Purpose

The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations.

Design/methodology/approach

An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments.

Findings

The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted.

Originality/value

This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

中文翻译：

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广义有限元法进行几何非线性分析

目的

本文的目的是在几何非线性分析的背景下评估广义有限元方法（GFEM）的功能。这种分析所特有的大位移和变形的影响会引起单元网格的严重变形，从而不利于标准有限元方法逼近的质量。这里的主要关注点是确定在总的和更新的拉格朗日公式下如何使用GFEM的富集策略，该策略通常会使该方法不易受到网格变形的影响。

设计/方法/方法

现有的允许线性和非线性分析的计算环境已用于通过GFEM使用不同的多项式充实来实现具有几何非线性的分析。

发现

在GFEM中考虑了使用总拉格朗日公式和最新拉格朗日公式的几何非线性分析。对经典问题进行了数值模拟，并突出了GFEM的准确性和鲁棒性。

创意/价值

这项研究显示了有关使用完整多项式空间进行GFEM分析的新颖研究，以丰富采用总的和更新的拉格朗日公式的几何非线性分析的近似值。在总拉格朗日公式的情况下，这种策略保证了较高的网格变形分析的高精度。另一方面，在更新的拉格朗日方法中，在增量和迭代解中更新自由度的需求在此首次被识别和讨论。