各向异性矩的定义方程线性弹性理论与二维约束旋转纯剪切问题

B. D. Annin, N. I. Ostrosablin, R. I. Ugryumov
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引用次数: 0

摘要

本文给出了四阶材料张量任意各向异性情况下的弹性线性矩理论方程。在定义关系中区分了对称分量和偏对称分量。考虑了线性定义关系的一些简化版本。当四阶材料张量不具有主对称时,允许存在柯西弹性的可能性。对于决定力和耦合应力的材料张量,我们引入了作为非弹性矩介质不变特征的本征模量和本征态。对于平面变形和受限旋转的情况,给出了仅存在剪应力时二维问题的完全解的一个例子。结果表明,各向异性和各向同性弹性介质的解有显著差异。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional Problem of Pure Shear with Constrained Rotation

The paper presents the equations of the linear moment theory of elasticity for the case of arbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetric components are distinguished in the defining relations. Some simplified versions of linear defining relations are considered. The possibility of Cauchy elasticity is allowed when material tensors of the fourth rank do not have the main symmetry. For material tensors that determine force and couple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of an elastic moment medium. For the case of plane deformation and constrained rotation, an example of a complete solution of the two-dimensional problem is given when there are only shear stresses. The solutions turn out to be significantly different for anisotropic and isotropic elastic media.

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来源期刊
Journal of Applied and Industrial Mathematics
Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering
CiteScore
1.00
自引率
0.00%
发文量
16
期刊介绍: Journal of Applied and Industrial Mathematics  is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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