工程结构分析的虚拟结构法

Virtual Structure Method of Structure Analysis

提出的虚拟结构法旨在解决形状不规则结构件的力学分析问题．虚拟一个形状规则的结构体，包容着不规则结构件；将虚拟结构边界上的虚拟力作为待定的未知量，通过控制方程和调整虚拟力的值，利用第一类数学规划加权残值法，使不规则结构的控制方程和边界条件得到满足．工程结构分析的虚拟结构法，实际上是加权残值配点法和线性规划法相结合的方法，是一种半解析方法．该方法应用于两个工程实际问题，计算结果表明，能很好地解决形状不规则结构的力学问题，是工程结构分析的一种有效方法．

The virtual structure method for mechanical analysis of irregular structures in engineering is presented. A regular shape structure, which contains an irregular shape structure, is invented, and the invented forces on the boundary of the regular shape structure are assumed unknown. Adjusting the value of unknown forces on the regular shape structure and using the first kind of mathematical programming on the weighted residual method, the governing differential equations and the boundary conditions of the irregular shape structure can be satisfied. The virtual structure method of structure analysis is one kind of semianalytic method on solid mechanics, which combines the collocated method with the linear mathematical programming. By using the virtual structure method, two problems of structure analysis are solved. The numerous results show that the method is especially applicable for the mechanical analysis on structures with irregular shapes. The virtual structure method is an effective method for structure analysis in engineering.