SYMBOLIC ALGEBRA AND THEOREM PROVING FOR FAILURE CRITERIA REDUCTION

机译：减少故障准则的符号代数和定理证明

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The present paper reports on recent efforts of utilizing symbolic computing for identifying failure criteria cross reducibility from the perspective of theorem proving. Utilizing equational theorem proving algorithms and Grobner Basis polynomial theorem provers implemented in Mathematica we have proven a number of interesting theorems related to the area of structural failure criteria for anisotropic and particularly orthotropic materials. The main contribution of this work is the demonstration of the tremendous utility of symbolic algebra for engineering applications as well as the demonstration of the idea that all failure criteria presented in the literature up to know can be proven under certain conditions to be special forms of general criteria relating to the strain energy density function associated with material continua. Two specific examples are presented and discussed along with a theorem proving the existence of a dual form of all stress space based criteria to equivalent one expressed in strain space.

机译：本文从定理证明的角度报道了利用符号计算来识别交叉可简化性的失效准则的最新成果。利用在Mathematica中实现的方程式定理证明算法和Grobner基多项式定理证明，我们已经证明了许多与各向异性特别是正交各向异性材料的结构破坏准则领域有关的有趣定理。这项工作的主要贡献是证明了符号代数在工程应用中的巨大效用，并证明了在一定条件下可以证明文献中提出的所有失效准则都是一般形式的特殊形式。有关与材料连续性相关的应变能密度函数的标准。提出和讨论了两个具体的例子，以及一个定理，证明了所有应力空间的标准都与应变空间中表示的等价形式存在对偶形式。

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《ASME international design engineering technical conferences and computers and information in engineering conference 2011.;vol. 2 pt. A.》|2011年|p.201-211|共11页
会议地点 Washington DC(US);Washington DC(US);Washington DC(US);Washington DC(US)
作者
John G. Michopoulos; Athanasios Iliopoulos;
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作者单位

Computational Multiphysics Systems Lab. Center of Computational Material Science Naval Research Laboratory Washington, DC 20375, USA;

Science Applications Int. Corp. resident at Naval Research Laboratory Washington DC 20375, USA;

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原文格式 PDF
正文语种 eng
中图分类工程设计;工程设计;
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SYMBOLIC ALGEBRA AND THEOREM PROVING FOR FAILURE CRITERIA REDUCTION

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