STABILITY AND CONVERGENCE OF A CLASS OF ENHANCED STRAIN METHODS

A stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity, which incorporates an enhanced strain field. The analysis is carried out for problems posed on polygonal domains in R(n), the finite element meshes of which are generated by affine maps from a master element. The formulation incorporates as a special case the classical method of incompatible modes. The problem initially has three variables, viz. displacement, stress, and enhanced strain, but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains. Two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent. Some features of nearly incompressible and incompressible problems are also investigated. For these cases it is possible to argue that locking will not occur, and that the only spurious pressures present are the so-called 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.