度中图分类号TU927；U443文献标志码AFatigue Performance of Steel-UHPC CompositeBridge DeckGU Ping , LU Fan ，ZHANG Zhiqiang , MA Jiahuan(College of Civil Engineering ,Tongjt University ,Shanghai ,China ,220022)AbstrrcC : To investinatu fatinue cnck patterns ang theis influence on sUuctural behavios of the steel-UHPC cempositu deck undes ceclinn loaninn i V enabU the fatigue desinn specification. Two full-scale bUdgc deck specimens weu desionen and fanricateh with the specific detailing anf dimensions in accerUancc to the putotypc bUdgc deck ol t reti bridgc fos static anf fatinuc tests. CompareC with thc test usp U s , thc FE-baseC cemputatiouai usp U s were found nuc with U u measuren s U css and dispUcement s U thc cencerning 卩0)111：5. Thc Utiguc cracki obseuen were prooc tu occus t the joints between the longiUldinci Ubs anf the ddphucm fos all specimens.It is ccncluUen thct when cock initiates in We Ub web , vero small chnge would occus in the Ub sWesses anf in the deUechou ol bridge deck. But with furthes deveUpment ol Utigue cracks in We Un web , anf delamination between the UHPC layes and We steel deck . the 00x1101 stiffness ol We bridde deck specimen decreaseC 501^0111:0,31x 1 a 33% increment in the deUeckou was obseuen in the tests. The two specimens , Wough were not identical the same in longituUinci steel收稿日期：202。
Value Engineering0引言近年来，随着我国经济实力的飞速崛起，基建能力的显著提高，高运量跨江、跨海大桥的需求量明显增多。
然而桥梁数量和通航船舶吨位的明显增多，伴随而来的是船桥碰撞矛盾日渐显现，重大碰撞事故发生的概率显著提高[1]。
如何提高桥梁抗船舶撞击能力，降低船桥碰撞的概率，已成为国内外学者及相关工程从业人员研究的重点[2]。
目前对船桥防撞领域的研究主要分为主动防撞和被动防撞两种，主动防撞系统是指通过对船舶的航行进行主动干预，避免碰撞事故发生[3]；被动防撞结构是指在桥墩上加固或者独立于桥墩外布置防护设施来抵抗船舶的撞击。
实际工程中，通常需要主动与被动两种方式共同作用来保证避免发生碰撞事故。
被动防撞装置按碰撞的力学行为可分为刚性防撞装置和柔性防撞装置。
刚性防撞装置虽有结构简单、施工难度相对较低等优势，但因其“硬碰硬”的特点经常会造成桥墩与船舶发生无法修复的巨大破坏。
柔性防撞装置因其结构特点能为桥-船双方提供更大程度的保护，更符合新时代防撞结构的设计理念[4]。
浮式柔性消能防撞装置主要是指空心套箱或浮箱，由钢结构箱体和橡胶护舷等柔性体达到消能目的。
当受到船舶撞击时，防撞圈吸收部分碰撞能量，同时拨动船头航向，从而改变撞击角度，减少船对桥的撞击力[5]。
随着有限元技术的发展、碰撞理论不断被完善，有限元仿真技术被广泛应用于船桥碰撞问题分析中。
本文针对一个实际桥船防撞案例，利用有限元方法对该桥的浮式柔性转动多级消能防撞结构进行建模分析，计算了多种工况下船舶撞击时防撞墩的应力分布情况，所得结论可以为该类桥梁柔性防撞结构的设计与优化提供参考。
1设计要点1.1设计概述与目标某桥全长600m ，宽33.5m ，采用（100+400+100）米三跨连续中承式钢桁系杆拱桥，大致呈南北走向。
该桥防撞设施采用独立混凝土桩群结构+复合材料浮式柔性转动防撞体。
防撞设施共设置4个，分别在桥轴线上下游22.5m ，距承台边线通航孔侧7.9m 处。
HULL(船体)ABS (American Bureau of Standard)美国船级社ANG (Angle Bar)角钢BFE (Builder Furnish Equipment)建造商提供设备BG (Bulk Carrier)散货船BHD (Bulkhead)舱壁BHP (Break Horsepower)制动马力BL (Base Line)基线BM (Breadth Molded)型宽BV (Bureau Veritas)法国船级社CAD (Computer Aided Design)计算机辅助设计CAM (Computer Aided Manufacturing)计算机辅助制造CB (Center of Buoyancy)浮心CCS (China Classification Society)中国船级社CF (Center of Floatation)漂心CFE (Contractor Furnish Equipment)承包商提供设备CG (Center of Gravity)重心CH (Channel)槽钢CM (Metacenter)稳心CPP (The Controllable Pitch Propeller)可调螺距桨CS (Carbon Steel)碳素钢DB (Double Bottom)双层底DK (Deck)甲板DM (Depth Molded)型深DNV (Det Norske Veritas)挪威船级社DWG (Drawing)图DWL (Design Waterline)设计水线DWT (Deadweight)载重量FAT (Factory Acceptance Test)工厂验收试验FB (Flat Bar)扁钢FEM (Finite Element Method)有限元法FPSO (Floating Production Storage Offloading) 浮（船）式生产储油卸油系统FSO (Floating Storage Offloading)浮（船）式储油卸油系统Fwd (Forward)向船艏GL (Germanischer Lloyd)德国船级社GM (Metacentric Height)初稳心高HP (Half Bulb Plate)球扁钢LBP (Length between Perpendiculars)垂线间长LCG (Longitudinal Center of Gravity)纵向重心LNG (Liquefied Natural Gas Vessel) 液化石油气船LOA (Overall Length)总长Long. (Longitudinal)纵骨LPG (Liquefied Petroleum Gas Vessel) 液化天然气船LR (Lloyd's Register)英国劳氏船级社MDK (Main Deck)主甲板MODU (Mobile Offshore Drilling Units)移动式近海钻井平台MS (Mild Steel)低碳钢MTO (Material Takeoff)材料估算NK (Nippon Kaiji Kyokai)日本海事协会OFE (Owner Furnished Equipment)船东提供设备OT (Oil Tight)油密PL (Plate)板RI (Register Italian)意大利船级社SB (Starboard)右舷Semi- (Semi-submersible Platform)半潜式钻井平台STLP (Suspended Tension Leg Platform)悬式张力腿平台TCG (Transverse Center of Gravity)横向重心TEU (Twenty-foot equivalent Unit)20英尺国际标准集装箱TLP (Tension Leg Platform)张力腿平台UCLL (Ultra Large Crude Carrier)超大型油船VCG (Vertical Center of Gravity)垂向重心VLCC (Very Large Crude Carrier)特大型油船WB (Web Bar)腹板WL (Waterline)水线WT (Water Tight)水密MECHANICAL & PIPING（轮机）：AHU (Air Handling Unit)通风装置BHP (Break Horsepower)制动马力A/C (Air Compressor)空气压缩机A/C (Air Conditioning)空调BB (Ball Bearing)滚珠轴承BRG (Bearing)轴承CAS NUT(Castle Nut)蝶型螺帽CCR (Central Control Room)中心控制室COW (Crude Oil Washing)原油洗舱DFO (Diesel Fuel Oil)柴油DPS (Dynamic Position System)动力定位系统DT (Double-Thread)双头螺纹FS (Forged Steel)锻钢FW (Fresh Water)淡水FO (Fuel Oil)燃油GRP (Glass-reinforced Plastic)玻璃钢HV AV (Heating Ventilation and Air-condition)暖通空调系统HPU (Hydraulic Power Unit)液压工作站LSA (Life Saving Apparatus)救生器具LCC (Local Control Console)机旁控制台LO (Lube Oil)滑油MDO (Marine Diesel Oil)船用柴油OS (Operation System)操作系统PLC (Programmable Logic Controller)逻辑控制单元PMS (Power Manage System)动力管理系统ELECTRICAL（电气）:AC (Alternative Current)交流电A VR (Automatic V oltage Regulation)自动电压调整计CCTV (Closed Circuit Television)闭路电视CMS (Cargo Monitoring System)货物监控系统DC (Direct Current)直流电DFT (Dry Film Thickness)干膜DG (Diesel Generator)柴油发电机DVD (Digital Video Disc) 数字化视频光盘EMSP (Emergency Shutter Panel)应急关断板ESS (Emergence Shutdown System)应急关闭系统GPS (Global Position System)全球定位系统HG (Harbor Generator)停泊发电机HT (High