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UBC Theses and Dissertations

The application of the mixed finite element method to the elastic contact problem Tseng, Jorgito

Abstract

The finite element method is applied in conjunction with Reissner's mixed variational principle to the investigation of two-dimensional elastic contact problems. The versatility of the mixed principle in incorporating boundary conditions pertinent to the contact problem is demonstrated. Contact conditions are modelled by appropriate manipulations of boundary variables. In cases where the contact region is independent of the applied loading, an iterative procedure is used to establish the sliding and adhering portions in the contact region. Numerical results for displacements and stresses are independently confirmed by the finite element analysis in conjunction with the minimum potential energy principle. In cases where the contact region is a function of the applied loading, or progressive contact, an incremental formulation is employed to describe the discretized contact stages. In the example of a frictionless contact between a long cylinder and a rigid base, good confirmation is obtained from Hertz's analytical solution. Criteria for taking one contact stage to another are also outlined for frictional progressive contact.

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