On the existence of solution in the linear elasticity with surface stresses

Holm Altenbach; Victor A. Eremeyev; Leonid P. Lebedev

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On the existence of solution in the linear elasticity with surface stresses

机译：关于表面应力的线性弹性解的存在性

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The mathematical investigation of the initial-boundary and boundary value problems in the linear elasticity considering surface stresses is presented. Weak setup of the problems based on mechanical variational principles is studied. Theorems of uniqueness and existence of the weak solution in energy spaces of static and dynamic problems are formulated and proved. Some properties of the spectrum of the problems under consideration are established. The studies are performed applying the functional analysis techniques. Finally, the Rayleigh principle for eigenfrequencies is constructed.

机译：提出了考虑表面应力的线性弹性中初始边界和边界值问题的数学研究。研究了基于机械变分原理的问题的弱设置。提出并证明了静态和动态问题的能空间的唯一性定理和弱解的存在性定理。建立了所考虑问题的频谱的某些性质。使用功能分析技术进行研究。最后，建立了本征瑞利原理。

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来源
《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2010年第3期|共10页
作者
Holm Altenbach; Victor A. Eremeyev; Leonid P. Lebedev;
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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Surface stresses; existence theorem; Sobolev’s spaces; eigenfrequencies;

机译：表面应力;存在性定理;Sobolev空间;本征频率;

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专利

1. On the existence of solution in the linear elasticity with surface stresses [J] . Holm Altenbach, Victor A. Eremeyev, Leonid P. Lebedev Zeitschrift fur Angewandte Mathematik und Mechanik . 2010,第3期

机译：关于表面应力的线性弹性解的存在性
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3. Existence, uniqueness solution for nonlinear mixed problem in two dimensional elasticity [J] . Oudaani Jaouad, Enseignant au Lycee Qualifiant, Ajdir a Khenifra International Journal of Applied Mathematical Research . 2014,第3期

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4. Nonlinear Sliding Surfaces; Computing and Existence of Solution [C] . Azad Ghaffari, Mohammad Javad Yazdanpanah International Conference on Control, Automation and Systems . 2008

机译：非线性滑动表面;解决方案的计算和存在
5. Axisymmetric problems in nonlinear elasticity: Existence and global injectivity of energy minimizers and new classes of exact solutions. [D] . Novozhilova, Lydia S. 2004

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6. Solution of the nonlinear elasticity imaging inverse problem: The incompressible case [O] . Sevan Goenezen, Paul Barbone, Assad A. Oberai -1

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7. On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. II. Mindlin's elasticity with microstructure and the first strain-gradient theory [O] . Ivan Hlaváček, Miroslav Hlaváček 1969

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8. Existence Theorem for the Dirichlet Initial-Boundry Value Problem in Incompressible Nonlinear Elasticity [R] . Hrusa, W. J., Renardy, M. 1986

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On the existence of solution in the linear elasticity with surface stresses

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