Finite elements based on Jacobi shape functions for the analysis of beams, plates and shells

Abstract

AbstractThis paper proposes the use of Jacobi polynomials to approximate higher‐order theories of beam, plate, and shell structures. The Carrera unified formulation is used in this context to express displacement kinematics in a hierarchical form. In this manner, classical to complex higher‐order theories can be implemented with ease. Particular attention is focused on the attenuation and the correction of the shear locking. Therefore, reduced integration as well as mixed interpolation of tensorial components methods are investigated against the new finite elements. Several case studies are taken into account to highlight the effectiveness and robustness of the proposed approach. Also, several benchmarks are provided for future assessments.