摄动－数学规划配点法求解薄板几何非线性问题

COMBINATION OF THE PERTURBATION METHOD AND MATHEMATICAL PROGRAMMING COLLOCATION FOR THE GEOMETRICALLY NONLINEAR PROBLEMS OF RECTANGULAR PLATES

本文把摄动法和数学规划配点法结合起来，分析了薄板的几何非线性问题．首先，采用摄动法将非线性偏微分方程化成一系列的线性偏微分方程．然后，用配点法得出数学规划方程并求解之．文中给出算例，结果表明了该法简便且有效．

This paper presents the combination of the perturbation method and mathematical programming to analyse the geometrically nonlinear problem of rectangular plates. The nonlinear partial differential eguatiions are first converted into several sets of linear equations by using perturbations.Then the optimzation equations are deduced from linear equations by using collocation method of weighted residuals. The numerical results have shown that this method is convenient and effective for analysis of plates and shells.