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

This paper proposes the use of Jacobi polynomials to approximate higher-ordertheories of beam, plate, and shell structures. The Carrera unified formulation isused in this context to express displacement kinematics in a hierarchical form.In this manner, classical to complex higher-order theories can be implementedwith ease. Particular attention is focused on the attenuation and the correctionof the shear locking. Therefore, reduced integration as well as mixed interpo-lation of tensorial components methods are investigated against the new finiteelements. Several case studies are taken into account to highlight the effective-ness and robustness of the proposed approach. Also, several benchmarks areprovided for future assessments.