Geometrically nonlinear dynamic formulation for three-dimensional co-rotational solid elements

This study presents a three-dimensional nonlinear dynamic formulation based on a co-rotational (CR) approach for solid elements. The CR formulation is relatively efficient, but it is based on the assumption of small strains during large displacement. The novel idea of the present formulation involves the use of the CR formulation through a three-dimensional solid element for inertial quantities in addition to an internal force vector and a stiffness matrix. The present dynamic formulation is derived from Lagrange's equation of motion. In this procedure, the CR formulation, (i.e., element-independent CR) is one of the most attractive features that is strongly manifested in an efficient manner. Consequently, this obtains the governing equation of motion including motion-driven inertial components (physical quantities induced by the prescribed motion). Four examples are presented to demonstrate the accuracy of the present dynamic formulation. Finally, the results are compared with those obtained by ABAQUS, and the findings reveal that the proposed dynamic formulation is in good agreement with existing predictions.