Application of methods for unconstrained optimization in computation of normal contact vector

Abstract eng:
The stability of the contact algorithm is significantly influenced by the local contact search procedure, which consists in the determination of the exact position of the slave node or integration point with respect to a given master segment. For a general quadrilateral contact segment it leads to the numerical solution of minimization problem. In this paper, various method like the Newton-Raphson, the quasi-Newton, the gradient methods and the simplex method for finding the local and global minimizers of this problem are presented. The attention is focused on the the line-search technique which is crucial for a general success of the quasiNewton and the gradient methods. The effectiveness of methods is tested by means of numerical example, which involves bending of two rectangular plates over a cylinder.

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