Explicit Fiber Beam-Column Elements for Impact Analysis of Structures

Abstract

The solution of impact problems requires advanced computational techniques to overcome the difficulties associated with large short-duration loads. Such cases typically use the explicit time integration method because it provides a stable solution for problems such as the analysis of structures subjected to shock and impact loads. However, most explicit-based finite elements were developed for continuum models such as membrane and solid elements, which renders the problem computationally expensive. On the other hand, the development of fiber-based beam finite elements allows for the simulation of the global structural behavior with very few degrees of freedom, while accounting for the detailed material nonlinearity along the element length. However, explicit-based fiber beam elements have not been properly formulated, in particular for the case of the emerging force-based beam element. This paper develops two fiber plane beam elements that consider an explicit time integration scheme for the solution of the dynamic equation of motion. The first element uses a displacement-based formulation, whereas the second element uses a force-based formulation. For the latter case, a new algorithm that eliminates the need for iterations at the element level is proposed. The developed elements require the use of a lumped mass matrix and a small time increment to ensure numerical stability. No iterations or convergence checks are required, which renders the problem numerically efficient. The developed explicit fiber beam-column models, particularly the force-based element, represent a simple yet powerful tool for simulating the nonlinear complex effect of impact loads on structures accurately while using very few finite elements. The traditional implicit method of analysis typically fails to provide numerically stable behavior for such short-duration problems. Two correlation studies are presented to highlight the efficiency of the developed elements in modeling impact problems in which the material models consider the strain rate effect. These examples confirm the accuracy and efficiency of the presented elements.