Two efficient hybrid-trefftz elements for plate bending analysis

Abstract

This study is devoted to the analysis of the Reissner-Mindlin plate bending. In this paper, the hybrid-Trefftz strategy will be utilized. Two novel and efficient elements are formulated in details. They are a Triangular element (THT) and a quadrilateral element (QHT), which have 9 and 12 degrees of freedom, respectively. In this approach, two independent displacement fields are defined; one within the element and the other on the edges of the element. The internal field is selected in such a manner that the governing equation of thick plates could be satisfied. Boundary field is related to the nodal degree of freedoms by the boundary interpolation functions. To calculate these functions, the edges of the element are assumed to behave like a Timoshenko beam. The high accuracy and efficiency of the proposed elements and absence of the shear locking in these formulations are all proven, using various numerical tests.

A novel smart hybrid‐Trefftz finite element for smart laminated composite plates

“…In order to establish the link between the neighboring elements, auxiliary interelement displacement fields, which are similar in form but not identical to the internal fields, are considered at the boundaries of the element assuming that each such boundary is a fictitious interelement and relating these auxiliary fields with the unknown constants of the internal fields, the continuity between the elements is enforced. Since its inception, the HTFE method has been successfully applied to various solid mechanics problems . Since the exact solutions of the governing equations of the element domain are derived a priori to form the Trefftz functions, the HTFE is highly convergent and locking free .…”

Computational aspects of the combined finite‐discrete element method in static and dynamic analysis of shell structures

“…As wellknown, the finite element method (FEM) is the most commonly used numerical tool in shell analysis, which is based on triangular, rectangular or quadrilateral finite elements [2][3][4]. An unrealistically stiff behaviour of shells in the first finite element method applications (the so-called shear locking phenomenon) called for a development of conforming finite elements and later for introduction of hybrid, mixed, and rotation-free elements [5][6][7][8][9][10][11][12]. It should be noted that the dynamic behaviour of shells under large displacements is still a subject of research [13,14].…”

Three dimensional hybrid‐Trefftz stress finite elements for plates and shells

“…In view of the fact that thin plates and shell structures are close to a plane state of stress, increasing the order of the stress and displacement bases in the direction normal to the average surface represents a misuse of the computational resource. Nodal triangular and quadrilateral hybrid‐Trefftz elements for thin and thick plates have been introduced by Rezaiee‐Pajand et al The elements are based on the homogeneous and particular solution of Kirchhoff and Reissner‐Mindlin theory. The set of solutions is described in terms of complex variables introduced by Herrera .…”

“…The set of solutions is described in terms of complex variables introduced by Herrera . The boundary displacement shape functions at the edges are related to the nodal degrees of freedom for 3‐node Euler‐Bernoulli beam and Timoshenko Beam theory . In the present work, we propose addressing the plate and shell structural problems by using a 3‐dimensional theory base on the Papkovith‐Neuber solution for isotropic materials where the proposed stress element is formulated in terms of generalized variables instead of nodes.…”