正交各向异性摩擦接触分析的一个二阶锥线性互补法  

A SECOND-ORDER CONE LINEAR COMPLEMENTARITY APPROACH FOR CONTACT PROBLEMS WITH ORTHOTROPIC FRICTION LAW

作　　者：李建宇[1,2] 张洪武[2] 潘少华[3] 

机构地区：[1]天津科技大学机械工程学院,天津300222 [2]大连理工大学工业装备结构分析国家重点实验室,运载工程与力学学部,工程力学系,大连116023 [3]华南理工大学应用数学系,广州540031

出　　处：《固体力学学报》2010年第2期109-118,共10页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10902077,10901058,10721062);国家自然科学重点基础研究基金(2010CB832704)资助

摘　　要：建立了用于各向异性摩擦接触分析的一个新型互补模型:二阶锥线性互补模型.通过与弹塑性力学的类比,并引入"线性二阶锥互补"的概念,将正交各向异性摩擦接触定律表达为一个二阶锥线性互补模型.在此基础上,在参变量变分原理的框架下,建立了正交各向异性摩擦接触问题的有限元列式.由于避免了对摩擦锥的显式线性化,使得该文模型的变量个数较线性互补模型小很多,而解的精度又高很多.文末通过算例,说明了方法对于正交各向异性摩擦接触分析的有效性.A second-order cone linear complementarity formulation for contact problems with orthotropic friction law is proposed by the parametric variational principle.Employing the concept of second-order cone complementarity,the contact condition with orthotropic friction law is formulated as a linear second-order cone complementarity condition through the analogy with the elastic-perfectly plastic constitutive model.Then,the governing equations of the contact problem can be reformulated as a linear second-order cone complementarity problem（SOCCP） via the parametric variational principle and the finite element method.The SOCCP formulation avoids the polyhedral approximation to the elliptical Coulomb friction cone so that the problem under consideration has much smaller size and the solution has better accuracy.Numerical results confirm the effectiveness and robustness of the SOCCP formulation.

关 键 词：三维接触问题 各向异性摩擦 二阶锥 互补 变分原理 

分 类 号：O313.5[理学—一般力学与力学基础]