结构力学英文课件 Chapter7
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结构力学英文
(1)Geometrically stable system
Under the action of the loads, the system still maintains its shape and remains its location if the small deformations of the members are neglected as shown in Fig.2.1
2.2 the concept of degrees of freedom and restraints
In the analyzing geometric construction of structures, it is very feasible to consider one part of the members or joints of a system as an object which possesses degrees of freedom, whereas other part of the members or joints of the system as restraints which restricts the movement of the object. The relationship of these two parts are then analyzed and whether or not the system will be determined. Accordingly, the concept of degrees of freedom and restraints of a system is discussed first of all
(2)Geometrically unstable system Under the action of the loads, the system will change its shape and its location if the small deformations of the members are neglected as shown in fig,2.2 Corresponding to geometrically stable and unstable system, there are internally stable and unstable systems as well. A structure is considered to be internally stable, or rigid, if it maintains its shape and remains a rigid body when detached from the supports
Under the action of the loads, the system still maintains its shape and remains its location if the small deformations of the members are neglected as shown in Fig.2.1
2.2 the concept of degrees of freedom and restraints
In the analyzing geometric construction of structures, it is very feasible to consider one part of the members or joints of a system as an object which possesses degrees of freedom, whereas other part of the members or joints of the system as restraints which restricts the movement of the object. The relationship of these two parts are then analyzed and whether or not the system will be determined. Accordingly, the concept of degrees of freedom and restraints of a system is discussed first of all
(2)Geometrically unstable system Under the action of the loads, the system will change its shape and its location if the small deformations of the members are neglected as shown in fig,2.2 Corresponding to geometrically stable and unstable system, there are internally stable and unstable systems as well. A structure is considered to be internally stable, or rigid, if it maintains its shape and remains a rigid body when detached from the supports
结构力学(英) Chapter2 Equilibrium and Geometric Stability PPT精品课件
P1 m
A
m
a
XA
l
YA V
M
N
YA
V
M N
P2 P3 B
YB
YB
6
Statically Determinate Structures
P
A
C
B
a
RA Pb l
Pb / l
b l
RB
Pa l
P
Pa / l
Shear Diagram
The equations of statics alone are sufficient to compute the reactions and the distribution of internal forces.
M1 M2
＋ Mx = M1,x M2,x = 0
z
＋ My = M1,y M2,y = 0
＋ Mz = M1,z M2,z = 0
x
3
Equilibrium of Planar Structure
4
External Forces
External Forces are the actions of other bodies to the structure under consideration.
n = number of structural components r = number of unknown reaction components If r = 3n, the structure is statically determinate If r > 3n, the structure is statically indeterminate
结构力学课件
2016/1/14
A
(b)刚结点
A
(c) 组合结点 图 1-5
34
结构力学
1-2-6
支座的简化及分类
理论力学中已经引入了支座的计算简图，现 归纳、补充如下： 支座是将结构和基础联系起来的装置，其作 用是将结构固定在基础上，并将结构上的荷载传
递到基础和地基。支座对结构的约束力称为支座
反力，支座反力总是沿着它所限制的位移方向。
在结构计算中，为了简化，对组成各构件的材 料一般都假设为连续的、均匀的、各向同性的、完 全弹性或弹塑性的。
