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Keywords
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Penalty method, Lagrange coefficients, Elimination method, Finite element method, Necessary boundary conditions
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Abstract
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Finite element method (FEM) uses for solving engineering problems as a powerful tool. This method uses the matrix algebra method to analyze structures and it leads to analyses the changes of the structures. Numerical methods need applying boundary conditions (BCs) to have the ability to solve problems. In FEM, applying necessary BCs is essential in stiffness matrix. In this paper, besides to examining the equations and their discretization by the standard Galerkin method, introducing and comparing the methods of applying necessary BCs such as the Penalty method, Lagrange coefficients, Elimination and Extended elimination have been discussed. Also, for comparison of mentioned methods, the deformation of a two-dimensional beam with two degrees of freedom has been investigated and then the obtained results have been compared with the results of the existing analytical method. The results of this study show that the error in various methods of applying the necessary BCs is very low compared to the analytical method, and also the different methods have almost the same error. In addition, according to the characteristics of the methods, Elimination method, Extended elimination and Penalty method for applying normal boundary conditions and Lagrange method for applying conditional boundary conditions are suggested.
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