Non‐iterative time integration scheme for non‐linear dynamic FEM analysis

Abstract

AbstractThis paper proposes a non‐iterative time integration (NITI) scheme for non‐linear dynamic FEM analysis. The NITI scheme is constructed by combining explicit and implicit schemes, taking advantage of their merits, and enables stable computation without an iteration process for convergence even when used for non‐linear dynamic problems. Formulation of the NITI scheme is presented and its stability is studied. Although the NITI scheme is not unconditionally stable when applied to non‐linear problems, it is stable in most cases unless stiffness hardening occurs or the problem has a large velocity‐dependent term.The NITI scheme is applied to dynamic analysis of the non‐linear soil–structure system and computation results are compared with those by the central difference method (CDM). Comparison shows that the stability of the NITI scheme is superior to that of the CDM. Accuracy of the NITI scheme is verified because its results are identical with those by the CDM in which the time step is set as 1/10 of that for the NITI scheme. The application of the NITI scheme to the mesh‐partitioned FEM is also proposed. It is applied to dynamic analysis of the linear soil–structure system. It yields the same results as a conventional single‐domain FEM analysis using the Newmark β method. This result verifies the usability of mesh‐partitioned FEM analysis using the NITI scheme. Copyright © 2003 John Wiley& Sons, Ltd.