Unconditionally Stable Explicit Displacement Method for Analyzing Nonlinear Structural Dynamics Problems

Abstract

This paper introduces a novel approach based on dimensional analysis for designing explicit displacement algorithms for use in analyzing nonlinear structural dynamics problems. Using this approach, a one-parameter family of three-step unconditionally stable explicit displacement algorithms with controllable numerical energy dissipation, the CQ-3 method, is developed. The proposed method is promising for solving nonlinear structural dynamics problems with its properties of unconditional stability; explicit formulations of both displacement and velocity; controllable numerical dissipation; second-order time accuracy for displacement, velocity, and acceleration; one solver within one time step; and no overshoot for both displacement and velocity. Numerical examples are presented to demonstrate the potential of the proposed method.