Geodesic
Homogenization of linear elasticity equations
Applications of Mathematics, Tome 27 (1982) no. 2, pp. 96-117

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The homogenization problem (i.e. the approximation of the material with periodic structure by a homogeneous one) for linear elasticity equation is studied. Both formulations in terms of displacements and in terms of stresses are considered and the results compared. The homogenized equations are derived by the multiple-scale method. Various formulae, properties of the homogenized coefficients and correctors are introduced. The convergence of displacment vector, stress tensor and local energy is proved by a simplified local energy method.
DOI : 10.21136/AM.1982.103951
Classification : 35B40, 49D50, 73K20, 74B99
Keywords: homogenization; approximation of material with periodic structure by homogeneous one; terms of displacements; terms of stresses; results compared; multiple-scale method; properties of homogenized coefficients; correctors; convergence of displacement vector; stress tensor; local energy; simplified local energy method 
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     author = {Franc\r{u}, Jan},
     title = {Homogenization of linear elasticity equations},
     journal = {Applications of Mathematics},
     pages = {96--117},
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     volume = {27},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103951/}
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Franců, Jan. Homogenization of linear elasticity equations. Applications of Mathematics, Tome 27 (1982) no. 2, pp. 96-117. doi: 10.21136/AM.1982.103951

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