2016/1/14
结构力学
42
1-2-8
荷载的简化
结构承受的荷载可分为体积力和表面力两大类。 在杆件结构中把杆件简化为轴线，因此不管是体积 力还是表面力都可以简化为作用在杆件轴线上的力。 荷载按其分布情况可简化为集中荷载和分布荷 载。
2016/1/14
结构力学
5
在水工结构方面： ① 公元前256-251年秦朝修建的岷江水利枢纽工程都江堰创 造了用竹笼装卵石堆砌的堤坝结构，使用至今，其结构 之简单，规模之宏伟，堪称世界之最。 在桥梁结构方面： ① 公元605-617年隋朝修建的河北赵县安济桥（也称赵州桥） 为敞肩石拱桥，造型优美、结构合理。 ② 宋代的广东潮州广济桥（开关活动式）。 ③ 福建泉州万安桥（即洛阳桥，筏形基础，砺房胶固）， 其独特结构型式在世界上都绝无仅有。
2016/1/14
ห้องสมุดไป่ตู้
结构力学
17
结构力学研究对象涉及较广，根据所涉及范围， 通常将结构力学分为“狭义结构力学”、“广义结
构力学”和“现代结构力学”。
狭义结构力学 其研究对象为由杆件所组成的体系。
这种体系能承担外界荷载作用，
A
(b)刚结点
A
(c) 组合结点 图 1-5
34
结构力学
1-2-6
支座的简化及分类
理论力学中已经引入了支座的计算简图，现 归纳、补充如下： 支座是将结构和基础联系起来的装置，其作 用是将结构固定在基础上，并将结构上的荷载传
递到基础和地基。支座对结构的约束力称为支座
反力，支座反力总是沿着它所限制的位移方向。
在结构计算中，为了简化，对组成各构件的材 料一般都假设为连续的、均匀的、各向同性的、完 全弹性或弹塑性的。
2016/1/14
结构力学
42
1-2-8
荷载的简化
结构承受的荷载可分为体积力和表面力两大类。 在杆件结构中把杆件简化为轴线，因此不管是体积 力还是表面力都可以简化为作用在杆件轴线上的力。 荷载按其分布情况可简化为集中荷载和分布荷 载。
2016/1/14
结构力学
5
在水工结构方面： ① 公元前256-251年秦朝修建的岷江水利枢纽工程都江堰创 造了用竹笼装卵石堆砌的堤坝结构，使用至今，其结构 之简单，规模之宏伟，堪称世界之最。 在桥梁结构方面： ① 公元605-617年隋朝修建的河北赵县安济桥（也称赵州桥） 为敞肩石拱桥，造型优美、结构合理。 ② 宋代的广东潮州广济桥（开关活动式）。 ③ 福建泉州万安桥（即洛阳桥，筏形基础，砺房胶固）， 其独特结构型式在世界上都绝无仅有。
2016/1/14
ห้องสมุดไป่ตู้
结构力学
17
结构力学研究对象涉及较广，根据所涉及范围， 通常将结构力学分为“狭义结构力学”、“广义结
构力学”和“现代结构力学”。
狭义结构力学 其研究对象为由杆件所组成的体系。
这种体系能承担外界荷载作用，
结构力学第七章-位移法(一)
由 M B = 0 同理可得，
FQAB 6i 6i 12i F A B 2 FQAB l l l
结构力学 第七章 位移法
2015年9月12日星期六
§7-2 等截面直杆的转角位移方程
等截面直杆的转角位移方程：
一端固端一端铰支的等截面直杆：
B端角位移不独立。
C
B A
AB：一端固定一端定向滑动 BC：一端固定一端定向滑动 BD：一端固定一端铰支
C
EI=c D B A
AB：两端固定 BC：一端固定一端定向滑动 BD：一端固定一端铰支
C
EI=c D B A
AB：两端固定 BC：两端固定 BD：一端固定一端铰支
C
EI=c D EI=c B A
AB：两端固定 BC：一端固定一端定向滑动 BD：两端固定
R1 = 0 R2 = 0 R3 = 0
R11 Z1
R21
R31
R12
R22 Z2
R32
R13
R23
R1P R33
R2P
P2
R3P
D EI=c A
E
F
D EI=c
E
F
D EI=c
E
F
P1
D EI=c A
E
F
B
C
A
B
C
A
B
C
B
C
(a)基本结构只发生 Z1
(b)基本结构只发生 Z 2
EI 1
B’ O
B
A’
EI
EI
EI
A EI
EI 1
不考虑杆件伸缩变形，AB 不能转动，无结点角位移
结构力学 第七章 位移法
清华大学土木工程系结构力学(英)Chapter7_812904391
14
Basic Concepts for the Force Method Construction of M,V,N diagrams
M - diag. 1) Direct-plotting 2) superposition
M M1 X 1 M 2 X 2 M P
V - diag. 1) Direct-plotting 2) Superposition N - diag. 1) Direct-plotting 2) Superposition
12
Basic Concepts for the Force Method
11 1n X1 D1P Flexibility matrix D NP n1 nn X N
q C
B
C
q
B X1
X2
Compatibility Equation:
A
A
Primary
D 1 11 X1 12 X 2 D 1 p 0 D 2 21 X1 22 X 2 D 2 p 0
Disp. due to X2 = 1
Disp. due to load
ij
— Non-diagonal coefficients
ij ji
Reciprocal theorem：
13
Basic Concepts for the Force Method
Several points:
(5) The force method = the method of consistent displacement
Basic Concepts for the Force Method Construction of M,V,N diagrams
M - diag. 1) Direct-plotting 2) superposition
M M1 X 1 M 2 X 2 M P
V - diag. 1) Direct-plotting 2) Superposition N - diag. 1) Direct-plotting 2) Superposition
12
Basic Concepts for the Force Method
11 1n X1 D1P Flexibility matrix D NP n1 nn X N
q C
B
C
q
B X1
X2
Compatibility Equation:
A
A
Primary
D 1 11 X1 12 X 2 D 1 p 0 D 2 21 X1 22 X 2 D 2 p 0
Disp. due to X2 = 1
Disp. due to load
ij
— Non-diagonal coefficients
ij ji
Reciprocal theorem：
13
Basic Concepts for the Force Method
Several points:
(5) The force method = the method of consistent displacement
结构力学英文课件 Chapter7培训资料
In the last chapter (force method), the unknowns of primary structure are forces. After obtaining unknown force, displacement of the structure can be solved.
(1)、Rotation displacements unknown
(2)、 Translation uasic assumptions
A
(1)、Small displacement is supposed. (2)、Axial force and shearing force are disregarded.
