ITERATION SOLUTION OF THE MIXED FORMULATION IN NONLINEAR FEM

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ITERATION SOLUTION OF THE MIXED FORMULATION IN NONLINEAR FEM

Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. However, the penalty has tobe chosen properly. If it is too large, the matrix equation may become ill-conditioned. Onthe other hand, the matrix equation may give incorrect answer if the penalty is too small.In non-linear regime, the difficulty is more serious because the magnitude order of the matrix varies considerably in the entire loading history. The paper suggests an iteration solution and applies it to non-linear FEM of rubber-like hyper-elasticity. This type of analysisis highly non-linear both in physics and in geometry as well as the strong constraint of incompressibility. The iteration solution is demonstrated to possess super precision and excellent convergence characteristics.