Temperature)高温JB (Junction Box)接线盒LED (Light Emitting Diode)发光二极管LT (Low Temperature)低温MCU (Main Control Unit)主控器箱MG (Main Generator)主发电机MUR (Manual V oltage Regulation)手动调压器NEMA (National Electrical Manufacturers Association)国际电气制造业协会PA (Public Address System)公共寻呼系统PWM (Pulse Width Modulation)脉宽调制ST (Starter)启动器SWBD (Switch Board)配电盘，配电板UPS (Uninterrupted Power Supply)不间断电源VCR (Video Cassette Recorder)录像机PAINTING（涂装）:ARD (Alkyd Resin Deck)醇酸树脂甲板漆ARF (Alkyd Resin Finish)醇酸树脂面漆ARP (Alkyd Resin Primer)醇酸树脂底漆A/C (Anti-corrosive Paint)防腐漆CAF (Compressed Asbestos Fiber)压缩石棉填料EDP (Epoxy Deck Paint)环氧甲板漆EFP (Epoxy Finish Paint)环氧面漆EPP (Epoxy Primer Paint)环氧底漆ETPF (Epoxy Tank Paint Finish)环氧舱室面漆ETPP (Epoxy Tank Paint Primer)环氧舱室底漆ETP (Epoxy Topside Paint)环氧干舷漆ERL (Erosion Resistant Lacquer)防腐漆ECP (Etching Primer) 磷化底漆EPR (Ethylene-Propylene Rubber)乙丙橡胶F/C (Finish Coating)面漆IZP (Inorganic Zinc Primer)无机锌底漆IZSP (Inorganic Zinc Shop Primer)无机锌车间底漆PUTP (Polyurethane Topside Primer)聚氨脂干舷漆TE (Tar Epoxy Paint)环氧焦油漆VTP (Vinyl Tar Primer)聚乙烯焦油底漆ZRP (Zinc Rich Primer)富锌底漆WELDING and Material（焊接与材料）ASTM (American Society for Testing Materials)美国材料实验协会AWS (American Welding Society)美国焊接协会FCAW (Flux Cored Arc Welding)药芯焊丝电弧焊FRP (Fiberglass Reinforced Polyester)玻璃钢GMAW (Gas Metal Arc Welding)气体保护金属极电弧焊GRP (Glass Reinforced Polyester)玻璃钢GTAW (Gas Tungsten Arc Welding)气体保护钨极电弧焊GW (Gravity Welding)重力焊MPI (Magnetic Particle Inspection) 磁粒检验NDE (Nondestructive Evaluation)无损鉴定NNDT (Nondestructive Testing)非破坏性检验PVC (Poly Vinyl Chloride)聚氯乙烯S/W (Spot Weld) 点焊SAW (Submerge Arc Welding)埋弧焊SMAW (Shielded Metal Arc Welding)手弧焊UT (Ultrasonic Test)超声波检验WPS (Welding Procedure Sheet)焊接程序表WQT (Welding Qualification Test)焊工资格检验AE (Assistant Engineer)助理工程师ANSI (American National Standards Institute)美国国家标准局API (American Petroleum Institute)美国石油协会ASME (American Society of Mechanical Engineers)美国机械工程师协会Bbls (Barrels) 桶（美制容量单位1桶= 159升），C.E. (Chief Engineer) 总工程师CEO (Chief Executive Officer)首席执行总裁CIS (Chinese Industrial Standard)中国工业标准CNOOC (China National Offshore Oil Company)中国海洋石油总公司Co Ltd.(Company Limited)（股份）有限公司cu.ft. (Cubic Feet) 立方英尺cu.in. (Cubic Inch) 立方英寸GB (Guo Biao)国标GM (General Manage)总经理H.Q. (Headquarters) 总部HSE (Health, Safety & Environment)健康，安全和环保ID (Inner Dimension)内径IEC (International Electro technical Commission)国际电工协会IMO (Intergovernmental Marine Organization)国际海事组织ISO (International Standardization Organization)国际标准化协会ITU (International Telecommunication Union)国际电信联盟Ksi (kilopounds per square inch)千磅/平方英寸N/A (None Applicable)不适用NACE (National Association of Corrosion Engineer)全国防蚀工程师协会NFPA (National Fire Protection Association)国家防火协会OD (outer Dimension)外径QA (Quality Assurance)质量保证QC (Quality Control)质量管理（检查）ST (Short Ton)短吨SOLAS (International Convention of the Safety of Life at Sea)国际海上人命安全公约Spec. (specification)说明书，规格书sq.ft. (Square Feet) 平方英尺sq.in. (Square Inch) 平方英寸S/L: subsea pipeline 海底管线S/O: subsea oilline 海底输油管线1: 一般缩写词S/W: subsea waterline 海底输水管线AI: artificial island 人工岛SA: satellite area 卫星区APP: accommodation/power platform 生活动力平台SBL: standard symbol list 标准符号表CAL: calculation 计算书SKT: sketch 设计草图CEP: central platform 中心平台SLP: storage / loading platform 储罐平台DDS: detailed data sheet 数据表SPC: specification 规格书DPP: drilling/production platform 钻采平台SPM: single point mooring 单点系泊DRP: drilling platform 钻井平台STD: standard drawing 标准图DWG: drawing 图纸SWH: subsea wellhead 水下井口FI: field 油气田WHP: wellhead platform 井口平台"FPS: floating productionand storage unit" 浮式生产储油装置WIP: water injection platform 注水平台FSU: floating storage unit 浮式储油装置2：结构专业常用缩写词GTP: gas treating plant 天然气处理厂approx: approximate 大约MEL: material and equipment list 材料及设备清单AFC: approved for construction 批准建造PA: pilot area 试验区C/W: complete with 配有PP: pressurizing platform 增压平台CDL: chart datum level 海图基准水位PRP: production platform 生产平台CH: checkered plate 花纹钢板PSP: production/storage platform 生产储罐平台CL: center line 中心线PWP: power platform 动力平台COG: center of gravity 重心RPT: report 报告DET: detail 详图S/C: subsea cable 海底电缆DIA: diameter 直径S/F: subsea flowline 海底出油管线DO: ditto 同上S/G: subsea gasline 海底输气管线DWG: drawing 图纸EHWL: extreme high water level 极端高水位OPP: opposite 对侧EL: elevation 标高PCS: pieces 件ELWL: extreme low water level 极端低水位PL: plate 板FB: flat bar 扁钢PSF: pounds per square foot 磅每平方英尺FIG: figure 图REF: reference 参考FRMG: framing REQ'D: required 需要FS: far side 背面REV: revision 修改GALV: galvanized 镀锌SEC: section 断面HA T: highest astronomical tide 最高天文潮SPEC: specification 规格或规格书HWL: high water level 高水位SQ: square 平方ID: inside diameter 内径STIFF: stiffener 加强筋IR: inside radius 内半径SUP'T: support 支架LAT: lowest astronomical tide 最低天文潮SWL: safe working load 安全工作荷载LG: length 长度THK: thickness 厚度LWL: low water level 低水位TOS: top of structure 结构顶面MAT'L: material 材料TYP: typical 典型的MAX: maximum 最大值U/S: under side 底侧MIN: minimum 最小值UNO: unless noted otherwise 除非另有说明ML: mud line 泥面WP: work point 工作点MSL: mean sea level 平均海平面WT: wall thickness 壁厚MTO: material take-off 材料估算单NO: number 数量、号码NS: near side 可见侧NTS: note to scale 未按比例OD: outside diameter 外径ABS (American Bureau of