An improved implicit method with dissipation control capability: The simple generalized composite time integration algorithm

In this paper, a simple and accurate implicit composite time integration scheme is newly developed for more efficient transient analyses of structural problems. The new scheme does not require the acceleration vector of the previous time step, and the initial acceleration vector is not needed, either. As a result, the factorization of the mass matrix is unnecessary, while factorizations of the effective coefficient matrix are still needed. Besides, the new method is designed to possess controllable algorithmic dissipation. Despite the absence of the acceleration vector of the previous time step, the numerical performance of the new method is equivalent to those of the existing methods. The excitation of an elastic bar problem and the simple nonlinear pendulum problem are numerically analyzed for the test of the new scheme. In the numerical experiments, the effects of consistent and lumped mass matrices are also discussed.