Orthogonal basic deformation mode method for zero-energy mode suppression of hyb

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mv#I/n[?_Q.r$D0Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

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Z#_ PbZ9L-K0Abstract:A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The resulting orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. Moreover, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.

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~0ei$aJ u%y o |0Can-hui ZHANG Dong-dong WANG Tong-shan LI Qian HUANG水利论文1k.kP4b*gEW&|

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Department of Civil Engineering, Xiamen University, Xiamen 361005, Fujian Province, P.R.China水利论文{d4zk8O|hgNEC

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期 刊:水利论文~-S5@/q4m

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应用数学和力学(英文版)水利论文I Z8uqZo+g y

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;[B;C:k'^,\ pH0APPLIED MATHEMATICS AND MECHANICS水利论文kKdq0~

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wx-E;O-a(kO?h02011, 32(1)水利论文5f[6o-NH7a

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分类号:

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(N!]-` i#RBwf0hybrid stress element水利论文T#V;rTh

:[L+uU(l0sa)NP0basic deformation mode水利论文 x@ p%m@{*y4D

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assumed stress mode水利论文#c ? t0j#N7Z2Q g

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mode orthogonality水利论文:g+Q&N9z@v @"w

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suppression of zero-energy deformation mode

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(an2G"bi0quadrilateral elements initial stress positive definiteness necessary condition material parameters hybrid element identification of finite elements relationship performance method of different physical approach addition examine simple found based set水利论文_-E,\`!Z5sR"[

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the National Natural Science Foundation of China,the Fundamental Research Funds for the Central Universities of China,the Scientific Program of Fujian Province of China

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