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

  • Thanh Xuan Nguyen Faculty of Building and Industrial Construction, Hanoi University of Civil Engineering, 55 Giai Phong road, Hai Ba Trung district, Hanoi, Vietnam
  • Long Tuan Tran Vietnamese - German Construction Vocational Training Centre, College of Urban Works Construction, Model House A13, Yen Thuong street, Gia Lam district, Hanoi, Vietnam
Keywords: variational formulation, finite element, time finite element, non-linear axial bar element, shape function, structural dynamics, accuracy

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.

Downloads

Download data is not yet available.
Published
31-10-2021
How to Cite
Nguyen, T. X., & Tran, L. T. (2021). A simplified variant of the time finite element methods based on the shape functions of an axial finite bar. Journal of Science and Technology in Civil Engineering (STCE) - HUCE, 15(4), 42-53. https://doi.org/10.31814/stce.huce(nuce)2021-15(4)-04
Section
Research Papers