复合材料力学讲义(第二版)-

1、Center for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology5Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite Materi

2、alscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology简单层板的宏简单层板的宏观力学性能观力学性能简单层板的微简单层板的微观

3、力学性能观力学性能简单层板的应简单层板的应力应变关系力应变关系简单层板的强简单层板的强度问题度问题刚度的弹性力刚度的弹性力学分析方法学分析方法刚度的材料力刚度的材料力学分析方法学分析方法强度的材料力强度的材料力学分析方法学分析方法简单层板的宏简单层板的宏观力学性能观力学性能Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite

4、 MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology经典层合理论经典层合理论层合板的层合板的强度问题强度问题层合板的应力层合板的应力应变关系应变关系刚度的刚度的特殊情况特殊情况层间应力层间应力强度分析方法强度分析方法层合板

5、设计层合板设计层合板的宏观层合板的宏观力学性能力学性能层合板的弯曲层合板的弯曲振动与屈曲振动与屈曲Center for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of

6、Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute

7、of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, H

8、arbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Compos

9、ite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite Mater

10、ialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of M

11、echanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbi

12、n Institute of TechnologyStrain-Stress RelationsMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of Technolo

13、gyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyStrain-Stress RelationsMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite Materi

14、alscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyPlane-Stress StateMechanics of Mechanics of Mechanics of Mechanics of Mec

15、hanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin

16、Institute of TechnologyPlane-Stress Constitutive EquationsMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute o

17、f TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyStrain-Stress Relations in Reference CoordinatesMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite Materials

18、coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyStrain-Stress Relations in Reference C

19、oordinatesMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harb

20、in Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite

21、 Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite Material

22、scoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology 1221662221121112210000Q QQ QQ QQ QQ Q 12216622211211122

23、10000S SS SS SS SS S x xy yy yx xx xy yy yx xQ QQ QQ QQ QQ QQ QQ QQ QQ Q662616262221161211 kkkQ 第第k k层的应力层的应力- -应变关系应变关系Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposi

24、te MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology0 z 0, 0 zyzx Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite

25、MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics

26、of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Tech

27、nologyCenter for Composite Materials, Harbin Institute of Technologyx,uy,vz,w变形前的横截面变形前的横截面变形后的横截面变形后的横截面XZ平面内的变形几何平面内的变形几何zxzcABCDu0 w0 ABCDzc Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite Materialsco

28、Mposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyB：中面上一点：中面上一点C：任意点：任意点 c cC Cz zu uu u0 是层合板中面在是层合板中面在X方向上的斜率方向上的斜率x xw w 0层合板

29、厚度上任意一点层合板厚度上任意一点z的位移的位移u为：为：x xw wz zu uu u 00同样，在同样，在yz平面内，平面内，y方向上的位移方向上的位移v为：为：y yw wz zv vv v 00zxzcABCDu0 w0 ABCDzc Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMpo

30、site MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology板内任一点的位移分量可表示为：板内任一点的位移分量可表示为：) )z z, ,y y, ,x x( (w ww w) )z z, ,y y, ,x x( (v vv v) )z z, ,y y, ,x

31、 x( (u uu u 由直法线不变假设，得由直法线不变假设，得00 z zy yz zx xz zy yw wz zv vv vx xw wz zu uu u) )y y, ,x x( (w ww w 00000Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsC

32、enter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyUndeformedClassical plate theoryFirst-order plate theoryThird-order plate theoryMechanics of Mechanics of Mechanics

33、 of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composit

34、e Materials, Harbin Institute of TechnologyDisplacement Fields of VariousLaminate TheoriesClassical plate theoryFirst-order plate theoryThird-order plate theoryMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMpo

35、site MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyClassical plate theoryy yw wz zv vv vx xw wz zu uu u) )y y, ,x

36、 x( (w ww w 00000Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Material

37、s, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology2020 x xw wz zx xu ux xu ux x 2020y yw wz zy yv vy yv vy y y yx xw wz zx xv vy yu ux xv vy yu ux xy y 02002 k k z z 0应变由位移确定如下应变由位移确定如下: :若用矩阵形式表示若用矩阵形式表示 x xv vy yu uy yv vx xu u 00000 y yx xw wy yw wx xw

