接触力学自适应无网格计算系统设计

Design of an Adaptive Meshless Computational System for Contact Mechanics

在求解弹塑性接触问题时,为了保证计算精度同时减少计算耗费,提出一种接触力学自适应无网格计算系统。利用无网格法结点排布灵活便于删减等优点,对采用基于应变能梯度的自适应无网格伽辽金-有限元方法求解接触问题的计算系统的原理、算法流程进行阐述,并考虑到自适应影响域半径、弹塑性等关键问题,采用模块化思想进行程序设计。通过圆柱体与弹塑性平面接触的算例验证了计算系统的正确性,并将自适应密化解与整体密化解比较,显现出良好的计算精度和效率。为接触力学自适应无网格分析软件商业化提供了一种理论和程序设计基础。

In order to improve the computational accuracy and efficiency, an adaptive meshless computational system programming for contact mechanics is introduced. The system is used to solve elasto -plastic contact model. The meshless method does not need any mesh information, and the nodes can be moved, inserted and deleted freely. An adaptive element - free Galerkin （EFG） computational system based on the gradient of strain energy for two - dimensional elasto -plastic contact problems is implemented, including principle explanation, arithmetic flowchart. Modularization in software engineering is used for programming realization, and the system takes into account the adaptive change of the influence domain radius, elasto - plastic property of material. By applying the adaptive model, a rigid cylinder contacting with an elastic -plastic plane is analyzed to validate the adaptive meshless computational system. Comparisons of the adaptive refinement solution with the uniform refinement solution are made, and the resuits indicate that the accuracy of the solutions from the adaptive refinement model is satisfactory and the CPU time cost is much less than that for the uniform refinement calculation. The theory and programming foundation for the businesslike development of software system for adaptive meshless analysis are provided.