Standard)美国船级社ANG (Angle Bar)角钢BFE (Builder Furnish Equipment)建造商提供设备BG (Bulk Carrier)散货船BHP (Break Horsepower)制动马力BM (Breadth Molded)型宽CAD (Computer Aided Design)计算机辅助设计CAM (Computer Aided Manufacturing)计算机辅助制造CB (Center of Buoyancy)浮心CCS (Chna Classification Society)中国船级社CF (Center of Floatation)漂心CFE (Contractor Furnish Equipment)承包商提供设备CG (Center of Gravity)重心CH (Channel)槽钢CM (Metacenter)稳心CPP (The Controllable Pitch Propeller)可调螺距桨CS (Carbon Steel)碳素钢DB (Double Bottom)双层底DK (Deck)甲板DM (Depth Molded)型深DNV (Det Norske Veritas)挪威船级社DWG (Drawing)图DWL (Design Waterline)设计水线DWT (Deadweight)载重量FAT (Factory Acceptance Test)工厂验收试验FB (Flat Bar)扁钢FEM (Finite Element Method)有限元法FPSO (Floating Production Storage Offloading) 浮（船）式生产储油卸油系统FSO (Floating Storage Offloading)浮（船）式储油卸油系统Fwd (Forward)向船艏GL (Germanischer Lloyd)德国船级社GM (Metacentric Height)初稳心高HP (Half Bulb Plate)球扁钢LBP (Length between Perpendiculars)垂线间长LCG (Longitudinal Center of Gravity)纵向重心LNG (Liquefied Natural Gas Vessel) 液化石油气船LOA (Overall Length)总长Long. (Longitudinal)纵骨LPG (Liquefied Petroleum Gas Vessel) 液化天然气船LR (Lloyd's Register)英国劳氏船级社MDK (Main Deck)主甲板MODU (Mobile Offshore Drilling Units)移动式近海钻井平台MS (Mild Steel)低碳钢MTO (Material Takeoff)材料估算NK (Nippon Kaiji Kyokai)日本海事协会OFE (Owner Furnished Equipment)船东提供设备OT (Oil Tight)油密PL (Plate)板RI (Register Italian)意大利船级社SB (Starboard)右舷Semi- (Semi-submersible Platform)半潜式钻井平台STLP (Suspended Tension Leg Platform)悬式张力腿平台TCG (Transverse Center of Gravity)横向重心TEU (Twenty-foot equivalent Unit)20英尺国际标准集装箱TLP (Tension Leg Platform)张力腿平台UCLL (Ultra Large Crude Carrier)超大型油船VCG (Vertical Center of Gravity)垂向重心VLCC (Very Large Crude Carrier)特大型油船WB (Web Bar)腹板WL (Waterline)水线WT (Water Tight)水密MECHANICAL & PIPING（轮机）：AHU (Air Handling Unit)通风装置BHP (Break Horsepower)制动马力A/C (Air Compressor)空气压缩机A/C (Air Conditioning)空调BB (Ball Bearing)滚珠轴承BRG (Bearing)轴承CAS NUT(Castle Nut)蝶型螺帽CCR (Central Control Room)中心控制室COW (Crude Oil Washing)原油洗舱DFO (Diesel Fuel Oil)柴油DPS (Dynamic Position System)动力定位系统DT (Double-Thread)双头螺纹FS (Forged Steel)锻钢FW (Fresh Water)淡水FO (Fuel Oil)燃油GRP (Glass-reinforced Plastic)玻璃钢HV A V (Heating Ventilation and Air-condition)暖通空调系统HPU (Hydraulic Power Unit)液压工作站LSA (Life Saving Apparatus)救生器具LCC (Local Control Console)机旁控制台LO (Lube Oil)滑油MDO (Marine Diesel Oil)船用柴油OS (Operation System)操作系统PLC (Programmable Logic Controller)逻辑控制单元PMS (Power Manage System)动力管理系统ELECTRICAL（电气）:AC (Alternative Current)交流电A VR (Automatic V oltage Regulation)自动电压调整计CCTV (Closed Circuit Television)闭路电视CMS (Cargo Monitoring System)货物监控系统DC (Direct Current)直流电DFT (Dry Film Thickness)干膜DG (Diesel Generator)柴油发电机DVD (Digital Video Disc) 数字化视频光盘EMSP (Emergency Shutter Panel)应急关断板ESS (Emergence Shutdown System)应急关闭系统GPS (Global Position System)全球定位系统HG (Harbor Generator)停泊发电机HT (High Temperature)高温JB (Junction Box)接线盒LED (Light Emitting Diode)发光二极管LT (Low Temperature)低温MCU (Main Control Unit)主控器箱MG (Main Generator)主发电机MUR (Manual V oltage Regulation)手动调压器NEMA (National Electrical Manufacturers Association) 国际电气制造业协会PA (Public Address System)公共寻呼系统PWM (Pulse Width Modulation)脉宽调制ST (Starter)启动器SWBD (Switch Board)配电盘，配电板UPS (Uninterrupted Power Supply)不间断电源VCR (Video Cassette Recorder)录像机PAINTING（涂装）:ARD (Alkyd Resin Deck)醇酸树脂甲板漆ARF (Alkyd Resin Finish)醇酸树脂面漆ARP (Alkyd Resin Primer)醇酸树脂底漆A/C (Anti-corrosive Paint)防腐漆CAF (Compressed Asbestos Fiber)压缩石棉填料EDP (Epoxy Deck Paint)环氧甲板漆EFP (Epoxy Finish Paint)环氧面漆EPP (Epoxy Primer Paint)环氧底漆ETPF (Epoxy Tank Paint Finish)环氧舱室面漆ETPP (Epoxy Tank Paint Primer)环氧舱室底漆ETP (Epoxy Topside Paint)环氧干舷漆ERL (Erosion Resistant Lacquer)防腐漆ECP (Etching Primer) 磷化底漆EPR (Ethylene-Propylene Rubber)乙丙橡胶F/C (Finish Coating)面漆IZP (Inorganic Zinc Primer)无机锌底漆IZSP (Inorganic Zinc Shop Primer)无机锌车间底漆UTP (Polyurethane Topside Primer)聚氨脂干舷漆TE (Tar Epoxy Paint)环氧焦油漆VTP (Vinyl Tar Primer)聚乙烯焦油底漆ZRP (Zinc Rich Primer)富锌底漆WELDING and Material（焊接与材料）:ASTM (American Society for Testing Materials)美国材料实验协会AWS (American Welding Society)美国焊接协会FCAW (Flux Cored Arc Welding)药芯焊丝电弧焊FRP (Fiberglass Reinforced Polyester)玻璃钢GMAW (Gas Metal Arc Welding)气体保护金属极电弧焊GRP (Glass Reinforced Polyester)玻璃钢GTAW (Gas Tungsten Arc Welding)气体保护钨极电弧焊GW (Gravity Welding)重力焊MPI (Magnetic Particle Inspection) 磁粒检验NDE (Nondestructive Evaluation)无损鉴定NDT (Nondestructive Testing)非破坏性检验PVC (Poly Vinyl Chloride)聚氯乙烯S/W (Spot Weld) 点焊SAW (Submerge Arc Welding)埋弧焊SMAW (Shielded Metal Arc Welding)手弧焊UT (Ultrasonic Test)超声波检验WPS (Welding Procedure Sheet)焊接程序表WQT (Welding Qualification Test)焊工资格检验OTHERS（其它）:AE (Assistant Engineer)助理工程师ANSI (American National Standards Institute)美国国家标准局API (American Petroleum Institute)美国石油协会ASME (American Society of Mechanical Engineers)美国机械工程师协会Bbls (Barrels) 桶（美制容量单位1桶= 159升），C.E. (Chief Engineer) 总工程师CEO (Chief Executive Officer)首席执行总裁CIS (Chinese Industrial Standard)中国工业标准CNOOC (China National Offshore Oil Company)中国海洋石油总公司Co Ltd.