The directional instability problem in systems with frictional contacts

The research summarized in this paper addresses the directional instability of finite dimensional systems with unilateral frictional contacts. Conditions for the occurrence of this divergence type instability are discussed, complementarity formulations are developed, and numerical procedures are proposed for the solution of the corresponding non-smooth stability eigenproblems. Various examples are analytically or numerically solved and discussed, namely some finite element examples that have instability modes involving evolution towards slip or stick in different portions of the contact surface.http://www.sciencedirect.com/science/article/B6V29-4B2CKPM-3/1/73c607a92e3ae8a3ac0468429856b8d

A nonsmooth algorithm for cone-constrained eigenvalue problems

International audienceWe study several variants of a nonsmooth Newton-type algorithm for solving an eigenvalue problem of the form $K\ni x \bot(Ax−Bx)\in K^+$. Such an eigenvalue problem arises in mechanics and in other areas of applied mathematics. The symbol $K$ refers to a closed convex cone in the Euclidean space $ℝ^n$ and $(A,B)$ is a pair of possibly asymmetric matrices of order $n$. Special attention is paid to the case in which $K$ is the nonnegative orthant of $ℝ^n$. The more general case of a possibly unpointed polyhedral convex cone is also discussed in detail

Cone-constrained eigenvalue problems: theory and algorithms

Complementarity conditions, Generalized eigenvalue problems, Convex cones,