分析结构非线性问题的杂交可变基Galerkin方法

基于渐近摄动理论和Galer-kin方法,本文提出分析结构非线性问题的杂交可变基Galer-kin方法。本文方法首次引入可变基函数的概念,可大幅度降低计算量,而且在有限元法等数值方法中易于推广应用,在解决非线性问题领域有广泛应用前景。最后本文分析圆板大挠度问题和扁球壳大挠度问题,以验证本文方法的有效性。

Hybrid Changeable Basis Galerkin Technique for Nonlinear Analysis of Structures

Based on the asymptotical perturbation method and the Galerkin technique,the hybrid changeable basis Galerkin technique is presented for predicting the nonlinear response of structures. By the idea of changeable basis functions firstproposed,it greatly reduces calculation and is easily used in other numericaldiscretization techniques, such as finite element method etc.It appears to have high potential for solution of nonlinear structural problems.Finally, the effec-tiveness of this technique is demonstrated by means of two numerical examples:the large deflection of circular plates objected to uniform normal load and the large deflection of spherical caps under centrally distributed pressures.