An enhanced single Gaussian point continuum finite element formulation using automatic differentiation

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design Pub Date : 2025-02-19 DOI:10.1016/j.finel.2025.104329

Njomza Pacolli , Ahmad Awad , Jannick Kehls , Bjorn Sauren , Sven Klinkel , Stefanie Reese , Hagen Holthusen

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引用次数: 0

Abstract

This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the inverse Jacobian. To this end, AD tools automate the computation and allow a direct evaluation of the inverse Jacobian, bypassing the need for a Taylor series expansion. Thus, the enhanced version, Q1STc+, is introduced. Numerical examples are conducted to compare the performance of both element formulations for finite strain applications, with particular focus on distorted meshes. Moreover, the performance of the new element formulation for an elasto-plastic material is investigated. To validate the obtained results, a volumetric locking-free element based on scaled boundary parametrization is used. Both the implementation of the element routine Q1STc+ and the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.14259791.

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本文提出了一种改进的低阶三维有限元计算方法，利用自动微分法（AD）实现沙漏稳定。在这里，前 Q1STc 公式通过无近似计算逆 Jacobian 得到了增强。为此，自动微分工具实现了计算自动化，并允许直接评估逆雅各比，而无需泰勒级数展开。因此，引入了增强版 Q1STc+。通过数值示例，比较了两种元素公式在有限应变应用中的性能，尤其侧重于扭曲网格。此外，还研究了弹塑性材料的新元素公式的性能。为了验证所获得的结果，使用了基于比例边界参数化的体积无锁定元素。元素例程 Q1STc+ 的实现和相应的材料子例程均可通过 https://doi.org/10.5281/zenodo.14259791 公开获取。

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

Finite Elements in Analysis and Design 工程技术-力学

CiteScore

4.80

自引率

3.20%

发文量

审稿时长

27 days

期刊介绍： The aim of this journal is to provide ideas and information involving the use of the finite element method and its variants, both in scientific inquiry and in professional practice. The scope is intentionally broad, encompassing use of the finite element method in engineering as well as the pure and applied sciences. The emphasis of the journal will be the development and use of numerical procedures to solve practical problems, although contributions relating to the mathematical and theoretical foundations and computer implementation of numerical methods are likewise welcomed. Review articles presenting unbiased and comprehensive reviews of state-of-the-art topics will also be accommodated.