层状材料的高阶连续统模型

基金项目: 国家自然科学基金

HIGHER ORDER CONTINUUM MODEL FOR LAMINATED COMPOSITES

摘要

摘要: 本文研究了由两种各向同性线性弹性材料组成的层状复合材料。同时利用位移在上下层面处的值及各阶导数对层内位移展开,并引用层面处应力矢量为参变量,使得层面处的应力和位移连续条件自动满足。然后利用Hamilton原理,按无约束条件变分,得到界面上的Euler方程,由此得到高阶连续统模型的场方程。考虑了场方程的长波近似和短波近似,所得结果和现存理论符合得很好。

Abstract: The paper deals with the laminated composites consisted of two different isotropic materials.With the displacements and their derivatives and stress vectors at the interfaces,the displacement in a layer is expanded.For such expansion the continuity conditions of displacement and stress at interfaces are satisfied automatically.By applying a variational theorem without constraint,Eider equations at interfaces are derived,from which the field equations of a higher order continuum model are obtained.Two extreme cases long wave and short wave approximations are considered.The calculated results for dispersion curve including the past band and stop band show a good agreement with the existing theory.