A new class of multilevel decomposition algorithms for non monotone problems based on the quasidifferentiability concept

Summarization: A convex, multilevel decomposition approach is proposed for the solution of static analysis problems involving non-monotone, possibly multivalued laws. The theory is developed here for model problems of structures having non-monotone interface or boundary conditions. First we decompose appropriately the non-monotone laws writing them as a difference of monotone constituents. In the general case, this is related to the quasidifferentiability concept. This permits us to obtain a system of convex variational inequalities, the solution s) of which describe the position s) of static equilibrium of the considered structure. Then the problems are formulated as min-min problems for appropriately defined Lagrangian functions. Convex optimization algorithms of various complexity are used in a multilevel scheme for the numerical solution of the considered structural analysis problem. Numerical results concerning the calculation of an elastic contact problem and an elastic stamp problem illustrate the theory.Παρουσιάστηκε στο: Computer methods in applied mechanics and engineerin