(Company Limited)（股份）有限公司cu.ft. (Cubic Feet) 立方英尺cu.in. (Cubic Inch) 立方英寸GB (Guo Biao)国标GM (General Manage)总经理H.Q. (Headquarters) 总部HSE (Health, Safety & Environment)健康，安全和环保ID (Inner Dimension)内径IEC (International Electro technical Commission)国际电工协会IMO (Intergovernmental Marine Organization)国际海事组织ISO (International Standardization Organization)国际标准化协会ITU (International Telecommunication Union)国际电信联盟Ksi (kilopounds per square inch)千磅/平方英寸N/A (None Applicable)不适用NACE (National Association of Corrosion Engineer)全国防蚀工程师协会NFPA (National Fire Protection Association)国家防火协会OD (outer Dimension)外径QA (Quality Assurance)质量保证QC (Quality Control)质量管理（检查）ST (Short Ton)短吨SOLAS (International Convention of the Safety of Life at Sea)国际海上人命安全公约Spec. (specification)说明书，规格书sq.ft. (Square Feet) 平方英尺sq.in. (Square Inch) 平方英寸PROPER NOUN（专有名词）:Basic Design(基础设计): Preparation of specification and plans/drawings outlining the design and in sufficient detail to gain Class approval.总括性的设计规格书和图纸等，其详细程度仅足可以通过船级社认可其设计思想。
第28卷增刊岩土力学Vol.28Supp.2008年11月Rock and Soil Mechanics Nov.2008收稿日期：5基金项目：国家自然科学基金资助项目(N 55)。
作者简介：艾智勇，男，66年出生，博士，副教授。
主要从事岩土及地下工程方面的研究工作。
：z y @j 文章编号：1000－7598－(2008)增刊－603－04间断伽辽金法(DGM)求解弹性地基梁问题艾智勇，王全胜，王熹（同济大学地下建筑与工程系岩土及地下工程教育部重点实验室上海200092）摘要：间断伽辽金法使用节点位移一类未知数作为测试函数，削弱了内部单元边界上的一阶及n 阶导数的连续性，大大降低了构造形函数的难度，特别适合控制方程为高阶微分方程问题的求解。
基于间断伽辽金法的基本原理，推导了弹性地基梁四阶微分控制方程的积分“弱”形式，编制了计算程序，进行了数值计算和收敛性分析。
计算结果表明：用间断伽辽金法求解弹性地基梁问题是十分有效率的。
关键词：间断伽辽金法；弹性地基梁；连续性；测试函数中图分类号：TU 470文献标识码：ADiscontinuous Galerkin method for elastic foundation beam problemsAI Zhi-yong,WANG Quan-sheng,WANG Xi(Department of Geotechnical Engineering ，Key Laboratory of Geotechnical and UndergroundEngineeri ng of Mini s try of Educati on,Tongji University,Shanghai 200092,C hina)Abstract:Discontinuous Galerkin method(DGM)used node displacement approximations as trial functions,and weakened the continuity of first order and n-th order differential in the internal element boundary,reduced the difficulty to construct the shape functions,so this method is especially fit for solving the problem of higher order differential equation.Based on the principle of DGM,the integral weak form of the forth order differential control equation of elastic foundation beam is established.Numerical calculation and convergence analysis are carried out by the computer program.The results of calculation show that it is efficient for DGM to solve the elastic foundation beam problems.Key words:discontinuous Galerkin method;rlastic foundation beam;continuity;trial functions1引言间断伽辽金法（DGM ）是有限单元法的一支，是使用完全不连续的分段多项式作为数值解以及测试函数的一种有效的数值方法。
Finite Element Simulation of Blast Loads on Reinforced ConcreteStructures using LS-DYNAAuthors:Yi, Zhuihua, Graduate Student, City College of the City University of New York, NY 10031.Anil K. Agrawal, Professor, City College of the City University of New York, NY 10031. Mohammed Ettouney, Principal, Weidlinger Associates, New York, NY.Sreenivas Alampalli, Director, Bridge Evaluation Services Bureau, New York State Department of Transportation, Albany, NY 12232Abstract: The behavior of reinforced concrete structures under blast load is analyzed by LS-DYNA. A new load generation method is proposed so that blast load can be applied to large civil engineering structures, such as highway bridges. The influence of time step and mesh size on simulation results is investigated. Three examples including flexural failed beam, brittle failed beam and undamaged column under blast load are presented. Numerical results match reasonably well with experimental data.I NTRODUCTIONA draft manual of performance criteria to reduce the potential for progressive collapse in buildings has been developed after the WTC progressive collapse events [NIST and USDOC,2006]. Although various research programs have provided mitigations [ASCE,2005, DOD,2003, Ettouney, et al.,1996], analytical tools for design professions are needed to implement guidelines and pre-standards [Lew,2006]. Many analysis methods exist to evaluate structure behavior under impact load. These methods include close-form wave propagation solution, single or multi-degree-of-freedom, pressure-impulse (P-I) diagrams, response surfaces developed from finite element analyses, and some Semi-empirical codes such as BlastX [Jones,1989, Li and Meng,2002, Naito and Wheaton,2006, SAIC,2006, Sunshine, et al.,2004, Symonds and Mentel,1958]. The most accurate analysis method is to simulate blast events using Hydro codes such as LS-DYNA [LSTC,2003] and EMFLEX developed by Weidlinger Associates, Inc. These hydro codes are designed for general purpose and specific requirements must be met to obtain correct simulation results for blast loaded reinforced concrete structures. Obviously, the effects of uncertainties in simulation parameters are of significant interest in understanding the usefulness of such simulations. Krauthammer and Otani (1997) have investigated mesh, gravity and load effects on finite element simulations of blast loaded RC concrete structures and concluded that models with lumping of reinforcements or one material counting the effects of both concrete and rebar cannot capture the correct state of stress. In this paper, effects of load generation, time step and mesh size on