常微分方程技术及其在固体力学计算中的应用

常微分方程(ODE——Ordinary Differential Equation)边值问题的最新计算求解技术的迅速发展推出了一批高质高效的通用软件,而工程中大量的ODE问题并非呈现为这些求解器(Solver)所接受的标准形式。然而,运用一些简单的ODE变换技巧可以将大量的不同类型的特殊问题转化为标准形式。本文列举了若干常用的变换技巧,并广泛地应用于各种固体力学问题的计算中,使大量的ODE问题在形式上得到统一,得以用标准的ODE Solver方便有效地求解。

ODE TECHNIQUES AND APPLICATIONS IN COMPUTATIONAL MECHANICS

The rapid advances of new computational technology in solution of ordinary differential equation (ODE) boundary value problems (BVPs) have made a number of high-quality general-purpose ODE solvers well available, but various ODE problems arising in scientific and engineering applications are frequently not in the 'standard' forms for these codes to accept. However, many problems can be transformed into such forms by using some simple and novel conversion techniques. In this paper, a number of ODE conversion techniques are summarised, and with special reference to computational solid mechanics many applications are presented by providing simple numerical examples. As a result, various BVPs such as eigen-value problems, geometrical nonlinear problems, material nonlinear problems, elastic contact and optimal design problems etc., can efficiently be solved in a unified manner by invoking the existing robust ODE solvers.