STABILITY AND CONVERGENCE OF A CLASS OF ENHANCED STRAIN METHODS

A stability and convergence analysis is presented of a recently propos ed variational formulation and finite element method for elasticity, w hich incorporates an enhanced strain field. The analysis is carried ou t for problems posed on polygonal domains in R(n), the finite element meshes of which are generated by affine maps from a master element. Th e formulation incorporates as a special case the classical method of i ncompatible modes. The problem initially has three variables, viz. dis placement, stress, and enhanced strain, but the stress is later elimin ated by imposing a condition of orthogonality with respect to the enha nced strains. Two other conditions on the choice of finite element spa ces ensure that the approximations are stable and convergent. Some fea tures of nearly incompressible and incompressible problems are also in vestigated. For these cases it is possible to argue that locking will not occur, and that the only spurious pressures present are the so-cal led checkerboard modes. It is shown that, as in the case of the Q(1) - P-0 element, the displacement and enhanced strain are convergent, and so is the pressure, after filtering out this mode.