Plates, Laminates and Shells - Asymptotic Analysis and Homogenization

Abstract

Mathematical preliminaries: function spaces, convex analysis, variational convergence. Elastic plates: three-dimensional analysis and effective models of composite plates thin plates in bending and stretching non-linear behaviour of plates moderately thick transversely symmetric plates sandwich plates with soft core. Elastic plates with cracks: unilateral cracks in thin plates unilateral cracks in plates with transverse shear deformation part-through the thickness cracks stiffness loss of cracked laminates comments and bibliographical notes. Elastic-perfectly plastic plates: mathematical complements homogenisation of functional with linear growth homogenisation of plates loaded by forces and moments comments and bibliographical notes. Elastic and plastic shells: linear and non-linear models of elastic shells homogenisation and stiffnesses of thin periodic elastic shells linear approach homogenised properties of thin periodic elastic shells undergoing moderately large relations around tangents perfectly plastic shells. Application of homogenisation methods in optimum design of plates and shells: mathematical complements two-phase plate in bending, Hashin-Shtrikamn bounds two-phase plate Hashin-Shtrikman bounds for the in-plane problem explicit formulae for effective bending stiffnesses and compliances of ribbed plates explicit formulae for effective membrane stiffnesses and compliance s of ribbed plates thin bending two-phase plates of minimum compliance minimum compliance problem for thin plates of varying thickness -application of young measures thin shells of minimum compliances Truss-like Michell continua.