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arXiv math/0312002math.NAcs.NA
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一种用于应变梯度相关损伤模型的不连续伽辽金公式

A discontinuous Galerkin formulation for a strain gradient-dependent damage model

G. N. Wells, K. Garikipati, L. Molari

AI总结:

本文提出一种不连续伽辽金公式,利用标准C0形函数求解应变梯度损伤模型,一维数值结果与基准解高度吻合,方法简洁且效果显著。

摘要:

应变梯度相关连续介质问题的数值求解一直受到基函数连续性要求的困扰。对于大多数普遍接受的模型,使用有限元方法求解需要形函数具有$C^{1}$连续性。本文探索并利用了不连续伽辽金方法的最新进展,用于求解一个典型的非线性应变梯度相关连续介质模型。我们开发了一种公式,使得使用标准$C^{0}$形函数能够严格求解应变梯度损伤模型。该公式在一维情况下进行了测试,采用了最简单的有限元公式:分段线性位移和(单元内)常数内变量。数值结果与基准解相比表现出色。鉴于所提公式的简洁性,这些结果令人瞩目。

英文摘要:

The numerical solution of strain gradient-dependent continuum problems has been dogged by continuity demands on the basis functions. For most commonly accepted models, solutions using the finite element method demand $C^{1}$ continuity of the shape functions. Here, recent development in discontinuous Galerkin methods are explored and exploited for the solution of a prototype nonlinear strain gradient dependent continuum model. A formulation is developed that allows the rigorous solution of a strain gradient damage model using standard $C^{0}$ shape functions. The formulation is tested in one-dimension for the simplest possible finite element formulation: piecewise linear displacement and constant (on elements) internal variable. Numerical results are shown to compare excellently with a benchmark solution. The results are remarkable given the simplicity of the proposed formulation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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