Homogenization of linear elastic shells. (English) Zbl 0558.73055

Lutoborski, Adam

J. Elasticity 15, 69-87 (1985).

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

Keywords:

energy method of homogenization; homogenized constitutive equations; Budiansky-Sanders linear, elastic shells; material parameters rapidly oscillating on the shell surface; homogenized shell model; elliptic; calculated effective material parameters; solution of the periodic shell model converges weakly; solution of the homogenized model; period tends to zero

Citations:

Zbl 0422.73052; Zbl 0373.73002

References:

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