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Improving the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems

Qing Xie (School of Highway, Chang’an University, Xi’an, China)
Yucai Hu (CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, China)
Yexin Zhou (Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, China)
Wanshui Han (School of Highway, Chang’an University, Xi’an, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 8 July 2019

Abstract

Purpose

Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.

Design/methodology/approach

A four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.

Findings

Numerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.

Originality/value

This paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.

Keywords

Acknowledgements

The authors acknowledge the support of Natural Science Foundation of Shaanxi Province (2018JQ5031), Natural Science Foundation of Jiangsu Province (BK20150479) and Jiangsu Natural Science Foundation for Universities and Colleges (15KJB130002). The authors would like to acknowledge Prof K.Y. Sze from the University of Hong Kong for the insightful suggestions during the preparation and revision of this paper.

Citation

Xie, Q., Hu, Y., Zhou, Y. and Han, W. (2019), "Improving the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems", Engineering Computations, Vol. 36 No. 6, pp. 1950-1976. https://doi.org/10.1108/EC-08-2018-0380

Publisher

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Emerald Publishing Limited

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