弹性力学求解体系的研究与进展 第十三届全国结构工程学术会议特邀报告

Research and Advances on Systematic Methodology for Elasticity

本文介绍弹性力学对偶求解体系的近期研究和进展:(1)提出一种新的正交关系。不用辛几何的概念,直接导出对偶微分方程组;(2)基于新正交关系,建立二维弹性力学特征函数展开直接解法,求得含可对角化边界条件下的显式封闭解:(3)将对偶求解体系推广到多坐标方向,建立多坐标方向的对偶微分方程和求解体系。(4)采用偏微分方程的算子解法,建立了板状弹性体的弯曲理论,把它的解分解为弯曲齐次解、特解、和衰减解:(5)将对偶求解体系推广应用于厚板和薄板问题,建立了有关的对偶微分方程,正交关系和变分原理。

This paper presents some recent research work and advances on systematic methodology for elasticity, (i) A new orthogonality relationship is firstly proposed, and the related system of dual equations can be derived out directly without the concept of symplectic geometry; (ii) Based on the new orthogonality relationship, a direct solution method by eigenfunction expansion is established for 2-D elasticity, and thus, the explicit close solutions under diagonalizable boundary conditions can be obtained; (iii) ...