Finite element methods for constrained problems in elasticity

Abstract

Abstract Several different variational formulations of boundary‐value problems with constraints are discussed, with particular reference to constrained problems in elasticity. Special attention is given to exterior penalty methods. A discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given. In particular, the use of reduced integration is discussed and criteria on the order of reduced integration rules sufficient to produce stable and convergent schemes are described. Applications of reduced integration‐penalty methods to incompressible elasticity problems and contact problems are described.