An FE-MPEC approach for limit load evaluation in the presence of contact and displacement constraints

This paper describes a mathematical programing based approach for the direct limit load evaluation of a structural system under simultaneous contact and limited displacement conditions. The contact model we adopt can simulate either a classical unilateral (nonassociative) Coulomb friction situation or a cohesive fracture idealization at the potential discontinuity interface between contacting bodies. The discrete FE model is constructed using locking free mixed finite elements. The main feature and novelty of our proposed approach is to compute in a single step the maximum load capacity of the structure, such that both the imposed displacement limitations and the contact conditions are satisfied. In essence, the formulation is a nontrivial extension of classical limit analysis. The analysis is cast in its most natural form, namely in mixed static-kinematic variables, and leads to, what is known in the mathematical programing literature, as a mathematical program with equilibrium constraints or MPEC. A nonlinear programing (NLP) based algorithm is proposed to solve the MPEC. Two examples are provided to illustrate application of the proposed scheme, and some comments regarding the various advantages of the adopted mathematical programing framework are made.