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

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.