When indeterminate structure is analyzed by using displacement method, every member is considered as a statically indeterminate beam with single span. So the primary structure is that every member is changed into an indeterminate beam with single span. A rigid arm is added at every rigid joint to prevent rotation of the joint (but can not prevent translation) at the same time, a link is added at joint where translation is possible. The link prevents translation of the joint.
(1)、Rotation displacements unknown
(2)、 Translation uasic assumptions
A
(1)、Small displacement is supposed. (2)、Axial force and shearing force are disregarded.
When indeterminate structure is analyzed by using displacement method, every member is considered as a statically indeterminate beam with single span. So the primary structure is that every member is changed into an indeterminate beam with single span. A rigid arm is added at every rigid joint to prevent rotation of the joint (but can not prevent translation) at the same time, a link is added at joint where translation is possible. The link prevents translation of the joint.
结构力学(英) Chapter4 Analysis of Statically Determinate Beam and Frame Structures PPT精品课件
MA 0:
YB
q0l 3
MB 0:
YA
q0l 6
11
Section Method for Internal Loadings
q0a l Vc
A
q0 B
Mc
c a
YA q0l
l
6
Vc
YA
1 2
q0a l
a
q0
l 2 3a2 6l
Mc
YA
a
1 2
•Axial Force:
+
NN
Positive axial force tends to elongate the segment.
9
Sign Convention (2)
•Shear Force:
+
VV
Positive shear force tends to rotate the segment clockwise.
Moment——Algebraic sum of moments against the considered point produced by loads acting to its left/right
（concave upward-positive, convex upward-negative）
q0 l
a
a
a 3
q0a
l2 a2 6l
12
Internal loadings over a beam
We frequently need to plot internal loading diagrams to describe the variation of shear and moment over a beam structure.
结构力学理论英文课程课件 CVG3140【Tutorial】
Tutorial #1
CVG3140 – Theory of Structures 1 Example #3
Tutorial #1
CVG3140 – Theory of Structures 1 To find X (M=0 ) :
Tutorial #1
CVG3140 – Theory of Structures 1 Example #4:
CVG3140 – Theory of Structures 1
Tutorial #1
Tutorial # 1
Subject : Review - V & M diagrams Example #1:
Reactions:
Shear and moment diagrams:
CVG3140 – Theory of Structures 1 Example #2:
Area
(A )
i
(h )i
( A)i ∗ (h
)
Alternative: table
i
∫ f ( x) ∗ f
1 0
L
2
( x)dx
1
Example # 4 - Frame Use virtual work to calculate the vertical displacement at point “c” of the frame shown given that EI is given as 1X 105 Kn-m2 .
SI = (3m + r ) -(3j +ec)
m= # of members r = # reactions j= # of frame joints • support = joint • where two or more members meet = joint • free end = joint
结构力学教学课件第7章
A
(c) M P 图
B
C
D
A
(d) M 图
例7-5-4
求:
A,B两端点的相对竖向位移AB
q=5kN/m
B
(a)
C
D 2m 2m
10kNm
12kNm B C
2kNm
D
(b) M P 图
B C
D
(c) M 图
§7.6 温度改变时静定结构的
位移计算
A B B`
静定结构受到温度改变的影响时，发 生满足约束允许的变形和位移，为零 内力状态。
虚力方程——求位移。
虚位移方程及应用 虚位移方程
使体系上真实的平衡力系，在体系 可能的任意微小的刚体虚位移上， 所作的外力总虚功等于零的方程。
虚位移方程用于求真实的未知力 （内力、约束力、支座反力）。
如图7-2-2(a)所示以杠杆（机构）， B端上有一集中荷载FP，求A端需用 多大的力FA，该杠杆体系能平衡。
1 F Ri ci ( 10) 2.5rad 4 1
2
()
§7.3 结构位移计算公式
变形体可分两大类 非线性变形体
线性弹性体
物理线性——材料的应力与应变 成正比例，即服从虎克定律。 几何线性——结构的变形（或位 移）是微小的，在进行结构的内 力和位移分析计算中，可按其原 有的几何尺寸考虑。
FA c FP a
B c A a
(↓)
例7-2-1试用单位位移法（虚位移
法）求图(a)所示简支梁的支座B的约 束反力。
(a)
a L
C
B
b
(b)
C` C
P
B` B ( B =1) B
分析：
(c) M P 图
B
C
D
A
(d) M 图
例7-5-4
求:
A,B两端点的相对竖向位移AB
q=5kN/m
B
(a)
C
D 2m 2m
10kNm
12kNm B C
2kNm
D
(b) M P 图
B C
D
(c) M 图
§7.6 温度改变时静定结构的
位移计算
A B B`
静定结构受到温度改变的影响时，发 生满足约束允许的变形和位移，为零 内力状态。
虚力方程——求位移。
虚位移方程及应用 虚位移方程
使体系上真实的平衡力系，在体系 可能的任意微小的刚体虚位移上， 所作的外力总虚功等于零的方程。
虚位移方程用于求真实的未知力 （内力、约束力、支座反力）。
如图7-2-2(a)所示以杠杆（机构）， B端上有一集中荷载FP，求A端需用 多大的力FA，该杠杆体系能平衡。
1 F Ri ci ( 10) 2.5rad 4 1
2
()
§7.3 结构位移计算公式
变形体可分两大类 非线性变形体
线性弹性体
物理线性——材料的应力与应变 成正比例，即服从虎克定律。 几何线性——结构的变形（或位 移）是微小的，在进行结构的内 力和位移分析计算中，可按其原 有的几何尺寸考虑。
FA c FP a
B c A a
(↓)
例7-2-1试用单位位移法（虚位移
法）求图(a)所示简支梁的支座B的约 束反力。
(a)
a L
C
B
b
(b)
C` C
P
B` B ( B =1) B
分析：
结构力学(双语)绪论
Some examples of structures
