弹性接触问题有限元分析的一个新方法

小变形弹性接触问题属于边界条件几何非线性问题弹性接触问题的非线性，是由于接触点的接触条件引起的。本文提出的有限元混合法适于求解此类局部非线性问题。该方法是利用弹性体的刚度矩阵求出接触边界的接触内力的影响系数矩阵，再由接触边界的连续性条件求解接触内力，从而把非线性问题转化到局部求解。计算表明：对求解此类复杂非线性问题，该方法在计算速度和机器存贮上仅比求解一般线性问题的花费略有增加甚至相当。

A NEW METHOD FOR ANALYSIS OF ELASTIC CONTACT PROBLEMS USING FINITE ELEMENT METHODS

This paper deals with elastic contact problems, which belongs to category of boundary condition nonlinearity with small deformation. The nonlinearity of elastic contact problems is due to the contact conditions of the points contacted.The mixed approach suggested by this paper are suited for solving the local nonlinear problems. The general ideas of this mixed approach using F.E.M are as following; after the discretion of elastic bodies, according the displacement field assumed, we can get the stiffness matrix of elastic bodies, thus the matrix of influence coefficients of contact stress at the contacting boundaries can be determined, further more regarding the contact stresses as unknown variables, the compatibility conditions at contact boundaries then were given. As a matter of fact, we thus performed a procedure which localized the nonlinearity of the problem.The computational result shows that to solve such class of problems with complex nonlinear boundary conditions by means of this method, the computational speed and storage are slightly greater or approach to those in solving general linear problems.