Comparative assessments of strain measures for nonlinear analysis of truss structures at large deformations
ISSN: 0264-4401
Article publication date: 19 November 2021
Issue publication date: 3 May 2022
Abstract
Purpose
In this paper the use of classical strain measures in analysis of trusses at finite deformations will be discussed. The results will be compared to the ones acquired using a novel strain measure based on the Hyperbolic Sine function. Through the evaluation of results, algebraic development and graph analysis, the properties of the Hyperbolic Sine strain measure will be examined.
Design/methodology/approach
Through graph plotting, comparisons between the novel strain measure and the classic ones will be made. The formulae for the implementation of the Hyperbolic Sine strain measure into a positional finite element method are developed. Four engineering applications are presented and comparisons between results obtained using all strain measures studied are made.
Findings
The proposed strain measure, Hyperbolic Sine, has objectivity and symmetry. The linear constitutive model formed by the Hyperbolic Sine strain and its conjugated stress presents an increasing stiffness, both in compression and tension, a behavior that can be useful in the modeling of several materials.
Research limitations/implications
The structural analysis performed on the four examples of trusses in this article did not consider the variation of the cross-sectional area of the elements or the buckling phenomenon, moreover, only elastic behavior is considered.
Originality/value
The present article proposes the use of a novel strain measure family, based on the Hyperbolic Sine function and suitable for structural applications. Mathematical expressions for the use of the Hyperbolic Sine strain measure are established following the energetic concepts of the positional formulation of the finite element method.
Keywords
Acknowledgements
The authors would like to thank the support from Fundação de Amparo á Pesquisa do Estado de Minas Gerais (FAPEMIG) [grant numbers TEC-PPM-00409-16, TEC-PPM-00444-18] and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant numbers 405183/2018-6, 302597/2019-0].
Citation
Greco, M. and Peixoto, D.H.N. (2022), "Comparative assessments of strain measures for nonlinear analysis of truss structures at large deformations", Engineering Computations, Vol. 39 No. 5, pp. 1621-1641. https://doi.org/10.1108/EC-01-2021-0056
Publisher
:Emerald Publishing Limited
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