simulation results obtained from finite element model of concrete beams with concrete and steel rebars modeled separately in LS-DYNA is investigated extensively.S IMPLY SUPPORTED REINFORCED CONCRETE BEAM CONFIGURATIONSConfiguration from ExperimentsDetailed information on two tested reinforced concrete beams under blast loading has beenobtained from Magnusson and Hallgren’s work [Magnusson and Hallgren,2004]. Properties anddimensions are given in Table 1 and Figure 1(a). The concrete beams were assembled in a testrig, which was positioned in the test area of the shock tube (1.6m×1.2m) as shown in Figure 1(b).Table 2 shows the results obtained from air blastr tests by Magnusson and Hallgren (2004).TABLE 1- PROPERTIES OF THE DIFFERENT BEAM TYPES.Beam type 1cc f (MPa)Tensile reinforcement Reinforcement ratio sy f (MPa) B40 43 165Φmm 0.34 604 B100(12) 81 124Φmm 0.087 555 1 Refers to the concrete compressive strength of 300150×Φmm cylinders.FIGURE 1- (A) D IMENSIONS (IN MM ) AND AN EXAMPLE OF REINFORCEMENT OF THE BEAMS . T HE AMOUNT OFTENSILE REINFORCEMENT WAS VARIED . (B ) E XPERIMENTAL SET -UP OF THE AIR BLAST TESTS .TABLE 2 - RESULTS FROM THE AIR BLAST TESTS BY MAGNUSSON AND HALLGREN, 2004.Beam r p kPa (psi) i kPasu tot F , (kN) u δ Mm (in.) Failure type B40-D4801249± (181.2±11.6)038.6± 348 17.5 (0.689) Brittle B100(12)-D3 151946± (282.2±2.2) 9.58 324 44.6 (1.756) Flexuralp r = maximum reflecting pressure (mean value ±scattering)i = impulse density (mean value ± scattering)F tot, µ = maximum total support reactionδu = ultimate deflection at mid-spanFinite Element Model DescriptionExplicit solver in LS-DYNA is used for the FE analysis. The beam model consists of 3632 solidelements, with element length approximately 1 inch. Hourglass control is applied to avoid zeroenergy modes. Given that the simulation duration is less than 10 ms and blast pressure is veryhigh, gravity loads are neglected in the simulation. Concrete beam is simulated by solid elementwith JOHNSON HOLMQUIST CONCRETE material model (MAT_111 in LS-DYNA). TheMat_111 model is capable of simulating concrete behavior during impact loads when thematerial experiences large strains, high strain rates and high pressures. Steel rebar is modeled as(A) (B)beam elements with PLASTIC KINEMATIC material (MAT_3 in LS-DYNA), assuming thatperfect bond exist between concrete and rebar at the shared nodes.Stress-strain relationship of reinforced concrete during high strain rates has been investigatedextensively by several researchers recently [Army,1990, Fu, et al.,1991, Malvar,1998]. It hasbeen observed that ultimate strain values for steel and concrete are almost constant asdemonstrated by many experiments and these values can be set as shown in Table 3.T ABLE 3 - U LTIMATE STRAIN R ATES FOR CONCRETE USED IN FEM SIMULATION .Failure strainSteel rebar 0.23Core concrete 0.005Cover concrete 0.002The failure process of reinforced concrete beams with moderate percentage of steel underblast loads typically has following modes: (a) Spalling of concrete on the back of loading face;(b) Cracking of tensile concrete in the section of region with maximum moment; Failure mode isinitiated by a yielding of the steel while the strains in the concrete are relatively low, with crackclimbing up to the compression region; (c) Severance of longitudinal tensile rebar; (d) Crushingof concrete in the compression region immediately after the severance of rebar. FEM model ofthe RC beam in Figure 2 can simulate all these stages of beam failure. As an example, thesimulation figures of beam B100(12)-D3 of Table 2 are shown in Figure 2. The failure time canbe taken as when the severance of longitudinal rebar occurs, as shown in Figure 2(c).FIGURE 2 - FAILURE PROCESS OF BEAM WITH MODERATE PERCENTAGE OF STEEL UNDERBLAST LOAD (BEAM B100)A IR BLAST LOAD GENERATION(c) t = 5.1 ms(d) t = 5.2 ms(b) t=3.75 ms(a) t= 2.4 msThere are 3 methods to generate blast load using LS-DYNA. First, a segment pressure can be applied to the structure surface directly according to ConWep, which is a collection of conventional weapon effects calculations from the equations and curves of TM 5-855-1 [Army,1998, Hyde,2005, USAE Engineer Research & Development Center,2005]. The ConWep equation has been merged into LS-DYNA to apply a pressure load to structures [LSTC,2003]. This method controls load magnitude accurately and does not consume extra calculation time. However, it is only suitable for analysis before failure of structures. When elements fail in the FEM simulation, eroding technique is used to avoid element distortion, i.e., “bad” elements or nodes are removed from the structure. The blast load would be lost when the load segment is removed from the structure. One solution for this problem is to define contact rule between the moving segment and the remaining portion of the structure where blast load is to be applied. However, the calculation cost will be significant, and the simulation results may still not be accurate.The second method is to simulate the detonation process using the