榫齿接触分析的互补算法

本文根据变分不等方程理论论证了含摩擦弹性接触问题解的存在性和唯一性, 并使其等价于二次规划问题。接触体系各部分离散后凝聚到接触边界上形成出口刚度矩阵, 并根据接触面上法向位移的非穿透条件和摩擦律等条件, 导出非负变量 υ,λ的线性互补方程。直接采用二次规划的 Lemke算法, 其求解规模仅限于接触边界。榫齿模型接触分析结果和实验结果吻合较好。 

A SUPPLEMENTARY ALGORITHM FOR LUG TOOTH CONTACT ANALYSIS

According the principles of the inequality variations,the existence and the uniqueness of the solution have been verified for elastic contact problems,which contain friction forces between the contact surfaces.Thus the contact problems are made to be equivalent to the quardratic programming problems.By using the basic idea of supplement,the objects of a contact system is discreted and then lumped to the contact boundaries,then an resultant stiffness matrix is formed and a linear supplementary equation of non negative variables,υ adn λ,is also derived in the light of the non penetration condition of the normal displacements of the contact surfaces and the Conlumb friction law,etc.By the direct use of the Lemke algorithm of quardratic programming method,the scope of solution is limited to the contact boundaries.The whole field information is therefore obtained from further solution of the subelements.Such an algorithm enables to eliminate effectively the convergence instability which used to appear in the iteration methods in solving the problems.The results of calculations of the lug tooths contact stresses are fitted with the experimental data quite well.