结构力学的主要研究对象是杆件结构 The main objective of structural mechanics is framed structures 杆件结构
Framed stuctures
平面杆件结构 Plane structures: all the members and the applied loads lie in a single plane Otherwise the structures are spacial structure 空间 杆件结构
做题练习是学习结构力学的重要环节。不做一定 量的习题就很难对基本概念和方法有深入的理解和 掌握，也很难培养较好的计算能力。 Do exercises to solve some concrete problems is a key link in the study of the subject. If we don’t do a definite quantity of exercises it is difficult to understand the basic concepts and master the basic methods, and difficult to develop good ability to calculate.
II 计算能力Computing ability
(1)具有对各种结构确定计算步骤,进行计算的能力
determine the calculation procedure and calculate the structures。 (2)具有对计算结果进行定量校核或定性判断的能力the ability to verify the results quantitatively and judge the results qualitatively.
结构力学专业英语
结构力学结构力学structural mechanics 结构分析structural analysis 结构动力学structural dynamics 拱Arch 三铰拱three-hinged arch 抛物线拱parabolic arch 圆拱circular arch 穹顶Dome 空间结构space structure 空间桁架space truss 雪载[荷] snow load 风载[荷] wind load 土压力earth pressure 地震载荷earthquake loading 弹簧支座spring support 支座位移support displacement 支座沉降support settlement 超静定次数degree of indeterminacy 机动分析kinematic analysis 结点法method of joints 截面法method of sections 结点力joint forces 共轭位移conjugate displacement 影响线influence line 三弯矩方程three-moment equation 单位虚力unit virtual force 刚度系数stiffness coefficient 柔度系数flexibility coefficient 力矩分配moment distribution 力矩分配法moment distribution method 力矩再分配moment redistribution 分配系数distribution factor 矩阵位移法matri displacement method 单元刚度矩阵element stiffness matrix 单元应变矩阵element strain matrix 总体坐标global coordinates 贝蒂定理Betti theorem 高斯--若尔当消去法Gauss-Jordan elimination Method 屈曲模态buckling mode 复合材料力学mechanics of composites 复合材料composite material 纤维复合材料fibrous composite 单向复合材料unidirectional composite 泡沫复合材料foamed composite 颗粒复合材料particulate composite 层板Laminate 夹层板sandwich panel 正交层板cross-ply laminate 斜交层板angle-ply laminate 层片Ply 多胞固体cellular solid 膨胀Expansion 压实Debulk 劣化Degradation 脱层Delamination 脱粘Debond 纤维应力fiber stress 层应力ply stress 层应变ply strain 层间应力interlaminar stress 比强度specific strength 强度折减系数strength reduction factor 强度应力比strength -stress ratio 横向剪切模量transverse shear modulus 横观各向同性transverse isotropy 正交各向异Orthotropy 剪滞分析shear lag analysis 短纤维chopped fiber 长纤维continuous fiber 纤维方向fiber direction 纤维断裂fiber break 纤维拔脱fiber pull-out 纤维增强fiber reinforcement 致密化Densification 最小重量设计optimum weight design 网格分析法netting analysis 混合律rule of mixture 失效准则failure criterion 蔡--吴失效准则Tsai-W u failure criterion 达格代尔模型Dugdale model 断裂力学fracture mechanics 概率断裂力学probabilistic fracture Mechanics 格里菲思理论Griffith theory 线弹性断裂力学linear elastic fracture mechanics, LEFM 弹塑性断裂力学elastic-plastic fracture mecha-nics, EPFM 断裂Fracture 脆性断裂brittle fracture 解理断裂cleavage fracture 蠕变断裂creep fracture 延性断裂ductile fracture 晶间断裂inter-granular fracture 准解理断裂quasi-cleavage fracture 穿晶断裂trans-granular fracture 裂纹Crack 裂缝Flaw 缺陷Defect 割缝Slit 微裂纹Microcrack 折裂Kink 椭圆裂纹elliptical crack 深埋裂纹embedded crack [钱]币状裂纹penny-shape crack 预制裂纹Precrack 短裂纹short crack 表面裂纹surface crack 裂纹钝化crack blunting 裂纹分叉crack branching 裂纹闭合crack closure 裂纹前缘crack front 裂纹嘴crack mouth 裂纹张开角crack opening angle,COA 裂纹张开位移crack opening displacement, COD 裂纹阻力crack resistance 裂纹面crack surface 裂纹尖端crack tip 裂尖张角crack tip opening angle, CTOA 裂尖张开位移crack tip opening displacement, CTOD 裂尖奇异场crack tip singularity Field 裂纹扩展速率crack growth rate 稳定裂纹扩展stable crack growth 定常裂纹扩展steady crack growth 亚临界裂纹扩展subcritical crack growth 裂纹[扩展]减速crack retardation 止裂crack arrest 止裂韧度arrest toughness 断裂类型fracture mode 滑开型sliding mode 张开型opening mode 撕开型tearing mode 复合型mixed mode 撕裂Tearing 撕裂模量tearing modulus 断裂准则fracture criterion J积分J-integral J阻力曲线J-resistance curve 断裂韧度fracture toughness 应力强度因子stress intensity factor HRR场Hutchinson-Rice-Rosengren Field 守恒积分conservation integral 有效应力张量effective stress tensor 应变能密度strain energy density 能量释放率energy release rate 内聚区cohesive zone 塑性区plastic zone 张拉区stretched zone 热影响区heat affected