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Numerical resolution of cone-constrained eigenvalue problems
Pinto da Costa,A.; Seeger,AlbertoGiven a convex cone K and matrices A and B, one wishes to find a scalar λ and a nonzero vector x satisfying the complementarity system K ∋ x ⊥(Ax-λ Bx) ∈ K+. This problem arises in mechanics and in other areas of applied mathematics. Two numerical techniques for solving such kind of cone-constrained eigenvalue problem are discussed, namely, the Power Iteration Method and the Scaling ...
The directional instability problem in systems with frictional contacts
Pinto da Costa, A.; Martins, J. A. C.; Figueiredo, I. N.; Júdice, J. J.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 ...
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