Optimization for Modeling of Nonlinear Interactions in Mechanics

G. E. Stavroulakis

ABSTRACT

General nonlinear interaction laws in mechanics can be expressed by means of monotone or nonmonotone, possibly multivalued, relations. Mathematical optimization provides a systematic and rigorous framework for modeling and numerical calculation of coupled field problems (for example, in fluid-structure or structure-foundation cases) with the above mentioned nonlinear interaction effects. The link is established through convex and nonconvex, in general nonsmooth, potential energy optimization. The optimality (respectively, critical point) conditions of the energy minimization problem are the governing relations of the mechanical model. A number of typical applications, including unilateral and adhesive contact modeling, are discussed in this article. Simple examples demonstrate the proposed approach. Hints for further applications, including the modeling of shape memory alloys of smart structures, and for efficient, parallel solution techniques are also included with appropriate references.