A coupled finite element and boundary element method is introduced for the analysis of two-dimensional elastic contact problems without friction. The Lagrange multiplier method is used to apply the contact constraints. A computer program, which can analyse axisymmetric, plane strain and plane stress problems, has been developed and used to demonstrate the accuracy of the method. The program is applied to a sphere in contact with a flat surface, a rigid punch pressed on to an elastic foundation and an elastic cylindrical punch in contact with an elastic plate. In all cases good agreement is obtained with analytical solutions for stresses near the contact region.
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