基于辛对偶体系的层合板自由边缘效应的分析解  

Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System

作　　者：姚伟岸[1] 聂臆瞩[1] 肖峰[2] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [2]大连医科大学计算机教研室,辽宁大连116044

出　　处：《应用数学和力学》2011年第9期1021-1029,共9页Applied Mathematics and Mechanics

基　　金：国家973重点基础研究计划资助项目(2010CB832704);国家自然科学基金资助项目(10772039)

摘　　要：在原变量——位移和其对偶变量——应力组成的辛几何空间,建立了Pipes-Pagano模型的复合材料层合板问题的辛对偶求解体系.与传统的单类变量不同,辛对偶变量有利于同时描述层间位移连续性条件和应力平衡条件.进入辛对偶体系以后,就可以应用辛对偶体系的统一解析求解方法,如分离变量和辛本征展开的方法对层合板问题进行解析分析和求解.对层合板自由边缘效应的分析求解,验证了辛对偶体系的方法对层合板问题的分析求解是十分有效的.In symplectic space composed of the original variables--displacements and their dual variables--stresses, the symplectic solution for the composite laminated based on the Pipes-Pagano model was established. In contrast to traditional technique, the symplectic dual variables include displacement components as well as stress components, so the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously. After introducing in- to the symplectic dual system, the uniform scheme, such as the separation of variables and symplectic eigenfunction expansion method, can be implemented conveniently to analyze prob- lem of composite laminates. An analytical solution for free edge effect of composite laminates was gained, and it shows that the symplectic dual method is efficient for the analysis of composite laminates.

关 键 词：层合板 边缘效应 Pipes-Pagano模型 层间应力 辛对偶体系 

分 类 号：O343[理学—固体力学]