A finite element method for elasto‐plastic structures and contact problems by parametric quadratic programming

In this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non‐associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto‐plastic structures is constructed. A series of PQP formulae for contact problems and elastic‐plastic structures is derived in the text, and some numerical examples are illustrated as well.