Searching for Local Contact Constraints by the Quasi-Newton Methods in the Finite Element Procedures for Contact-Impact Problems

Abstract eng:
The essential part of the solution of a contact problem in the finite element method is to locate probable contact areas reliably and efficiently. Most contact searching algorithms are based on the definition of master and slave contact surfaces, when the slave nodes/integration points are checked on against master segments for penetration. The present paper deals with the local search problem which comprises the calculation of the exact position of the slave node/integration point with respect to a given master segment. Since the analytical solution for finding the distance does not exist for a general quadrilateral contact segment, the iterative numerical procedure is solved. Several methods for the solution of non-linear algebraic systems are tested: the Newton-Raphson procedure, the least square projection, the steepest descent method, Broydens method, BFGS method, DFP method and the simplex method. The effectiveness of methods is tested by means of a contact-impact problem of two colliding thick plates, for which analytical solution is available.

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