hydro codes. Detonation of high explosives can be simulated using Arbitrary-Lagrangian- Eulerian mesh and *MAT_HIGH_EXPLOSIVE_BURN control card in LS-DYNA. This method simulates the process of detonation and gives accurate evaluation of incident blast wave pressure through the explosive material. It is useful to simulate close range explosion [Wang,2001]. However, in simulation of blast loads on civil engineering structures, reflected pressure, impulse through media and reflecting boundaries are attractive. Theoretically, we can simulate the reflection process by setting air mesh and reflecting boundaries appropriately. Problems arise when we assume air as an ideal gas. Although it is impossible to simulate the correct pressure field accurately using the equation of state of ideal gas, the ALE method in LSDYNA has its own advantages. First, it can predict the reflection and diffraction of the blast waves. When structure size is small, the structure will suffer a squashing overpressure acting on all parts and a suction force on the back side when the blast wave front passes over. Secondly, in the case the structure surface is eroded under severe load, the blast wave load can still be applied on the rest of the structure.To overcome the difficulties met in the first two approaches, a new method of blast load generation is presented in this paper. In this approach, ConWep pressure load is applied on an air layer near structural components, and ALE air mesh is allowed to interact with Lagrangian structure element to apply the load. This method has merits of the first two methods: Generate correct pressure field, retain the arriving time of blast waves generated by ConWep and simulate both wave reflection and diffraction. For example, Figure 3 shows the simulation of blast waves on the beam B100 by ConWep and proposed LSDYNA approaches. In this case, the concrete cover of beam underwent spalling before 5 ms and the blast wave positive duration phase lasted for 50 ms. Neither ConWep equation method nor the ALE detonation simulation method alone can predict this behavior well. The combination of these two methods gave a good prediction shown in Figure 3. Note that the value of ConWep pressure is for free air blast and that of LS-DYNA is for system with beam structure. Therefore, the pressure in LS-DYNA is smaller after 10 ms because of dissipation of energy by the beam. High nonlinearity of contact and eroded beam elements contributes to the fluctuation of pressure in the simulation of LS-DYNA.When the generatin of blast loads in required for complex geometries, such as inter-explosion in buildings, other experiment data or program such as BlastX [Corporation,2006] are necessary to calibrate the load effect parameters in the combined method of ConWep and ALE.FIGURE 3: COMPARISON OF BLAST WAVE PRESSURE USINGCONWEP AND LSDYNA.I NFLUENCE OF TIME STEPGenerally, a critical time step size should satisfy [Belytschko, et al.,2000]:ee e crit c t l min ≤∆ (1) where e lis the smallest distance between any two nodes of the element and c is the instantaneous wave speed. (1) means that in each time step, the stress wave should not propagatefurther than the shortest length of one element to guarantee the numerical stability. Time stepwill influence the maximum pressure in air elements. Several simulation cases with differenttime step control (from 5.0E-9 to 2.0E-6 sec) were set to investigate the influence of time step toload prediction. It was observed that the change of time step causes approximately 3% error inthe prediction of maximum pressure of blast wave. Time step also affects the simulation resultsof structure and contact. Simulation of structure with elastic material showed that contactpressure was nearly reciprocal to time step size. Although Structure with elastic properties isconsidered here, the simulation is still a nonlinear one since the contact is very nonlinear. Timestep determined by (1) is difficult to predict because of the nonlinearity of contact algorithm.In the simulation of structures with nonlinear material properties, while concrete material isin elastic range, the blast wave pressure applied on the structure is the same as those in the elasticsimulation, which means the peak pressure is sensitive to both time step and penalty factor.When the blast load is large enough to push concrete material into nonlinear range, themechanism of contact is different since the elastic modulus of structure material is equal to oronly a little bigger than zero, which makes the interaction between air and structure more likeinteraction between two fluid materials. In this case, the contact pressure is relatively insensitiveto both time step and penalty factor. This is illustrated through the simulation of B100 beam asan example. Two cases use the same penalty factor (PFAC = 2.06E-6). Time Step size for case Ais 4E-8 sec and that for case B is 5E-8 sec. Figure 4 shows the pressure predicted for the twocases are almost the same as compared to experimental results shown in Table 2 for