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Composites: Mechanics, Computations, Applications: An International Journal
ESCI SJR: 0.354 SNIP: 0.655 CiteScore™: 1.2

ISSN Imprimir: 2152-2057
ISSN En Línea: 2152-2073

Composites: Mechanics, Computations, Applications: An International Journal

DOI: 10.1615/CompMechComputApplIntJ.v8.i2.40
pages 147-170

INTEGRAL FORMULAS IN ELECTROMAGNETIC ELASTICITY OF HETEROGENEOUS BODIES. APPLICATION IN THE MECHANICS OF COMPOSITE MATERIALS

Vladimir I. Gorbachev
Department of Composite Mechanics, Mechanics and Mathematics Faculty, M.V. Lomonosov Moscow State University, 1 Leninskie Gory, Moscow, 119991, Russia

SINOPSIS

Equilibrium of an elastic body from inhomogeneous material, possessing piezo properties, is considered. Deformed and electrical states of such body are described by a system of four coupled partial differential equations with variable coefficients relative to three components of the displacement vector and the scalar electrostatic potential. The problem for the heterogeneous body is called the initial problem. Along with the initial problem, we consider just the same problem for a homogeneous body of the same shape, i.e., the accompanying problem. New integral formulas that allow expressing the solution of the initial boundary-value problem in terms of the solution of the accompanying boundary-value problem and the Green tensor of the initial problem are obtained. From the integral formulas there follow the expressions for effective characteristics of arbitrarily inhomogeneous piezomaterial. The use of such expressions for specific computations requires a preliminary solution of auxiliary boundary-value problems. These problems are stated and an analytical solution for a partial case of an infinite nonuniform (over the thickness) layer is found. Exact analytical expressions for effective electromechanical characteristics are constructed. Moreover, the integral formulas were used to derive an equivalent representation of the solution of the initial problem in the form of series with respect to all possible derivatives of the solution of the accompanying problem. Recurrent equations are obtained for coefficients of the series (structural functions).


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