Contact Problems in Industrial Applications Using FreeFEM

Abstract

This paper presents an algorithm and a method to solve mechanical contact problems between two bodies or more, for linear elastic and finite deformation problems. The contact problem is considered as an optimization one, more specifically as a minimization problem. The interior point method is used to solve the minimization problem. This algorithm is symmetric and the user does not need to specify anymore a slave and a master body. The algorithm was developed using FreeFEM and IPOPT software.

Regularized frictional contact problems with the interior point method

“…xl is the projection point of x on the body Ω l h , where l = 1, 2 and n is the outward unit normal vector at xl . Note that the two constraints in the problem (167) describe the non-penetration in a weak sense, and it is a symmetric formulation, in other words the user does not need to specify anymore a slave and a master body, see [16] for details. φ (l) i are the shape functions on the n Cl nodes of the contact area Γ Cl .…”

“…In addition the non-penetration constraints are imposed in a symmetrical manner, in other words, non-penetration constraints are prescribed on the slave body to forbid the penetration of the latter into the master one, in addition to non-penetration constraints which are prescribed on the master body to forbid the penetration of the latter into the slave one. Generally, the symmetrical non-penetration constraints can be redundant or linearly dependent therefore numerical difficulties can be generated, we can see in [16] how these numerical difficulties are avoided when using the interior point method. In short, we have two loops, the exterior one is for the Tresca problems and the interior one is for the non-linearity of the constraints in the finite deformation case.…”