ESTIMATES FOR DEVIATIONS FROM EXACT SOLUTIONS TO PLANE PROBLEMS IN THE COSSERAT THEORY OF ELASTICITY

S. Repin; M. E. Frolov

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ESTIMATES FOR DEVIATIONS FROM EXACT SOLUTIONS TO PLANE PROBLEMS IN THE COSSERAT THEORY OF ELASTICITY

机译：概论中的从精确解到平面问题的偏差估计

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A functional a posteriori estimate is obtained for control of the accuracy of approximate solutions to plane problems arising in the Cosserat theory of elasticity. We deal with the case where displacements and independent rotation are given on the boundary of the domain, a continuous medium is isotropic, and there is a linear dependence between stresses and strains. The proposed method is based on the duality theory of Calculus of Variations and can be also applied to the case of anisotropic media. Bibliography: 41 titles.

机译：获得了一个函数后验估计，以控制Cosserat弹性理论中出现的平面问题的近似解的准确性。我们处理以下情况：在域的边界上给出位移和独立旋转，连续介质是各向同性的，并且应力和应变之间存在线性关系。所提出的方法基于变分微积分的对偶理论，并且也可以应用于各向异性介质的情况。参考书目：41种。

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《Journal of Mathematical Sciences》 |2012年第2期|p.281-291|共11页
作者
S. Repin; M. E. Frolov;
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V. A. Steklov Institute of Mathematics RAS 27, Fontanka, St. Petersburg 191011, Russia;

St.-Petersburg State Polytechnical University 29, Politekhnicheskaya ul., St.-Petersburg 195251, Russia;

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2. Estimates of deviations from exact solutions for elasticity problems with nonlinear boundary conditions [J] . P. NEITTAANMAEKI, S. REPIN, J. VALDMAN Russian Journal of Numerical Analysis and Mathematical Modelling . 2013,第6期

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3. Exact solutions for the vibration of finite granular beam using discrete and gradient elasticity cosserat models [J] . Massoumi Sina, Challamel Noel, Lerbet Jean Journal of Sound and Vibration . 2021,第1期

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5. Observational Constraints, Exact Plane Wave Solutions, and Exact Spherical Solutions in Einstein-Aether Theory [D] . Oost, Jacob. 2019

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6. Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity [O] . Elena Atroshchenko, Stéphane P. A. Bordas -1

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8. An Exact Plane-Stress Solution for a Class of Problems in Orthotropic Elasticity. [R] . erb, d. a. cooper, p. a. 1982

机译：一类正交各向异性弹性问题的精确平面应力解。

ESTIMATES FOR DEVIATIONS FROM EXACT SOLUTIONS TO PLANE PROBLEMS IN THE COSSERAT THEORY OF ELASTICITY

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