Stressed Composite Structures: Homogenized Models for Thin-Walled Nonhomogeneous Structures with Initial Stresses(Foundations of Engineering Mechanics)

The basic concepts of traditional mechanics of stressed structures are suitable for classical uniform structures made of homogeneous materials but not for complex structures such as a network plate or structures made of composite materials. In this book a new approach to stressed inhomogeneous structures is presented, leading to significant changes in the classical concepts of stressed bodies, especially plates, membranes, rods and beams. The approach is based on the rigorous mathematical asymptotic homogenization method and its newly elaborated modifications. It can be applied to the analysis, mechanical design and optimization problems of composite structures, including buckling problems.

Table of Contents:
1. Introduction in the Homogenization Method as Applied to Stressed Composite Materials.- 1.1. Linear Model of a Stressed Elastic Body.- 1.2. Homogenization Method in the Mechanics of Composites. The Basic Approaches.- 1.3. Homogenization Method in the Mechanics of Stressed Composites.- 2. Stressed Composite Plates and Membranes.- 2.1. Stressed Plates (2-D Model).- 2.2. Stressed Plates (Transition from 3-D to 2-D Model, In-Plane Initial 27 Stresses).- 2.3. Stressed Plates (Transition from 3-D to 2-D Model, Moments of Initial Stresses).- 2.4. 2-D Boundary Conditions Derived from the 3-D Boundary Problem.- 2.5. 3-D and 2-D “Energy Forms” for a Stressed Plate and a Stability Criterion for a Plate.- 2.6. Membrane (2-D model).- 2.7. Membrane (Transition from 3-D to 2-D Model).- 2.8. Plates with no Initial Stresses. Computing of Resultant Initial Stresses.- 3. Stressed Composite Beams, Rods and Strings.- 3.1. Stressed Beam (1-D model).- 3.2. Stressed Beams (Transition from 3-D to 1-D Model,Initial Axial Stresses).- 3.3. Stressed Beams (Transition from 3-D to 1-D Model, Moments of Initial Stresses).- 3.4. 1-D boundary Conditions Derived from 3-D Elasticity Problem.- 3.5. 3-D and 1-D “Energy Forms” for a Stressed Beam and a Stability Criterion for a Beam.- 3.6. Strings (1-D Model).- 3.7. Strings (Transition from a 3-D to a 1-D Model).- 3.8. Beams with no initial stresses. Computing of resultant initial stresses and moments.- 4. Calculation and Estimation of Homogenized Stiffnesses of Plate-Like and Beam-Like Composite Structures.- 4.1. Variational Principles for Stiffnesses of Nonhomogeneous Plates.- 4.2. Variational Principles for Stiffnesses of Nonhomogeneous Beams.- 4.3. The Homogenization Method Modified for Lattice Plats.- 4.4. The Homogenization Method Modified for Lattice Beams.- 4.5. Review of Software Suitable for Homogenization Procedures.- Appendix A. Plates and Beams in Different Coordinate Systems.- A1. Homogenized Stiffnesses of a Plate in Different Coordinate Systems.- A2. Homogenized Stiffnesses of a Beam in Different Coordinate Systems.- Appendix B. Critical Loads for Some Composite Plates.- References.

Review :

"It is a book that can be useful to engineers, physicists and mathematicians, among others. ... In my opinion the book is well written, with clear explanations, and develops a very practical theme in the field of composite materials. The text and bibliography are a source of significant knowledge for specialists of different areas." (Reinaldo Rodríguez-Ramos, Mathematical Reviews, September, 2020)