An improved mixed finite element based on a modified least‐squares formulation for hyperelasticity
An improved mixed finite element based on a modified least‐squares formulation for hyperelasticity
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基于超弹性修正最小二乘公式的改进混合有限元
DOI：
10.1002/pamm.201410109
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
und B. Müller
中科院分区：
文献类型：
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作者：
A. Schwarz;K. Steeger;J. Schröder;G. Starke;und B. Müller
本文研究了用最小二乘有限元法（LSFEM）求解几何非线性弹性问题。主要目标是获得更好的性能和精确的近似，特别是对于低阶元素。混合单元的基础是由经典最小二乘法得到的一阶应力-位移公式。与施瓦茨等人[1]的思想类似，通过引入一个控制应力对称条件的附加项，导出了一个修正的弱形式。未知量的近似遵循与传统最小二乘法相同的程序，参见例如CAI & STARKE [2]。建议修改后的配方相比，最近开发的经典LSFEM，以显示性能和精度的提高。（© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
The present work deals with the solution of geometrically nonlinear elastic problems solved by the least‐squares finite element method (LSFEM). The main goal is to obtain an improved performance and an accurate approximation in particular for lower‐order elements. Basis for the mixed element is a first‐order stress‐displacement formulation resulting from a classical least‐squares method. Similar to the ideas in SCHWARZ ET AL. [1] a modified weak form is derived by the introduction of an additional term controlling the stress symmetry condition. The approximation of the unknowns follows the same procedures as for a conventional least‐squares method, see e.g. CAI & STARKE [2]. The proposed modified formulation is compared to recently developed classical LSFEMs, in order to show the improvement of performance and accuracy. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
基于不同超弹性模型的几何非线性LSFEM公式的比较
DOI：
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发表时间：
2013
期刊：
影响因子：
--
作者：
K. Steeger;A. Schwarz;J. Schröder;G. Starke;B. Müller
通讯作者：
B. Müller