摘要
本文将以现代常微分方程求解器为支撑软件的线法推广应用于含时间变量的粘弹性力学问题。其基本思想是先用拉普拉斯积分变换把问题的控制偏微分方程组和定解条件进行变换,得到拉氏变换空间中的定常问题,然后用传统的线法借助于常微分方程求解器得到该变换空间中的数值解,再应用拉氏数值逆变换求得原时空域中的数值解。文中还给出方法的基本原理和实施过程。算例表明,采用拉普拉斯积分变换于线法分析结构粘弹性力学等含时间变量的力学问题是十分有效的。
In this paper, the method of lines is applied for solving viscoelastic mechanics. By means of the Laplace integral transformation, the governing equations and boundary conditions are firstly changed into the problems being foreign to time in the Laplace space. Then the numerical solutions in the space are obtained by means of traditional method of lines in virtue of Ordinary Differential Equation Solver. Finally, the time - dependent solution can be obtained through the technique of numerical Laplace inverse transform. The numerical examples indicate that the present method of lines recurring to ordinary differential equation solver is validated, accurate and terse for analyzing the time - dependent mechanical problems.
出处
《力学季刊》
CSCD
2000年第2期209-213,共5页
Chinese Quarterly of Mechanics
关键词
粘弹性
线法
拉氏空间
物理空间
结构
viscoelasticity
method of lines
Laplace space
physical space
