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Transient dynamic analysis of bars and trusses by the adaptive generalized finite element method

Leticia Col Debella (Department of Civil Engineering, Federal University of Parana, Curitiba, Brazil and Department of Civil Engineering, State University of Ponta Grossa, Ponta Grossa, Brazil)
Carolina Castro Cittadin (Department of Civil Engineering, Federal University of Parana, Curitiba, Brazil)
Marcos Arndt (Department of Civil Construction, Federal University of Parana, Curitiba, Brazil)
Roberto Dalledone Machado (Center for Civil Engineering Studies, Federal University of Parana, Curitiba, Brazil)

Engineering Computations

ISSN: 0264-4401

Article publication date: 4 September 2019

Issue publication date: 8 April 2020

Abstract

Purpose

This paper aims to present an adaptive approach of the generalized finite element method (GFEM) for transient dynamic analysis of bars and trusses. The adaptive GFEM, previously proposed for free vibration analysis, is used with the modal superposition method to obtain precise time-history responses.

Design/methodology/approach

The adaptive GFEM is applied to the transient analysis of bars and trusses. To increase the precision of the results and computational efficiency, the modal matrix is responsible for the decoupling of the dynamic equilibrium equations in the modal superposition method, which is used with only the presence of the problem’s most preponderant modes of vibration. These modes of vibration are identified by a proposed coefficient capable of indicating the influence of each mode on the transient response.

Findings

The proposed approach leads to more accurate results of displacement, velocity and acceleration when compared to the traditional finite element method.

Originality/value

In this paper, the application of the adaptive GFEM to the transient analysis of bars and trusses is presented for the first time. A methodology of identification of the preponderant modes to be retained in the modal matrix is proposed to improve the quality of the solution. The examples showed that the method has a strong potential to solve dynamic analysis problems, as the approach had already proved to be efficient in the modal analysis of different framed structures. A simple way to perform h-refinement of truss elements to obtain reference solutions for dynamic problems is also proposed.

Keywords

Citation

Col Debella, L., Cittadin, C.C., Arndt, M. and Machado, R.D. (2020), "Transient dynamic analysis of bars and trusses by the adaptive generalized finite element method", Engineering Computations, Vol. 37 No. 3, pp. 789-821. https://doi.org/10.1108/EC-10-2018-0451

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited