Efficiency Study of Implicit and Explicit Time Integration Operators for Finite Element Applications

Direct integration techniques (step-by-step) are widely used for the time integration of discretized equations of motion that result from applying numerical techniques such as the finite element method to structural dynamic problems. In this study, the Newmark Beta-Method is examined for stability, accuracy, and efficiency, wherein Beta = 0 provides an explicit algorithm, while Beta - 0 provides an implicit algorithm. Both algorithms are used in the same finite element program to solve a soil-structure boundary value problem composed of a cylindrical steel sheel encased in a relatively soft rock-like material and subjected to a surface blast loading. The implicit method was significantly more efficient as measured by computer time. For nonlinear systems, the two methods were approximately equivalent in efficiency. A combined explicit-implicit integration technique is proposed that employs explicit integration in the soft material and implicit integration in the stiff material with a potential increase in efficiency by an order of magnitude over either method applied individually.