通过邻接线性算子求解具有混合边界条件的静态线性弹性的应力解

IF 1.2 3区 数学 Q1 MATHEMATICS
Ivan Gudoshnikov, Michal Křížek
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引用次数: 0

摘要

我们重温了线性弹性中的应力问题,从几何和函数分析的角度提供了一个视角。对于具有混合边界条件的线性弹性静态应力问题,我们提出了相关的一对无界邻接算子。尽管有关该主题的文献很多,但我们还是第一次明确地写出了这样一对算子。我们用它来寻找应力解,将其作为邻接算子的(仿射平移的)基本子空间的交集。特别是,我们以算子形式处理平衡方程,其中涉及边界部分的迹空间,即所谓的 Lions-Magenes 空间。我们对混合边界条件问题的一对邻接算子的分析依赖于位移边界条件问题的一对类似算子的性质,这也包括在本文中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators
We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functional-analytic points of view. For the static stress problem of linear elasticity with mixed boundary conditions we present the associated pair of unbounded adjoint operators. Such a pair is explicitly written for the first time, despite the abundance of the literature on the topic. We use it to find the stress solution as an intersection of the (affinely translated) fundamental subspaces of the adjoint operators. In particular, we treat the equilibrium equation in the operator form, which involves the spaces of traces on a part of the boundary, known as the Lions-Magenes spaces. Our analysis of the pair of adjoint operators for the problem with mixed boundary conditions relies on the properties of the analogous pair of operators for the problem with the displacement boundary conditions, which we also include in the paper.
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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