The Beam-to-Beam Contact Smoothing with Bezier’s Curves and Hermite’s Polynomials

Abstract

This contribution concerns a key issue in numerical treatment of contact by the FEM, i.e. ensuring the C¹-continuity of contacting facets. After a discussion of basic issues of the frictional beam-to-beam contact two methods of curve construction – inscribed curve and node-preserving ones, are presented. Each of them is combined with a curve representation by Hermite’s polynomials and Bezier’s curves. In this way four possibilities of determination of a position vector for an arbitrary point on the curve are obtained. The resulting four different beam contact finite elements are briefly described. Then, on a base of this derivation and results of representative numerical examples, the elements are compared. To this end several criteria as: accuracy of curve approximation, number of degrees of freedom, code length, computer time and smoothing effectiveness, are used. The final conclusion is that despite the complicated, long code the inscribed curve method combined with the Hermite’s polynomials should be preferred.