zone, HAZ 延脆转变温度brittle-ductile transition temperature 剪切带shear band 剪切唇shear lip 无损检测non-destructive inspection 双边缺口试件double edge notched specimen, DEN specimen 单边缺口试件single edge notched specimen, SEN specimen 三点弯曲试件three point bending specimen, TPB specimen 中心裂纹拉伸试件center cracked tension specimen, CCT specimen 中心裂纹板试件center cracked panel specimen, CCP specimen 紧凑拉伸试件compact tension specimen, CT specimen 大范围屈服large scale yielding 小范围攻屈服small scale yielding 韦布尔分布Weibull distribution 帕里斯公式paris formula 空穴化Cavitation 应力腐蚀stress corrosion 概率风险判定probabilistic risk assessment, PRA 损伤力学damage mechanics 损伤Damage 连续介质损伤力学continuum damage mechanics 细观损伤力学microscopic damage mechanics 累积损伤accumulated damage 脆性损伤brittle damage 延性损伤ductile damage 宏观损伤macroscopic damage 细观损伤microscopic damage 微观损伤microscopic damage 损伤准则damage criterion 损伤演化方程damage evolution equation 损伤软化damage softening 损伤强化damage strengthening 损伤张量damage tensor 损伤阈值damage threshold 损伤变量damage variable 损伤矢量damage vector 损伤区damage zone 疲劳Fatigue 低周疲劳low cycle fatigue 应力疲劳stress fatigue 随机疲劳random fatigue 蠕变疲劳creep fatigue 腐蚀疲劳corrosion fatigue 疲劳损伤fatigue damage 疲劳失效fatigue failure 疲劳断裂fatigue fracture 疲劳裂纹fatigue crack 疲劳寿命fatigue life 疲劳破坏fatigue rupture 疲劳强度fatigue strength 疲劳辉纹fatigue striations 疲劳阈值fatigue threshold 交变载荷alternating load 交变应力alternating stress 应力幅值stress amplitude 应变疲劳strain fatigue 应力循环stress cycle 应力比stress ratio 安全寿命safe life 过载效应overloading effect 循环硬化cyclic hardening 循环软化cyclic softening 环境效应environmental effect 裂纹片crack gage 裂纹扩展crack growth, crack Propagation 裂纹萌生crack initiation 循环比cycle ratio 实验应力分析experimental stress Analysis 工作[应变]片active[strain] gage 基底材料backing material 应力计stress gage 零[点]飘移zero shift, zero drift 应变测量strain measurement 应变计strain gage 应变指示器strain indicator 应变花strain rosette 应变灵敏度strain sensitivity 机械式应变仪mechanical strain gage 直角应变花rectangular rosette 引伸仪Extensometer 应变遥测telemetering of strain 横向灵敏系数transverse gage factor 横向灵敏度transverse sensitivity 焊接式应变计weldable strain gage 平衡电桥balanced bridge 粘贴式应变计bonded strain gage 粘贴箔式应变计bonded foiled gage 粘贴丝式应变计bonded wire gage 桥路平衡bridge balancing 电容应变计capacitance strain gage 补偿片compensation technique 补偿技术compensation technique 基准电桥reference bridge 电阻应变计resistance strain gage 温度自补偿应变计self-temperature compensating gage 半导体应变计semiconductor strain Gage 集流器slip ring 应变放大镜strain amplifier 疲劳寿命计fatigue life gage 电感应变计inductance [strain] gage 光[测]力学Photomechanics 光弹性Photoelasticity 光塑性Photoplasticity 杨氏条纹Young fringe 双折射效应birefrigent effect 等位移线contour of equal Displacement 暗条纹dark fringe 条纹倍增fringe multiplication 干涉条纹interference fringe 等差线Isochromatic 等倾线Isoclinic 等和线isopachic 应力光学定律stress- optic law 主应力迹线Isostatic 亮条纹light fringe 光程差optical path difference 热光弹性photo-thermo -elasticity 光弹性贴片法photoelastic coating Method 光弹性夹片法photoelastic sandwich Method 动态光弹性dynamic photo-elasticity 空间滤波spatial filtering 空间频率spatial frequency 起偏镜Polarizer 反射式光弹性仪reflection polariscope 残余双折射效应residual birefringent Effect 应变条纹值strain fringe value 应变光学灵敏度strain-optic sensitivity 应力冻结效应stress freezing effect 应力条纹值stress fringe value 应力光图stress-optic pattern 暂时双折射效应temporary birefringent Effect 脉冲全息法pulsed holography 透射式光弹性仪transmission polariscope 实时全息干涉法real-time holographic interferometry 网格法grid method 全息光弹性法holo-photoelasticity 全息图Hologram 全息照相Holograph 全息干涉法holographic interferometry 全息云纹法holographic moire technique 全息术Holography 全场分析法whole-field analysis 散斑干涉法speckle interferometry 散斑Speckle 错位散斑干涉法speckle-shearing interferometry, shearography 散斑图Specklegram 白光散斑法white-light speckle method 云纹干涉法moire interferometry [叠栅]云纹moire fringe [叠栅]云纹法moire method 云纹图moire pattern 离面云纹法off-plane moire method 参考栅reference grating 试件栅specimen grating 分析栅analyzer grating 面内云纹法in-plane moire method 脆性涂层法brittle-coating method 条带法strip coating method 坐标变换transformation of Coordinates 计算结构力学computational structural mechanics 加权残量法weighted residual method 有限差分法finite