Displaying similar documents to “Asymptotic solution of the theory of shell boundary value problem.”

On Asymptotic Theory of Beams, Plates and Shells

L.A. Aghalovyan, M.L. Aghalovyan (2016)

Curved and Layered Structures

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Bases of asymptotic theory of beams, plates and shells are stated. The comparison with classic theory is conducted. New classes of thin bodies problems, for which hypotheses of classic theory are not applicable, are considered. By the asymptotic method effective solutions of these problems are obtained. The effectiveness of the asymptotic method for finding solutions of as static, as well as dynamic problems of beams, plates and shells is shown.

Stability for dissipative magneto-elastic systems

Reinhard Racke (2003)

Banach Center Publications

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In this survey we first recall results on the asymptotic behavior of solutions in classical thermoelasticity. Then we report on recent results in linear magneto-thermo-elasticity and magneto-elasticity, respectively.

Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer

Victor Péron (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present equivalent conditions and asymptotic models for the diffraction problem of elastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength, this problem is well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the fourth order for the elastic displacement....

Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part I – Model Development

D. A. Hadjiloizi, A.L. Kalamkarov, Ch. Metti, A. V. Georgiades (2014)

Curved and Layered Structures

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A comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly-varying thickness is developed in the present paper. A rigorous three-dimensional formulation is used as the basis of multiscale asymptotic homogenization. The asymptotic homogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell’s equations. The work culminates in the derivation of a set of differential...

On the change of energy caused by crack propagation in 3-dimensional anisotropic solids

Martin Steigemann, Maria Specovius-Neugebauer (2014)

Mathematica Bohemica

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Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows...

COMPUTATION of generalized stress intensity factors for bonded elastic structures

Marius Bochniak, Anna–Margarete Sändig (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider coupled structures consisting of two different linear elastic materials bonded along an interface. The material discontinuities combined with geometrical peculiarities of the outer boundary lead to unbounded stresses. The mathematical analysis of the singular behaviour of the elastic fields, especially near points where the interface meets the outer boundary, can be performed by means of asymptotic expansions with respect to the distance from the geometrical and structural...