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首页> 外文会议>Proceedings of the Fifteenth international conference on civil, structural and environmental engineering computing >Geometric and Material Non-Linear Formulation for Three-Dimensional Solids with the Positional Finite Element Method
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Geometric and Material Non-Linear Formulation for Three-Dimensional Solids with the Positional Finite Element Method

机译：用位置有限元方法对三维实体进行几何和材料非线性表示

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摘要

This paper presents a new nonlinear formulation taking into account both geometric and material nonlinear behaviour in tri-dimensional solids. The nonlinear geometric solution, the so called position finite element method, is based in positions instead of displacements (as usual in the literature). This approach has been published in many papers since 2003, including the solid formulation for elastic linear materials in static and dynamic analysis. Here in this paper, the nonlinear material formulation considers the Drucker-Prager criterion. In addition, moderated high order finite elements are used to avoiding locking. For three-dimensional problems an isoperimetric tetrahedron with cubic approximation for positions is adopted. Furthermore, the Newton-Raphson procedure is applied for the nonlinear response. Some examples are explored to show the versatility and accuracy of the proposed procedure.
机译：本文提出了一种新的非线性公式，其中考虑了三维实体中的几何和材料非线性行为。非线性几何解决方案，即所谓的位置有限元方法，是基于位置而不是位移（如文献中通常的那样）。自2003年以来，这种方法已在许多论文中发表，包括用于静态和动态分析的弹性线性材料的固体配方。在本文中，非线性材料公式考虑了Drucker-Prager准则。另外，使用适度的高阶有限元来避免锁定。对于三维问题，采用等距四面体，其位置近似为三次方。此外，将牛顿-拉夫森程序用于非线性响应。探索了一些示例以显示所提出程序的多功能性和准确性。

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