دانلود کتاب Series on Advances in Mathematics for Applied Sciences, Volume 52 : Plates, Laminates and Shells - Asymptotic Analysis and Homogenization

Some of the most effective gauges in field theory are non-covariant gauges of the axial kind, such as the light-cone gauge and the temporal gauge. The principal advantage of these gauges stems from the decoupling of the fictitious particles in the theory. The purpose of this volume is to give a clear and readable account of the basic features and mathematical subtleties of these ghost-free gauges, and of their truly enormous range of applicability. In addition to explicit one-loop computations in Yang-Mills and Chern-Simons theory, the book contains detailed analyses of the unifield-gauge formalism and of the renormalization of Yang-Mills theory in the presence of non-local terms 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