elasticsimulation.Another trend that we observe from Figure 4 is that the pressure attenuates faster in case A .Since case A uses a smaller time step size, numerical dissipation is higher in the fluid solver forsmaller time step [Gong,2006]. Therefore, largest constant time step which satisfies the criticaltime step condition is applied in simulations presented in this paper to avoid excessive numerical dissipation.FIGURE 4- CONTACT PRESSURE BETWEEN STRUCTURE AND BLAST WAVEFOR TWO SIMULATIONS WITH DIFFERENT TIME STEP CONTROL.I NFLUENCE OF MESH SIZESIn the simulation of structures with nonlinear material properties, the calculation usually becomes unstable and results do not converge with mesh size. This kind of difficulty has been discovered in computational analysis for unstable material models since 1970s. Bazant and Belytschko [Bazant and Belytschko,1985] deduced a closed-form solution to explain these difficulties. Bazant [Bazant,2002] showed that there existed a characteristic length for concrete material fracture. Hillerborg et al. (1976) resolved these difficulties by matching the dissipation in fracture to the energy dissipated in the element which exceeds the stability threshold. In the FEM model described above, material models for concrete and steel don’t have instability problem [LSTC,2003]. However, when concrete and steel are combined in the FEM model, the bond slip problem is an unstable one, since the numerical model is strain-independent and is a strain-softening type because of the eroding elements (elements deleted when the failure criteria is satisfied). Although there are several approaches for modelling bond slip in numerical modeling of reinforced concrete [Chen and Baker,2003, De Nardin, et al.,2005, Limkatanyu and Spacone,2002, Limkatanyu and Spacone,2002, Mendola,1997, Salem and Maekawa,2004], they all encountered difficulty in terms on stability during the blast load simulation, since eroding always involves removal of distorted elements, which causes high level of nonlinearity in the interaction between concrete and steel rebar. In this research, the authors have extended Hillerborg et al. (1976) approach for stability of mesh sizes to the bond slip problem. In this approach, the bond between concrete and steel is taken as a nonlinear material parameter and its dissipation energy is matched with that of the element size.It is assumed that the bond length is a characteristic length associated with concrete and steel. Therefore, the proper mesh size corresponding to the characteristic length should be found out for a successful simulation. Four FEM models of the B100 beam with different element sizes are investigated to study the influence of mesh sizes on bond slip length. Material parameters remain the same as in Table 1. The results of simulation are presented in Table 5.Table 5 shows that mesh size affects the interaction between ALE air mesh and Lagrangian structure mesh significantly. Contact parameter PFAC (penalty factor) needs to be verified with experimental data to apply the correct blast pressure load on structures instead of using defaultvalues in LS-DYNA. It is observed that the midpoint deflection of the beam at failure decreaseswith decrease in mesh size. It is observed from Table 2 that the experimental measured value ofdeflection at failure is 44.6 mm (1.76 in.). This corresponds with the result of case C in Table 5.Hence, the mesh size and PFAC of case C should be used in this simulation.One interesting thing is that the reaction force varies little (less than 5%) in Table 5 while thedeflection at failure deflection varies over 400% with mesh size. This means the calculation oftransferred loads from beam to supports is stable. In other words, the response of the column canbe predicted accurately no matter how much confidence we have for the simulation of bridgegirder, if a simply supported bridge with accidental explosion on the deck is analyzed.TABLE 5 - INFLUENCE OF MESH SIZESCase Mesh size length (in.) Deflection at failure (in.) Reaction (lb) Penalty factor PFAC Segment Pressure (psi)A 2.46 4.8465 -251041 0.0294 282.0B 1.64 2.064 -230241 0.0052 282.9C 1.08 1.756 -246334 2.06E-03 282.9D 0.7874 1.11 -211869 4.10E-04 282.3E XAMPLES OF SIMULATION OF BLAST LOADS ON BEAMS AND COLUMNSBrittle Failure of Simple Supported Beam: An over-reinforced concrete beam B40 ofconfiguration in Figure 1 has been subject to blast loads similar to experimental loads in Table 1and 2. When the over-reinforced beam is loaded to failure, the failure is initiated by the crushingof the concrete followed by a sudden disintegration of the compression zone while the stress inthe relatively large area of steel has not reached its yield point. Table 6 and Figure 5 showsimulation results by using the element mesh size on the basis of B100 simulation. It is observedthat the calculated value of deflection at failure for B40 beam matches very well with that of theexperimental value in Table 2.TABLE 6: PARAMETERS AND SIMULATED DEFLECTION FOR BEAM B40 Failure strain of core concrete 0.005Failure strain of cover concrete 0.002Failure strain of steel rebar 0.23Element size (in.) 1.12Deflection (in.) 0.6869FIGURE 5- FAILURE PROCESS OF OVERREINFORCED BEAM UNDER BLAST LOAD (BEAM B40).