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We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in table tennis or football. The theory of elasticity is essential to the recent developments of applied and fundamental science, such as the bio-mechanics of DNA filaments and other macro-molecules, and the animation of virtual characters in computer graphics and materials science. In this book, the emphasis is on the elasticity of thin bodies (plates, shells, rods) in connection with geometry. It covers such topics as the mechanics of hairs (curled and straight), the buckling instabilities of stressed plates, including folds and conical points appearing at larger stresses, the geometric rigidity of elastic shells, and the delamination of thin compressed films. It applies general methods of classical analysis, including advanced non-linear aspects (bifurcation theory, boundary layer analysis), to derive detailed, fully explicit solutions to specific problems. These theoretical concepts are discussed in connection with experiments. The book is self-contained. Mathematical prerequisites are vector analysis and differential equations. The book can serve as a concrete introduction to non-linear methods in analysis. -- 'A most welcome addition to the literature with a refreshingly new approach, first in that it discusses in depth how the differential geometry of surfaces is connected with the theory of elastic plates and shells, second in that, as a consequence of this perspective, it sheds new light and understanding on practical problems.'-Philippe Ciarlet, City University of Hong Kong --Book Jacket.

Elasticity --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Mathematics. --- Properties --- Mathematics

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Elasticity. --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties

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In the science of physics, elasticity is the ability of a deformable body (e.g., steel, aluminum, rubber, wood, crystals, etc.) to resist a distorting effect and to return to its original size and shape when that influence or force is removed. Solid bodies will deform when satisfying forces are applied to them. Elasticity solution of materials will be grouped in forms of linear and nonlinear elasticity formulations. The main subject of this book is engineering elasticity and consists of five chapters in two main sections. These two main sections are ""General Theorems in Elasticity"" and ""Engineering Applications in Theory of Elasticity."" The first chapter of the first section belongs to the editor and is entitled ""Analytical and Numerical Approaches in Engineering Elasticity."" The second chapter in the first section is entitled ""A General Overview of Stress-Strain Analysis for the Elasticity Equations"" by P. Kumar, M. Mahanty, and A. Chattopadhyay. The first chapter of the second section is entitled ""FEA and Experimental Determination of Applied Elasticity Problems for Fabricating Aspheric Surfaces"" by Dr. D.N. Nguyen. The second chapter is entitled ""Concept of Phase Transition Based on Elastic Systematics"" by Dr. P.S. Nnamchi and Dr. C.S. Obayi. The third chapter is entitled ""Repair Inspection Technique Based on Elastic-Wave Tomography Applied for Deteriorated Concrete Structures"" by Dr. K. Hashimoto, Dr. T. Shiotani, Dr. T. Nishida, and Dr. N. Okude. Finally, this book includes the basic principles of elasticity and related engineering applications about theory and design.

Elasticity. --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties --- Engineering --- Physical Sciences --- Engineering and Technology --- Structural Engineering --- Civil Engineering

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This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional an

Elasticity. --- Homogenization (Differential equations) --- Differential equations, Partial --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties

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Nonlinear elasticity is concerned with nonlinear effects associated with deformations of elastic bodies subjected to external forces or temperature variations. It has important applications in many areas, including the aerospace and rubber industries, and biomechanics. This book, written by a group of leading researchers invited especially for the purpose, provides an up-to-date and concise account of the fundamentals of the theory of nonlinear elasticity and a comprehensive review of several major current research directions in this important field. It combines the characteristics of coherence and detail found in standard treatises with the strength and freshness of research articles. The emphasis is placed firmly on coverage of modern topics and recent developments rather than on the very theoretical approach often found. The book will be an excellent reference source for both beginners and specialists in engineering, applied mathematics and physics. It is also ideally suited for graduate courses.

Elasticity. --- Nonlinear theories. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Elastic properties --- Young's modulus --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties