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Computational and Programming Aspects of Transition Elements in a Three-dimensional Finite Element Program

机译：三维有限元程序中过渡元素的计算和编程方面

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The performance of any finite element (FE) structural analysis is directly related to the global number of nodes and degrees of freedom (DOF) of the discretized structure and mesh distribution attributes. It is obvious that the appropriate numerical analysis needs finer elements in the zone of interest, e.g. zone of high stress concentration and intensity, and coarser elements for farther portion of the structure. The transition element concept achieves this aim and with variable number of nodes of each element in the transition zone it creates coarser elements in the outward zones of the discretized structure. These elements have larger size with variable number of nodes per element and their number of nodes is between the number of nodes per elements of the inner and outer zones. In spite of the fact that the concept of transition element is not so new and dates back to the last few decades but to the authors' knowledge an obvious and clear programming strategy and the method of implementation in a FE program have not been depicted in particular in the related literature. In this study the main concept of transition element is completely presented with clear instances and the computational methodology of accounting for this subject is covered; then the programming strategy of the transition elements in a three-dimensional computer program of finite element method together with the related computer program parts in FORTRAN programming language are brought and finally a validating example is considered and the analogy between the results of the finite element program and analytical anticipation is made.
机译：任何有限元（FE）结构分析的性能都与节点的总数以及离散化结构的自由度（DOF）和网格分布属性直接相关。显然，适当的数值分析需要在感兴趣区域中使用更精细的元素，例如高应力集中和高强度的区域，以及结构较远部分的较粗单元。过渡元素的概念达到了这一目的，并且在过渡区域中每个元素的节点数量可变，因此在离散结构的向外区域中创建了较粗糙的元素。这些元素的大小较大，每个元素的节点数可变，并且它们的节点数在内部区域和外部区域的每个元素的节点数之间。尽管过渡元素的概念并不是那么新，可以追溯到过去的几十年，但是据作者所知，FE程序中没有明确而清晰的编程策略和实施方法。在相关文献中。在这项研究中，过渡元素的主要概念已通过清晰的实例得以完整呈现，并涵盖了该主题的会计计算方法;然后提出了有限元方法的三维计算机程序中过渡元素的编程策略，以及FORTRAN编程语言中的相关计算机程序部分，最后给出了一个验证实例，并对有限元程序的结果进行了类比并做出分析预期。

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