A General Procedure to Formulate 3D Elements for Finite Element Applications

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2023-10-03 DOI:10.3390/computation11100197

Adnan Shahriar, Arsalan Majlesi, Arturo Montoya

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引用次数: 0

Abstract

This paper presents a general procedure to formulate and implement 3D elements of arbitrary order in meshes with multiple element types. This procedure includes obtaining shape functions and integration quadrature and establishing an approach for checking the generated element’s compatibility with adjacent elements’ surfaces. This procedure was implemented in Matlab, using its symbolic and graphics toolbox, and complied as a GUI interface named ShapeGen3D to provide finite element users with a tool to tailor elements according to their analysis needs. ShapeGen3D also outputs files with the element formulation needed to enable users to implement the generated elements in other programming languages or through user elements in commercial finite element software. Currently, finite element (FE) users are limited to employing element formulation available in the literature, commercial software, or existing element libraries. Thus, the developed procedure implemented in ShapeGen3D offers FEM users the possibility to employ elements beyond those readily available. The procedure was tested by generating the formulation for a brick element, a brick transition element, and higher-order hexahedron and tetrahedron elements that can be used in a spectral finite element analysis. The formulation obtained for the 20-node element was in perfect agreement with the formulation available in the literature. In addition, the results showed that the interpolation condition was met for all the generated elements, which provides confidence in the implementation of the process. Researchers and educators can use this procedure to efficiently develop and illustrate three-dimensional elements.

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有限元应用中三维单元的通用程序

本文给出了在多种单元类型的网格中形成和实现任意顺序的三维单元的一般程序。该过程包括获得形状函数和积分正交，并建立了一种方法来检查生成的单元与相邻单元表面的兼容性。该程序在Matlab中使用Matlab的符号和图形工具箱实现，并编译成一个名为ShapeGen3D的GUI界面，为有限元用户提供一个根据分析需求定制元素的工具。ShapeGen3D还输出带有所需元素公式的文件，使用户能够在其他编程语言中或通过商业有限元软件中的用户元素实现生成的元素。目前，有限元(FE)用户仅限于使用文献、商业软件或现有元素库中可用的元素公式。因此，在ShapeGen3D中实现的开发程序为FEM用户提供了使用超出那些现成的元素的可能性。通过生成可用于谱有限元分析的砖单元、砖过渡单元以及高阶六面体和四面体单元的公式，对该程序进行了测试。所得的20节点单元公式与文献中的公式完全一致。结果表明，生成的各单元均满足插值条件，为该过程的实现提供了信心。研究人员和教育工作者可以使用这个程序来有效地开发和说明三维元素。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.