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.
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.
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.
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.
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.
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
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