38、 w k k 222222Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, H

39、arbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology) )x xw w( (k kx x22 ) )y yw w( (k ky y22 ) )y yx xw w( (k kx xy y 22T T)x xv vy yu u( (, ,y yv v, ,x xu u 00000T T y yx xw w, ,y yw w, ,x xw w k k 222222Mechanics of Mechanics of Mechanics of Mechanics of Mec

40、hanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin

41、Institute of Technologyy yw wz zv vx xw wz zu uz zw wz zy yz zx xz z 0y yx xz zv vv vz zu uu u) )y y, ,x x( (w ww w 000 x xz zx xu ux xu ux xx x 0y yz zy yv vy yv vy yy y 0) )x xy y( (z zx xv vy yu ux xv vy yu uy yx xx xy y 00 ) )x xy y( (y yx x k k y yx xy yx xMechanics of Mechanics of Mechanics of

42、 Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite M

43、aterials, Harbin Institute of Technology k k z z 0 k kk kk kQ Q x xy yy yx xx xy yy yx xx xy yy yx xk kk kk kz zQ QQ QQ QQ QQ QQ QQ QQ QQ Q000662616262221161211Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMpo

44、site MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyLaminateStraindistributionStressdistributionMechanics of Mecha

45、nics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCe

46、nter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute

47、 of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposit

48、e MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology定义作用在单位宽度上层合板的平均内力定义作用在单位宽度上层合板的平均内力 Ni 和内力矩和内力矩Mi为为 2h2hiidzN/ 22/ /h h/ /h hi ii i

49、z zd dz zM M（i=x，y，xy）xyzNyxNyNxyNxxyz层合平板的力矩层合平板的力矩MyMyxMxyMxMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institu

50、te of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyMechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMpos

51、ite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology N1kzzkxyyx2t2txyyxxyyxdzdzNNNk1k/ N Nk kz zz zk kx xy yy yx x/ /t t/ /t tx xy yy

52、yx xx xy yy yx xd dz zz zz zd dz zM MM MM Mk kk k1221N层层合板上作用的全部合力和力矩为：层层合板上作用的全部合力和力矩为： 2t2tiidzN/ 2t2tiizdzM/Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite Materi

53、alsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology k kk kk kk kz zz zx xy yy yx xz zz zx xy yy yx xN Nk kk kx xy yy yx xz zd dz zk kk kk kd dz zQ QQ QQ QQ QQ QQ

54、QQ QQ QQ QN NN NN N110001662616262221161211 k kk kk kk kz zz zx xy yy yx xz zz zx xy yy yx xN Nk kk kx xy yy yx xd dz zz zk kk kk kz zd dz zQ QQ QQ QQ QQ QQ QQ QQ QQ QM MM MM M1120001662616262221161211不是不是z的函数而是中面值可以从的函数而是中面值可以从积分中提出积分中提出Mechanics of Mechanics of Mechanics of Mechanics of Mechanics

55、of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institu

56、te of Technology x xy yy yx xx xy yy yx xx xy yy yx xk kk kk kB BB BB BB BB BB BB BB BB BA AA AA AA AA AA AA AA AA AN NN NN N662616262221161211000662616262221161211 k kk kk kk kz zz zx xy yy yx xz zz zx xy yy yx xN Nk kk kx xy yy yx xz zd dz zk kk kk kd dz zQ QQ QQ QQ QQ QQ QQ QQ QQ QN NN NN N110001

57、662616262221161211Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materia

58、ls, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology x xy yy yx xx xy yy yx xx xy yy yx xk kk kk kD DD DD DD DD DD DD DD DD DB BB BB BB BB BB BB BB BB BM MM MM M662616262221161211000662616262221161211 k kk kk kk kz zz zx xy yy yx xz zz zx xy yy yx xN Nk kk

59、 kx xy yy yx xd dz zz zk kk kk kz zd dz zQ QQ QQ QQ QQ QQ QQ QQ QQ QM MM MM M1120001662616262221161211Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of Mechanics of coMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialscoMposite MaterialsCenter

60、 for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of TechnologyCenter for Composite Materials, Harbin Institute of Technology N Nk kk kk kk ki ij ji ij jN Nk kk kk kk ki ij ji ij jN Nk kk kk kk ki ij ji ij j) )z zz z( (Q QD D) )z zz z( (Q QB B)