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Continuum modelling of laminates with a slowly graded microstructure

Szymczyk J., Woźniak Cz.

Archives of Mechanics

2006

Vol. 58, nr 4-5

445-458

The considerations are concerned with modelling and analysis of the dynamic response for micro-laminated two-phased solids. The main attention is focussed on modelling of the laminates which have a slowly graded microstructure in the direction normal to the layering (slowly graded laminates, SGL). Periodic and functionally graded laminates can be treated as special cases of SGL. A new mathematical model which couples micro- and macro-response of the linear elastic SGL is proposed. It is shown that for laminates with a weak transversal inhomogeneity, the derived model equations can be decomposed into asymptotic equations which describe the behavior of a laminate independently on the macro- and micro-level. This decomposition is estimated on the example of a specific vibration problem.