An analysis of an implicit finite element algorithm for geometrically nonlinear problems of structural dynamics part 1. Stability

A series of implicit finite element algorithms for the geometrically nonlinear structural dynamics problem are proposed. The proposed algorithms require only the solution of a linear system at each time step. Thus, they are computationally efficient. In addition, the algorithms are discrete conservation laws. The conservative nature of the proposed schemes has a positive effect in providing a stable approximation. The stability of the algorithms is analyzed using energy methods. One of the proposed computational methods is shown to be unconditionally stable.