非线性Cosserat介质动力学问题的变分公式

Q3 Mathematics

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI:10.1016/j.jappmathmech.2017.07.007

E.V. Zdanchuk, V.V. Kuroyedov, V.V. Lalin, I.I. Lalina, E.A. Provatorova

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引用次数: 2

摘要

给出了几何和物理非线性弹性Cosserat介质动力学问题的变分公式，其形式为Hamilton泛函的定常点求问题。计算了应变和旋转张量以及线速度和角速度矢量的变化。证明了具有自然边界条件的欧拉方程与具有原始边界条件的运动方程在势能和扭矩载荷情况下的等价性。得到了转矩(体载荷和面载荷)的非平凡势性条件。

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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Variational formulation of dynamic problems for a nonlinear Cosserat medium

A variational formulation of dynamic problems for a geometrically and physically nonlinear elastic Cosserat medium is obtained in the form of the problem of finding the stationary point of Hamilton's functional. Variations of the strain and rotation tensors and the linear and angular velocity vectors are calculated. The equivalence of the Euler equations with natural boundary conditions to the equations of motion with the original boundary conditions in the case of potential force and torque loads is proved. A nontrivial potentiality condition of the torque (bulk and surface) loads is obtained.

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来源期刊

Pmm Journal of Applied Mathematics and Mechanics 物理-力学

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is a cover to cover translation of the Russian journal Prikladnaya Matematika i Mekhanika, published by the Russian Academy of Sciences and reflecting all the major achievements of the Russian School of Mechanics.The journal is concerned with high-level mathematical investigations of modern physical and mechanical problems and reports current progress in this field. Special emphasis is placed on aeronautics and space science and such subjects as continuum mechanics, theory of elasticity, and mathematics of space flight guidance and control.