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Homogenization of linear elastic shells. (English) Zbl 0558.73055

Homogenization techniques were used by G. Duvaut [J. d’Anal. nonlin., Proc., Besançon 1977, Lect. Notes Math. 665, 56-69 (1978; Zbl 0422.73052) and Theor. appl. Mech., Proc. 14th IUTAM Congr., Delft 1976, 119-132 (1977; Zbl 0373.73002)] in the asymptotic analysis of 3- dimensional periodic continuum problems and periodic von Kármán plates. In this paper we homogenize Budiansky-Sanders linear, elastic shells with material parameters rapidly oscillating on the shell surface. We obtain a homogenized shell model which is elliptic and depends on explicitly calculated effective material parameters. We show that the solution of the periodic shell model converges weakly to the solution of the homogenized model when the period tends to zero.

MSC:

74K15 Membranes
74E05 Inhomogeneity in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
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