Robust Implicit Dynamic Integration Procedure for Simulating Geometrically Nonlinear Responses of Spatial Structures

This study employs a robust implicit dynamic finite-element (FE) procedure with solid elements for simulating geometrically nonlinear responses of spatial structures. Based on the concept of equivalent nodal secant structural coefficients and the lumped-mass idealization, the incremental-iterative equations are decoupled for all degrees of freedom. Corotational coordinates with the rigid body rule are utilized to evaluate the internal nodal resisting and damping forces of 3D solid elements. In this study, a straightforward and precise method is proposed to predict the rigid-body rotation of 3D solid elements at each time step. Numerical results reveal that the proposed method can accurately determine the 3D rigid-body rotation, and that the proposed dynamic FE procedure is a more robust, accurate, and efficient approach for analyzing complicated structures under extreme loads compared with conventional dynamic FE procedures. This procedure can be applied to various engineering fields, especially earthquake engineering.