(a) t = 3.62 ms (b) t = 4.58 msThree models with different element sizes were built to demonstrate the mesh size influence discussed previously. Other parameters in the simulation are the same as presented in Table 6.. The results of simulation are shown in Table 7.TABLE 7 - INFLUENCE OF MESH SIZE ON SIMULATION OF BEAM B40Final deflection (in.)Element size (in.) Element number Deflection (in.) atfailureCase 1 1.97 2578 0.676 2.18462 1.57 4471 0.63 0.935CaseCase 3 1.12 5745 0.687 0.819When the section of overreinforced beam fails, the concrete in compression zone contributesthe failure process mainly. Deflection at failure predicted in Table 6 matches well with experimental data, irrespective of the element size. However, if we define final deflection as the deflection at which the beam lost its whole section, the model with a larger mesh size results in yields a larger deflection because of bond-slip problem involved.Column of Club El Nogal: Authorities in Colombia reported that attackers detonated a car bomb at 8 p.m. on Feb 7, 2003, as members and guests at the El Nogal social club celebrated a wedding and a children's party. Figure 6 shows that a column 10 ft away from the bomb (square column on the left side of the picture) survived after the attack. Parameters of the column are shown in Table 8.TABLE 8 - PARAMETERS OF COLUMN IN CLUB EL NOGAL [CE676,2003].Item ValueWidth 0.9 m ×0.9 m (35.4 in. × 35.4 in.)Concrete Strength 20.68 MP (3000 psi)Reinforcement Ratio 1.44%Charge weight 440 lb ANFOElement # of fine mesh 165148Element # of coarse mesh 25955F IGURE 6-(A)E L N OGAL S ITE AFTER THE BOMB ATTACK;(B)FEM S IMULATION OF E L N OGAL R EINFORCEDC ONCRETE C OLUMN.FEM simulation model of the column in LS-DYNA is shown in Figure 6(B). It is observed from Figure 6(B) that only the concrete cover suffered spalling and the core concrete of thecolumn remained intact. The maximum midpoint deflection is about 0.12 in in this case. The simulation results match with observed damages to the column qualitatively.If we build the model again with bigger element size, the difference in max deflection of the two models is less than 2%. This means that once we know that one member will not undergo severe damage during a blast event, it can be modeled by a coarser mesh without significantly affecting the simulation results.C ONCLUSIONSIn this paper, some computational aspects of finite element simulation of blast loads on reinforced concrete structures are discussed. Some important observations are:1.This paper proposes a new method to simulate the blast load in FEM analysis by combiningempirical ConWep equation and ALE detonation simulation method in LS-DYNA. It has been seen that this approach satisfies required accuracy for engineering analysis.2.For simulation of blast load effects on elastic structure, the change of time step may causesmall error in the prediction of maximum pressure due to blast waves.3.In the simulation of structure with nonlinear properties, the contact pressure is relativelyinsensitive to both time step and penalty factor after the yielding of material. With the decrease of the time step, numerical dissipation will rise significantly in the fluid solver, resulting in underestimation of blast wave pressure.4.Deflection increases with increase in mesh size. The influence can be as high as 400%.5.The bond-slip problem under blast load has been identified as an unstable process. Anapproach to address bond-slip problem has been proposed by treating bond-slip as a nonlinear material parameter. In this approach, the element size must be calibrated using some experimental data for a particular site condition to obtain realistic simulation results. 6.Simulation results on three examples (flexural failure beam, brittle failure beam, columnunder car bomb events) are presented in this paper. The simulation results correlate well with those of observed experimental and field results. Hence, the approach described in this paper is suitable as a computational tool for structures subject to blast loads.A CKNOWLEDGMENTThis research is supported by the grants from Multidisciplinary Center for Earthquake Engineering through Earthquake Engineering Research Centers Program of the National Science Foundation, under award number EEC-9701471 and a research grant from the Region II FHWA University Transportation Research Center at the City College of New York. The views presented in this paper represent those of the authors and not necessarily of the agencies represented by the authors and sponsoring organizations.R EFERENCES[1] Army, D. o. t., Structures to Resist the Effects of Accidental Explosions. Washington, D.C.: ArmyTechnical Manual 5-1300/Navy Publication NAVFAC P-397/Air Force Manual (AFM) 88-22 (TM 5-1300), 1990.[2] Army, U. S. 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