GEOMETRICALLY NONLINEAR METHOD OF INCOMPATIBLE MODES IN APPLICATION TO FINITE ELASTICITY WITH INDEPENDENT ROTATIONS

We discuss a geometrically non-linear method of incompatible modes. Th e model problem chosen for the discussion is the finite elasticity wit h independent rotations. The conditions which ensure the convergence o f the method and the methodology to construct incompatible modes are p resented. A detailed derivation of variational equations and their lin earized form is given for a two-dimensional plane problem. A couple of geometrically non-linear two-dimensional elements with independent ro tational freedoms are proposed based on the presented methodology. The elements exhibit a very satisfying performance over a set of problems in finite elasticity.