On jets, almost symmetric tensors, and traction hyper-stresses

IF 1 Q4 MECHANICS

Mathematics and Mechanics of Complex Systems Pub Date : 2017-10-28 DOI:10.2140/memocs.2018.6.101

R. Segev, J. Sniatycki

引用次数: 2

Abstract

The paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational kth order hyper-stress is an object that acts on jets of generalized velocities to produce power densities. The traction hyper-stress is introduced as an object that induces hyper-traction fields on the boundaries of subbodies. Additional aspects of multilinear algebra relevant to the analysis of these objects are reviewed.

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在喷流上，几乎对称张量，和牵引力超应力

研究了不含度量结构和平行结构的可微流形上的高阶连续介质力学的表述。对于将广义速度建模为某个矢量束的截面，变分k阶超应力是作用于广义速度射流以产生功率密度的对象。引入了牵引超应力作为在子体边界上诱发超牵引场的对象。与这些对象的分析相关的多线性代数的其他方面进行了审查。

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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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.