Two-Step Unconditionally Stable Noniterative Dissipative Displacement Method for Analysis of Nonlinear Structural Dynamics Problems

Abstract

When solving structural dynamic problems, the displacement algorithm needs only calculating and storing structure’s displacements in the main calculation process, which makes the displacement algorithm have advantages over multivariable algorithms in calculation efficiency and storage requirements. By using a novel approach based on dimensional analysis firstly given by the first author, a one-parameter family of two-step unconditionally stable noniterative displacement algorithms, referred to as the CQ-2x method, is developed. Compared with other unconditionally stable noniterative multivariable algorithms such as the representative KR- $\alpha$ method, the proposed method has advantages in several aspects. The CQ-2x method is unconditionally stable regardless of stiffness hardening or stiffness weakening, while the KR- $\alpha$ method is only conditionally stable in case of stiffness hardening. The CQ-2x method needs only one solver within one time step, while the KR- $\alpha$ method needs two solvers within one time step, which makes the CQ-2x method show higher efficiency. Numerical examples are presented to demonstrate the potential of the proposed method.