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.
Highlights
Since the early days of the finite element method era, many elements have been proposed for the analysis of thick plates bending
The findings of this study show that the triangular element They are a Triangular element (THT) with 7 Trefftz functions and the quadrangular element QHT with 11 Trefftz functions have the highest level of accuracy for plate analysis
Similar to the square plate case, the solutions obtained for THT and QHT elements, are close to exact answers when they are compared to other well-known elements
Summary
Since the early days of the finite element method era, many elements have been proposed for the analysis of thick plates bending. Polynomial functions have been used for displacement field in this technique, which do not satisfy the related governing differential equation. In this version of formulation, efficiency of the finite element is increased by enlarging the element’s degrees of freedom [8, 28]. Between years 1965 to 1975, researchers’ main concern was to achieve high accuracy by complex elements On this base, numerous elements with various specifications have been developed to analyze thin and thick plates bending. Accuracy and efficiency of these formulations are proven by utilizing several numerical tests
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