复合材料力学讲义(第二版)-5

CenterforCompositeMaterials,HarbinInstituteofTechnology复合材料力学5CenterforCompositeMaterials,HarbinInstituteofTechnology复合材料力学重点内容简单层板的宏观力学性能简单层板的微观力学性能简单层板的应力应变关系简单层板的强度问题刚度的弹性力学分析方法刚度的材料力学分析方法强度的材料力学分析方法简单层板的宏观力学性能CenterforCompositeMaterials,HarbinInstituteofTechnology复合材料力学重点内容经典层合理论层合板的强度问题层合板的应力应变关系刚度的特殊情况层间应力强度分析方法层合板设计层合板的宏观力学性能层合板的弯曲振动与屈曲CenterforCompositeMaterials,HarbinInstituteofTechnology层合板的宏观力学性能CenterforCompositeMaterials,HarbinInstituteofTechnology复合材料两个典型特征CenterforCompositeMaterials,HarbinInstituteofTechnology引言CenterforCompositeMaterials,HarbinInstituteofTechnology复合材料的尺度CenterforCompositeMaterials,HarbinInstituteofTechnology引言CenterforCompositeMaterials,HarbinInstituteofTechnologyStrain-StressRelationsCenterforCompositeMaterials,HarbinInstituteofTechnologyStrain-StressRelationsCenterforCompositeMaterials,HarbinInstituteofTechnologyPlane-StressStateCenterforCompositeMaterials,HarbinInstituteofTechnologyPlane-StressConstitutiveEquationsCenterforCompositeMaterials,HarbinInstituteofTechnologyStrain-StressRelationsinReferenceCoordinatesCenterforCompositeMaterials,HarbinInstituteofTechnologyStrain-StressRelationsinReferenceCoordinatesCenterforCompositeMaterials,HarbinInstituteofTechnology引言•层合板定义：是由两层或多层简单层板粘合在一起作为一个整体的结构单元–各单层的材料主方向的布置应使结构元件能承受几个方向的载荷•单层板是层合板或层合结构分层的基本单元，对它的宏观力学研究是分析层合结构的基础•层合板各单层的材料、厚度和弹性主方向等可以互不相同。适当地改变这些参数，人们就可以设计出最有效地承受特定外载的结构元件，这是复合材料层合板突出的优点之一CenterforCompositeMaterials,HarbinInstituteofTechnology引言•有不同物理性质和几何尺寸单层组成的层合板具有最一般的各向异性性质•层合板不一定有确定的主方向–这种层合板在厚度方向具有客观的非均匀性和力学性质的不连续性–对层合板的力学分析就变得更为复杂•已知单层的性质，主要关注沿厚度方向的应力和应变的变化CenterforCompositeMaterials,HarbinInstituteofTechnology单层板的应力-应变关系1221662221121112210000QQQQQ1221662221121112210000SSSSSxyyxxyyxQQQQQQQQQ662616262221161211kkkQ第k层的应力-应变关系层与层过渡和层与层的结合方式的考虑？沿厚度方向的积分CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论（ClassicalLaminatePlateTheory）•层间变形一致性假设–层合板各单层之间粘合层非常薄，单层边界两边的位移是连续的，层间不能滑移，无相对位移•直法线不变假设–假设垂直于层合板中面的一根初始直线，在层合板受到拉伸和弯曲后，仍保持直线并垂直于中面；变形前垂直与板中面的直线在变形后仍保持垂直，且长度不变–板的克希荷夫假设(Kirchhoff)–壳的克希荷夫-勒普假设(Kirchhoff-Love)•在上述假设基础上建立的层合板理论称为经典层合板理论0z0,0zyzxCenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论•经典层合板理论的假设没有针对层合平板的限制，层合板也可以是曲面或壳•另外–单层平面应力状态假设：层合板中各单层都可近似地认为处于平面应力状态,在厚度方向上的正应力于其它应力相比很小，可忽略不计CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论x,uy,vz,w变形前的横截面变形后的横截面XZ平面内的变形几何zxzcABCDu0w0ABCDzcCenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论B：中面上一点C：任意点cCzuu0是层合板中面在X方向上的斜率xw0层合板厚度上任意一点z的位移u为：xwzuu00同样，在yz平面内，y方向上的位移v为：ywzvv00zxzcABCDu0w0ABCDzcCenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论板内任一点的位移分量可表示为：)z,y,x(ww)z,y,x(vv)z,y,x(uu由直法线不变假设，得00zyzxzywzvvxwzuu)y,x(ww00000CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论UndeformedClassicalplatetheoryFirst-orderplatetheoryThird-orderplatetheoryCenterforCompositeMaterials,HarbinInstituteofTechnologyDisplacementFieldsofVariousLaminateTheoriesClassicalplatetheoryFirst-orderplatetheoryThird-orderplatetheoryCenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论Classicalplatetheoryywzvvxwzuu)y,x(ww00000CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论2020xwzxuxux2020ywzyvyvyyxwzxvyuxvyuxy02002}k{z}{}{0应变由位移确定如下:若用矩阵形式表示xvyuyvxu}{00000yxwywxw}k{222222CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论分别称为中面面内应变列阵和中面弯曲应变列阵)xw(kx22)yw(ky22称为曲率)yxw(kxy22称为扭曲率T)}xvyu(,yv,xu{}{00000T}yxw,yw,xw{}k{222222CenterforCompositeMaterials,HarbinInstituteofTechnology剪切变形理论ywzvxwzuzwzyzxz0yxzvvzuu)y,x(ww000xzxuxuxx0yzyvyvyy0)xy(zxvyuxvyuyxxy00)xy(yx}k{yxyx不为零CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论}k{z}{}{0kkkQxyyxxyyxxyyxkkkzQQQQQQQQQ000662616262221161211每一层的Qij是不同的CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论LaminateStraindistributionStressdistribution因层合板沿厚度方向物理性质不连续导致应力的不连续CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论定义作用在单位宽度上层合板的平均内力Ni和内力矩Mi为2h2hiidzN//22/h/hiizdzM（i=x，y，xy）xyzNyxNyNxyNxxyz层合平板的力矩MyMyxMxyMxCenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论N1kzzkxyyx2t2txyyxxyyxdzdzNNNk1k//Nkzzkxyyx/t/txyyxxyyxdzzzdzMMMkk1221N层层合板上作用的全部合力和力矩为：2t2tiidzN//2t2tiizdzM//CenterforCompositeMaterials,HarbinInstituteofTechnology经典层合理论