大变位下多体系统摩擦接触问题线性规划求解方法  

Linear programming algorithm for solving friction-contact problems of multi-body systems under large displacements

作　　者：黎勇[1] 栾茂田[1] 冯夏庭[2] 王泳嘉[2] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室 [2]东北大学资源与土木工程学院,辽宁沈阳110006

出　　处：《大连理工大学学报》2003年第6期806-811,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(10172022);教育部跨世纪优秀人才培养计划研究基金资助项目;教育部优秀青年教师奖励计划资助项目;霍英东教育基金资助项目(71048);大连理工大学青年教师培养计划研究基金资助项目.

摘　　要：建立了多体系统中摩擦接触问题的整体控制方程,在大变位情况下将其分解成两个线性互补问题,一般通过两次线性规划求解可完成一次接触问题的求解,大大地减少了接触问题求解的迭代次数和计算量,并且可直接得到系统中接触界面上的接触应力,从而克服了对于多体系统求解接触问题需要多次迭代和难于直接得到接触应力的缺陷.数值算例表明了该方法的合理性和有效性,为大变位下多体系统中接触问题的求解提供了有效的手段.The global control equations of the friction contact problem of the multi-body systems are developed and the corresponding numerical formulations are given based on the generalized finite elements and the contact-force elements presented by the authors. In order to consider the effect of variation of configuration including the contact position and the contact area during large-scale deformation on the equilibrium of forces, the resulting mathematical programming is partitioned into two linear complementary problems of mathematical programming. The numerical procedure for solving these linear programming problems is given. Accordingly, the configuration and the contact forces or stresses under the condition of large displacements can be defined accurately. It is shown by a numerical example that the proposed method is reasonable, effective and powerful for solving the contact problem of the multi-body system under large displacements.

关 键 词：大变位 多体系统 线性规划 线性互补问题 接触力元 广义有限单元 界面 

分 类 号：TU4[建筑科学—土工工程] O342[理学—固体力学]