Hybrid‐Trefftz stress elements for plate bending

Abstract

Summary The hybrid‐Trefftz stress element is used to emulate conventional finite elements for analysis of Kirchhoff and Mindlin‐Reissner plate bending problems. The element is hybrid because it is based on the independent approximation of the stress‐resultant and boundary displacement fields. The Trefftz variant is consequent on the use of the formal solutions of the governing Lagrange equation to approximate the stress‐resultant field. In order to emulate conventional elements, nodal functions are used to approximate the displacements on the boundary of the element. Duality is used to set up the element solving system. The associated variational statements and conditions for existence and uniqueness of solutions are recovered. Triangular and quadrilateral elements are tested and characterized in terms of convergence, sensitivity to shear‐locking, and shape distortion. Their relative performance is assessed using assumed strain Mixed Interpolation of Tensorial Components (MITC) elements and recently proposed Trefftz‐based elements. This relative assessment is extended to a hypersingular problem to illustrate the effect of enriching the domain and boundary approximation bases.

An efficient isostatic mixed shell element for coarse mesh solution

“…Consequently, the resulting formulation allows accurate and efficient numerical solution to be obtained. In this regards, notable contributions are the hybrid Trefftz element for Mindlin-Reissner plates proposed by Cen et al, 23 the hybrid plates by Teixeira de Freitas and Tiago, 24 the plate and shell elements by Martins et al 25 and the FE for bending analysis by Rezaiee-Pajand and Karkon. 26,27 The Trefftz method has also been used by Horak et al 28 within isogeometric formulations.…”