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Effective models of composite periodic plates. II: Simplifications due to symmetries. (English) Zbl 0762.73054

Summary: [For part I see the preceding entry.]
This paper is aimed at investigating how material and geometrical symmetries of a composite plate simplify the formulae derived in Part I by the asymptotic method. It occurs that the symmetry with respect to the middle plane results in splitting the subsequent overall and local problems into membrane and bending problems. Additional assumptions of orthotropy of the material and of certain symmetries of the cell periodicity imply far-reaching simplifications, e.g. the vanishing of some terms in the first-order correctors for displacements, and the cancellation of discrepancies in the formulation of some boundary conditions. In the last section, a computational algorithm for evaluating the effective stiffnesses is suggested.

MSC:

74E30 Composite and mixture properties
74K20 Plates
74E15 Crystalline structure
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