多体系统非连续变形的弹性及弹塑性分析方法(I)——基本原理

ELASTIC AND ELASTOPLASTIC ANALYSIS METHODS OF DISCONTINUOUS DEFORMATION FOR MULTI-BODY SYSTEM(I) —— FUNDAMENTALS

非连续变形是多体系统的一个重要特性。从一般的平面问题出发,建立了多体系统的非连续变形分析的分区参变量最小势能原理,阐明了其理论基础,并推导了多体系统的非连续变形的弹性和弹塑性分析的整体控制方程,探讨了其求解的数值算法。该方法能够仿真模拟多体系统的变形和应力,不仅能够对多体系统进行静、动力耦合分析,而且还能够逐步模拟与预测多体系统的变形与应力响应及接触界面上的接触应力和相对运动等复杂的非线性过程。

Discontinuous deformation is a fundamental character of multi-body system. For the general plane problem,divisional parameter principle of minimum potential energy is employed to establish the computational model for discontinuous deformation analysis of multi-body system in this paper. Mathematical formulations of global controlling equations of elastic and elastoplastic analysis of discontinuous deformation of multi-body system are presented and the numerical solution approach is developed. The mothod can not only perform both static and dynamic coupling analysis,but also conduct step-by-step simulation and prediction of deformations and stresses of multi-body system together with complex nonlinear process such as contact stress and relative movement along contact interfaces. The theoretical basis is established for numerical model of discontinuous deformation computational mechanics.