Explicit Time Step Partitioning in Nonlinear Transient Dynamics

Abstract

This paper presents a technique for spatial partitioning of the time increment in the explicit central-difference time integration scheme commonly used for finite-element modeling of fast transient dynamic phenomena. The time increment varies not only in time, as is usual to account for mesh distortion and for evolution of material properties, but also in space at the finite element level following local stability limitations rather than global ones. This may lead to substantial savings of computer time whenever the material properties that govern wave propagation speed and/or the mesh size are largely non-uniform in the numeri-cal model, as is typical of many large industrial applications, especially in 3D, and even more so in the presence of fluid-structure interactions. The proposed partitioning algorithm, which is completely automatic and does not require any specific input data, may be applied in principle to all types of elements and material models. As shown by numerical examples, it preserves the outstanding numerical properties i.e. the renowned accuracy and robustness—of the classical uniform-step explicit time integration scheme, of which it may be considered a powerful generalization. Once fully implemented and validated in a general explicit computer code, the present tech-nique has the potential for freeing the engineer from the main limitation of explicit analysis, usually related through stability requirements to the size of the smallest element. In fact, the computational mesh may be locally refined virtually at will without the usual prohibitive ef-fects on computational costs. This might open the way to applications which are simply out of reach with the classical algorithms. The present paper first introduces the basic spatial partitioning technique within a Lagran-gian formulation. Then it briefly outlines the treatment of boundary conditions and the exten-sion to fluids via an Arbitrary Lagrangian Eulerian formulation. Finally, some numerical examples are presented.