difference method 有限[单]元法finite element method 配点法point collocation 里茨法Ritz method 广义变分原理generalized variational Principle 最小二乘法least square method 胡[海昌]一鹫津原理Hu-Washizu principle 赫林格-赖斯纳原理Hellinger-Reissner Principle 修正变分原理modified variational Principle 约束变分原理constrained variational Principle 混合法mixed method 杂交法hybrid method 边界解法boundary solution method 有限条法finite strip method 半解析法semi-analytical method 协调元conforming element 非协调元non-conforming element 混合元mixed element 杂交元hybrid element 边界元boundary element 强迫边界条件forced boundary condition 自然边界条件natural boundary condition 离散化Discretization 离散系统discrete system 连续问题continuous problem 广义位移generalized displacement 广义载荷generalized load 广义应变generalized strain 广义应力generalized stress 界面变量interface variable 节点node, nodal point [单]元Element 角节点corner node 边节点mid-side node 内节点internal node 无节点变量nodeless variable 杆元bar element 桁架杆元truss element 梁元beam element 二维元two-dimensional element 一维元one-dimensional element 三维元three-dimensional element 轴对称元axisymmetric element 板元plate element 壳元shell element 厚板元thick plate element 三角形元triangular element 四边形元quadrilateral element 四面体元tetrahedral element 曲线元curved element 二次元quadratic element 线性元linear element 三次元cubic element 四次元quartic element 等参[数]元isoparametric element 超参数元super-parametric element 亚参数元sub-parametric element 节点数可变元variable-number-node element 拉格朗日元Lagrange element 拉格朗日族Lagrange family 巧凑边点元serendipity element 巧凑边点族serendipity family 无限元infinite element 单元分析element analysis 单元特性element characteristics 刚度矩阵stiffness matrix 几何矩阵geometric matrix 等效节点力equivalent nodal force 节点位移nodal displacement 节点载荷nodal load 位移矢量displacement vector 载荷矢量load vector 质量矩阵mass matrix 集总质量矩阵lumped mass matrix 相容质量矩阵consistent mass matrix 阻尼矩阵damping matrix 瑞利阻尼Rayleigh damping 刚度矩阵的组集assembly of stiffness Matrices 载荷矢量的组集consistent mass matrix 质量矩阵的组集assembly of mass matrices 单元的组集assembly of elements 局部坐标系local coordinate system 局部坐标local coordinate 面积坐标area coordinates 体积坐标volume coordinates 曲线坐标curvilinear coordinates 静凝聚static condensation 合同变换contragradient transformation 形状函数shape function 试探函数trial function 检验函数test function 权函数weight function 样条函数spline function 代用函数substitute function 降阶积分reduced integration 零能模式zero-energy mode P收敛p-convergence H收敛h-convergence 掺混插值blended interpolation 等参数映射isoparametric mapping 双线性插值bilinear interpolation 小块检验patch test 非协调模式incompatible mode 节点号node number 单元号element number 带宽band width 带状矩阵banded matrix 变带状矩阵profile matrix 带宽最小化minimization of band width 波前法frontal method 子空间迭代法subspace iteration method 行列式搜索法determinant search method 逐步法step-by-step method 纽马克法Newmark 威尔逊法Wilson 拟牛顿法quasi-Newtonmethod 牛顿-拉弗森法Newton-Raphson method 增量法incremental method 初应变initial strain 初应力initial stress 切线刚度矩阵tangent stiffness matrix 割线刚度矩阵secant stiffness matrix 模态叠加法mode superposition method 平衡迭代equilibrium iteration 子结构Substructure 子结构法substructure technique 超单元super-element 网格生成mesh generation 结构分析程序structural analysis program 前处理pre-processing 后处理post-processing 网格细化mesh refinement 应力光顺stress smoothing 组合结构composite structure。
结构力学英文课件chapter 8
• It is important to realize that the ordinate of the influence line at any position x is equal to the magnitude of RB due to a unit load acting at the position x on the beam. • Generally, a graph indicating the variation of a response function such as one of reactions or internal forces of a structure, across which a downward unit load is moving, is termed as an influence line. For the graph, the position of the unit load, x, is abscissa, the value of the response function is ordinate. When constructing an influence line, the base line represents the possible moving range of the unit concentrated load, and the positive value of the influence line is depicted on the upper side of the base line and vice versa. The dimension of the ordinate is equal to the dimension of the response function divide by the dimension of the unit load.
