Finite element analysis of compressible transversely isotropic hyperelastic shells

Abstract

The focus of the current work is on the large deformation analysis of shells made of a transversely isotropic material. For this purpose, a higher-order shell model is adopted and strains are derived and subsequently the stress field of a hyperelastic medium is extracted. Then, by taking advantage of the principle of virtual work, the so-called weak form is obtained. A four-node shell element is developed enriched by remedies for alleviation of locking incorporating transverse shear, membrane and curvature-thickness locking for a compressible anisotropic medium. Finally, some examples are addressed to show the performance of the proposed element as well as anisotropy effects. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.