Introduction To Linear Elasticity

This applications-oriented introduction fills an important gap in the field of solid mechanics. Offering a thorough grounding in the tensor-based theory of elasticity for courses in mechanical, civil, materials or aeronautical engineering, it allows students to apply the basic notions of mechanics to such important topics as stress analysis. Further, they will also acquire the necessary background for more advanced work in elasticity, plasticity, shell theory, composite materials and finite element mechanics. This second edition features new chapters on the bending of thin plates, time-dependent effects, and strength and failure criteria.

This is an intermediate book for beginning postgraduate students and junior researchers, and offers up-to-date content on both continuum mechanics and elasticity. The material is self-contained and should provide readers sufficient working knowledge in both areas. Though the focus is primarily on vector and tensor calculus (the so-called coordinate-free approach), the more traditional index notation is used whenever it is deemed more sensible. With the increasing demand for continuum modeling in such diverse areas as mathematical biology and geology, it is imperative to have various approaches to continuum mechanics and elasticity. This book presents these subjects from an applied mathematics perspective. In particular, it extensively uses linear algebra and vector calculus to develop the fundamentals of both subjects in a way that requires minimal use of coordinates (so that beginning graduate students and junior researchers come to appreciate the power of the tensor notation).

"Elasticity is one of the crowning achievements of Western culture!" exclaimed my usually reserved colleague Professor George Zahalak during a meeting to discuss the graduate program in Solid Mechanics. Although my thoughts on the theory of elasticity had not been expressed in such noble terms, it was the same admiration for the creative efforts of the premier physicists, mathe maticians and mechanicians of the 19th and 20th century that led me to attempt to popularize the basis of solid mechanics in this introductory form. The book is intended to provide a thorough grounding in tensor-based theory of elasticity, which is rigorous in treatment but limited in scope. It is directed to advanced undergraduate and graduate students in civil, mechanical or aeronautical engineering who may ultimately pursue more applied studies. It is also hoped that a few may be inspired to delve deeper into the vast liter ature on the subject. A one-term course based on this material may replace traditional Advanced Strength of Materials in the curriculum, since many of the fundamental topics grouped under that title are treated here, while those computational techniques that have become obsolete due to the avail ability of superior, computer-based numerical methods are omitted. Little, if any, originality is claimed for this work other than the selection, organization and presentation of the material. The principal historical contributors are noted in the text and several modem references are liberally cited.

This augmented and updated fourth edition introduces a new complement of computational tools and examples for each chapter and continues to provide a grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical and biomedical engineering and materials and earth science. Professor Gould’s proven approach allows faculty to introduce this subject early on in an educational program, where students are able to understand and apply the basic notions of mechanics to stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials and finite element mechanics. With the introductory material on the use of MATLAB, students can apply this modern computational tool to solve classic elasticity problems. The detailed solutions of example problems using both analytical derivations and computational tools helps student to grasp the essence of elasticity and practical skills of applying the basic mechanics theorem.

This book is intended for researchers, engineers and students in solid mechanics, materials science and physics who are interested in using the power of modern computing to solve a wide variety of problems of both practical and fundamental significance in elasticity. Extensive use of Mathematica in the book makes available to the reader a range of recipes that can be readily adjusted to match particular tastes or requirements, to visualize solutions, and to carry out symbolic and numerical analysis and optimization.

Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.

Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide. Contains exercises for student engagement as well as the integration and use of MATLAB Software Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of

This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and variational principles, generalized solutions and conditions for solvability.Introduction to Mathematical Elasticity will also be of essential reference to engineers specializing in elasticity, and to mathematicians working on abstract formulations of the related boundary value problems.