A simplified variant of the time finite element methods based on the shape functions of an axial finite bar

Abstract

In the field of structural dynamics, the structural responses in the time domain are of major concern. There already exist many methods proposed previously including widely used direct time integration methods such as ones in the β-Newmark family, Houbolt’s method, and Runge-Kutta method. The time finite element methods (TFEM) that followed the well-posed variational statement for structural dynamics are found to bring about a superior accuracy even with large time steps (element sizes), when compared with the results from methods mentioned above. Some high-order time finite elements were derived with the procedure analogous to the conventional finite element methods. In the formulation of these time finite elements, the shape functions are like the ones for a (spatial) 2-order finite beam. In this article, a simplified variant for the TFEM is proposed where the shape functions similar to the ones for a (spatial) axial bar are used. The accuracy in the obtained results of some numerical examples is found to be comparable with the accuracy in the previous results.