Penalty Based Algorithms for Frictional Contact Problems
Tomme: LVII (LXI) Fascicle: 3 | 2011
Pages: 119-130
Abstract text:
The finite element method is a numerical method that can be successfully used to generate solutions for problems belonging to a vast array of engineering fields: stationary, transitory, linear or nonlinear problems. For the linear case, computing the solution to the given problem is a straightforward process, the displacements are obtained in a single step and all the other quantities are evaluated afterwards. When faced with a nonlinear problems, in this case with a contact nonlinearity, one needs to account for the fact that the stiffness matrix of the systems varies with the loading, the force vs. stiffness relation being unknown prior to the beginning of the analysis. Modern software using the finite element method to solve contact problems usually approaches such problems via two basic theories that, although different in their approaches, lead to the desired solutions. One of the theories is known as the penalty function method, and the other as the Lagrange multipliers method. The hereby paper briefly presents the two methods emphasizing the penalty based ones. The paper also underscores the influence of input parameters for the case of the two methods on the results when using the software ANSYS 12.
Key Words:
finite element method; pure penalty methods; Lagrange multipliers method; H-adaptive meshing.
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