The solution of large displacement frictionless contact problems using a sequence of linear complementarity problems

Abstract

SUMMARYA Newton method for solution of frictionless contact problems is presented. A finite element discretization is performed and the contact constraints are given as complementarity conditions. The resulting equations, which represent the equilibrium of the system, are formulated as a generalized equation. Generalized equations, from the discipline of Mathematical Programming, are a way of writing multi-valued relations, such as complementarity conditions, in a way that is similar to ordinary equations. Newton's method is then used, in a straightforward way, to solve the present non-linear generalized equation, resulting in a sequence of Linear Complementarity Problems (LCP's).

Frictional instabilities in orthotropic hollow cylinders

“…Klarbring and Björkman [4,13,15] had already considered the effect of curvature in the tangent stiffness matrix for the purpose of computing equilibrium states or for analyzing the stability of frictionless equilibrium states. Notice that, due to the change of variables (27), the variables of problem (28)-(30) belong to cones with a much simpler structure than the cones defined by (25,26).…”

Engineering and Economic Applications of Complementarity Problems

“…Solution methods for such problems were based on quadratic programming formulations. Recent references on these problems include [3,16,17,91,92]. Contact problems with Coulomb friction have been treated extensively by Klarbring and his colleagues [18,82,90,93,94,95,96,97] as well as in [4,108,109,111,115,116,145,187,191].…”

Finite-Dimensional Variational Inequalities and Complementarity Problems

“…This proposal leads to the B-differentiable Newton method for solving the NCP (F ); see Example 7.2.16. Led by Klarbring, this group at Linköping University pioneered the use of the Josephy-Newton SLCP method [57,326,328,329] and is at the forefront of using nonsmooth Newton methods for solving contact problems [290,291]. Led by Klarbring, this group at Linköping University pioneered the use of the Josephy-Newton SLCP method [57,326,328,329] and is at the forefront of using nonsmooth Newton methods for solving contact problems [290,291].…”