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

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.

Hexahedral finite elements with enhanced fixed‐pole interpolation for linear static and vibration analysis of 3D micropolar continuum

“…Grbčić et al 20 proposed a first‐order hexahedral finite element enhanced with incompatible modes, which considerably reduced the computational cost. Moreover, while Grbčić et al 21,22 developed triangular and quadrilateral finite elements for linear micropolar continuum theory using linked interpolation, Xie et al 23 proposed a hybrid FE formulation to improve the bending response of four‐node quadrilateral and eight‐node hexahedral for Cosserat elasticity problems without compromising the constant couple‐stress path test.…”