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The present paper describes four kinds of methods to enforce essential boundary conditions in conjunction with the stress analysis method, which utilizes structured cells and boundary segments to discretize the weak-formed governing equations and the related boundary conditions . The proposed methods for enforcement of essential boundary conditions include the method using multipoint constraint, the Lagrange multiplier method, the penalty function method and the direct method discretizing the modified variational principle. The aspects of the implementation of these methods are outlined and the analyses of two-dimensional elastic problems having small deformation are performed.The calculated results are compared with the theoretical and conventional FEM results to illustrate the accuracy.

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