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3 6 2 8 2
so translation unknowns of original structure are 2.
4, Degree of indeterminacy
nn n The degree of indeterminacy (n) is:
n426
5, Primary structure
(a) Standing on the side of deformation, joint 1 can’t rotate (Z1) due to rigid arm; translation (Z2) at joint 2 can’t exit due to link in the primary structure. But , Z1, Z2 are existences in original structure. In order to eliminate the difference, a rotation Z1 and translation Z2 can be enforced at joint 1 and joint 2 respectively in primary structure.
Shearing force —— clockwise is positive about isolating body (free body).
Rotation angle —— clockwise is positive
The following sign is established: Translation —— clockwise rotation of the whole member is positive.
Suppose end B is hinged.
3
M 0 2i(2 AB)
M BA
BAl
F 0
AB
1( 3 AB1 F )
M B 2 A
l 2i BA
The following sign is established: Bending moment —— clockwise is positive relative to end of member; counterclockwise is negative relative to rigid joint or support.
C
C
C
B
D
3、How to decide the number of primary unknowns
(1)、The number of rotation displacements ( n ) is equal to the number of
rigid joints. (2)、The number of translation unknowns ( n ) The method of determining the translation unknowns is as following.
11
2
l
( l 1) 1
11
22 E I 2
3
3E I
1 (1 l 1) 1 1 l
12
21
EI 2
3
6EI
l 1 ( B )
1p E I
l
l 1 ( A )
2p
EI
l
1
(R • C ) (R
AC
1
R
BC
)
2
(1 0 1
l
l
)
AB
Fig.shows a beam, it is fixed at two ends. EI is constant. The beam is subjected
to a force P, rotation at end A is , and rotation at end B is
, the
A
B
translation at end B relative end A is A B , bending moments at end A, B are
desired.
Solution: let solve it using force method.
(1) The primary structure
Ml l l Ml l l F A B 2 2(2B A )
B F A 2 2(2A B )
if original structure is that one end is fixed and the other end is hinged, its
slope-deflection can be deduced .
All rigid joints (including fixed supports) are changed into hinges; calculate degree of freedom of the new structure. The degree of freedom of the new structure is equal to the number of translation unknown of the original structure.
AB
l
2
(R • C )
ABlLeabharlann We havel l
3
E
I
l 1 6EI
B AB
2 EI •l l
A
l
l 6EI
l 1 3EI
A AB
2 EI •l l
B
2EI (2
1
l
A
3 l l l B
AB ) l
2
2
(2
B
)
A
2
2EI l
(2
B
3 l l l A
In the last chapter (force method), the unknowns of primary structure are forces. After obtaining unknown force, displacement of the structure can be solved.
(a) A (b) A (c) A (d) A
q øB
B øB
l
l
øB B
q
øB
B øB
Bq
C Notice: (1) The flexural deformation of the flexural members in the frame is taken into account, but the shearing and axial deformations of which are
AB ) l
2
2
(2
A
)
B
let i E I
l
linear rigidity
We have
3
M 2i(2 AB)
M AB
A
B
l
F AB
M 2i(2
3 AB)
F
M BA
B
A
l
BA
is referred to as “slopedeflection equation”
Solution: (1) It is indeterminate to the second degree (2) Primary Structure:
(3)Canonical equations In order to solve this problem, we must find out the differences between original structure and primary structure at first.
The end moment, end shearing force and end reaction are listed in table for convenience.
Section 4 Analysis of indeterminate Structure using displacement method
Chapter 7 Slope-Deflection Method
Section 1 Introduction
Slope-deflection method (or simply the displacement method) is another method to analyze the statically indeterminate structure.
