Composite and Reinforced Elements of Constructions

Little excuse is necessary for a book on composite materials in general and on the mechanics of composite materials in particular. The dramatic increase in the use of composite materials and structural elements for almost all conceivable applications increasingly calls for the development of rigorous mathematical models capable of predicting their mechanical behaviour under any given set of conditions. The composites with a regular structure that are the subject matter of this book, are not only worth considering because of their numerous practical uses in a wide range of fields but also have an obvious advantage over many other composite material types in their being more amenable to theoretical analysis. A very effective tool that has been developed for treatment of such systems is the asymptotic method of homogenization of differential equations with rapidly oscillating coefficients. The method has been given a strict mathematical justification and yields an asymptotically correct solutions when used in its domain of applicability. It is by application of this method that the author has discussed the elastic, heat conduction and thermoelastic properties of the composite materials and composite or structurally nonhomogeneous thin-walled elements of constructions. The book is largely based on the author's original work carried out over the past decade, and it contains also the relevant results provided by the Russian researchers.

Table of Contents:
Part 1 Mechanics of inhomogeneous deformable solids: basic relations of continuum mechanics; basic equations of thermoelasticity and electroelasticity; mechanical models of composite materials. Part 2 Asymptotic homogenization of regular structures: homogenization techniques for periodic structures; homogenization method for regions with a wave boundary; local problems and effective coefficients. Part 3 Elasticity of regular composite structures: homogenization of the linear elasticity problem; laminated composites - effective properties and fracture criteria; effective characteristics of unidirectional fibre composites; plane elasticity problem for a periodic composite with a crack; homogenization of the geometrically nonlinear elasticity problem for a periodic composite; elastic stability equatiions. Part 4 Thermoelasticity of regular composite structures: homogenization of thermoelasticity problem; fibre composites - local stresses and effective properties; laminated composite with prescribed thermoelastic properties; composite material design. Part 5 General homogenization models for composite shells and plates with rapidly varying thickness: elasticity problem for a shell of a regularly nonhomogeneous material with wavy surfaces; thermal conductivity of a curved thin shell of a regularly nonhomogeneous material with corrugated surfaces; thermoelasticity of a curved shell of regularly nonhomogeneous material with corrugated surfaces; geometrically nonlinear problem for a thin regularly nonhomogeneous shell with corrugated faces. Part 6 Structurally nonhomogeneous periodic shells and plates: local problem formulation for structurally nonhomogeneous shells and plates of orthotropic material; an approximate method for determining the effective properties of ribbed and wafer shells; effective properties of a three-layered shell with a honeycomb filler; elastic moduli and local stresses in wafer type plates and shells, including the interaction between cell elements; stretching of shells or plates reinforced by regular system of thin surface strips; shells and plates with corrugated surfaces of regular structure. Part 7 Network and framework reinforced shells and plates with regular structure; effective elastic moduli of a network reinforced shell; effective thermoelastic properties of network reinforced shells; heat conduction of network reinforced plates and shells; constitutional equations for network reinforced plates and shells of rectangular, rhombic and triangular structure; composite shells with high stiffness framework type reinforcement. Part 8 The fundamental solution of the periodic elasticity problem: the derivation of a doubly periodic fundamental solution of the three-dimensional elasticity problem; transformation of the doubly periodic fundamental solution of the elasticity problem; singly periodic fundamental solution of the plane elasticity. Appendices.