(2) Canonical equations
1
11 1
12 2
13 3
1p
1
A
2
21 1
22 2
23 3
2p
2
B
Because
M
3
0
11 1
12 2
1p
1
A
21
1
22
2
2p
2
B
Solution:
(3) Determine coefficients (Graph Multiplication)
When indeterminate structure is analyzed by using displacement method, every member is considered as a statically indeterminate beam with single span. So the primary structure is that every member is changed into an indeterminate beam with single span. A rigid arm is added at every rigid joint to prevent rotation of the joint (but can not prevent translation) at the same time, a link is added at joint where translation is possible. The link prevents translation of the joint.
so translation unknowns of original structure are 2.
4, Degree of indeterminacy
nn n The degree of indeterminacy (n) is:
n426
5, Primary structure
(a) Standing on the side of deformation, joint 1 can’t rotate (Z1) due to rigid arm; translation (Z2) at joint 2 can’t exit due to link in the primary structure. But , Z1, Z2 are existences in original structure. In order to eliminate the difference, a rotation Z1 and translation Z2 can be enforced at joint 1 and joint 2 respectively in primary structure.
Shearing force —— clockwise is positive about isolating body (free body).
Rotation angle —— clockwise is positive
The following sign is established: Translation —— clockwise rotation of the whole member is positive.
Suppose end B is hinged.
3
M 0 2i(2 AB)
M BA
BAl
F 0
AB
1( 3 AB1 F )
M B 2 A
l 2i BA
The following sign is established: Bending moment —— clockwise is positive relative to end of member; counterclockwise is negative relative to rigid joint or support.
C
C
C
B
D
3、How to decide the number of primary unknowns
(1)、The number of rotation displacements ( n ) is equal to the number of
rigid joints. (2)、The number of translation unknowns ( n ) The method of determining the translation unknowns is as following.
11
2
l
( l 1) 1
11
22 E I 2
3
3E I
1 (1 l 1) 1 1 l
12
21
EI 2
3
6EI
l 1 ( B )
1p E I
l
l 1 ( A )
2p
EI
l
1
(R • C ) (R
AC
1
R
BC
)
2
(1 0 1
l
l
)
AB
Fig.shows a beam, it is fixed at two ends. EI is constant. The beam is subjected
to a force P, rotation at end A is , and rotation at end B is
, the
A
B
translation at end B relative end A is A B , bending moments at end A, B are
desired.
Solution: let solve it using force method.
(1) The primary structure
Ml l l Ml l l F A B 2 2(2B A )
B F A 2 2(2A B )
if original structure is that one end is fixed and the other end is hinged, its
slope-deflection can be deduced .
All rigid joints (including fixed supports) are changed into hinges; calculate degree of freedom of the new structure. The degree of freedom of the new structure is equal to the number of translation unknown of the original structure.
AB
l
2
(R • C )
ABlLeabharlann We havel l
3
E
I
l 1 6EI
B AB
2 EI •l l
A
l
l 6EI
l 1 3EI
A AB
2 EI •l l
B
2EI (2
1
l
A
3 l l l B
AB ) l
2
2
(2
B
)
A
2
2EI l
(2
B
3 l l l A
In the last chapter (force method), the unknowns of primary structure are forces. After obtaining unknown force, displacement of the structure can be solved.
(a) A (b) A (c) A (d) A
q øB
B øB
l
l
øB B
q
øB
B øB
Bq
C Notice: (1) The flexural deformation of the flexural members in the frame is taken into account, but the shearing and axial deformations of which are
AB ) l
2
2
(2
A
)
B
let i E I
l
linear rigidity
We have
3
M 2i(2 AB)
M AB
A
B
l
F AB
M 2i(2
3 AB)
F
M BA
B
A
l
BA
is referred to as “slopedeflection equation”
Solution: (1) It is indeterminate to the second degree (2) Primary Structure:
(3)Canonical equations In order to solve this problem, we must find out the differences between original structure and primary structure at first.
The end moment, end shearing force and end reaction are listed in table for convenience.
Section 4 Analysis of indeterminate Structure using displacement method
Chapter 7 Slope-Deflection Method
Section 1 Introduction
Slope-deflection method (or simply the displacement method) is another method to analyze the statically indeterminate structure.
(2) Canonical equations
1
11 1
12 2
13 3
1p
1
A
2
21 1
22 2
23 3
2p
2
B
Because
M
3
0
11 1
12 2
1p
1
A
21
1
22
2
2p
2
B
Solution:
(3) Determine coefficients (Graph Multiplication)
When indeterminate structure is analyzed by using displacement method, every member is considered as a statically indeterminate beam with single span. So the primary structure is that every member is changed into an indeterminate beam with single span. A rigid arm is added at every rigid joint to prevent rotation of the joint (but can not prevent translation) at the same time, a link is added at joint where translation is possible. The link prevents translation of the joint.