A Concise Course in Elasticity: Nonlinear and Linear Theories with Statics and Dynamics

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Jiashi Yang

A Concise Course in Elasticity

Nonlinear and Linear Theories with Statics and Dynamics

Jiashi Yang

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English

Birkhauser Verlag AG
08 April 2025

Cybernetics & systems theory; Differential calculus & equations; Classical mechanics; Mechanics of solids

Series: Advances in Mechanics and Mathematics

This textbook presents a concise and comprehensive treatment of the theory of elasticity. It covers both the linear and nonlinear aspects of the theory, including both statics and dynamics. Written to be accessible to the graduate student reader, this text promotes approachability by minimizing the use of complex mathematical tools, and instead emphasizing the formulation of the initial boundary value problems. This approach makes it an ideal resource for students as well as instructors seeking a textbook designed for a one-semester graduate course in elasticity.

Divided into ten chapters, the book begins with a brief review of the mechanics of materials. The theory of Cartesian tensors is then introduced, which serves as a mathematical preparation for the concise treatment of the nonlinear theory of elasticity that follows. The theory of linear elasticity is covered next with the remainder of the book then focusing on problem solving in linear elasticity. These chapters cover topics such as antiplane problems, plane-stress and plane-strain problems, and elastodynamics. Five appendices appear at the end, which include basic equations of elasticity in cylindrical, polar, and spherical coordinates, as well as a collection of vector identities that appear throughout the book.

A Concise Course in Elasticity is an ideal textbook for a one-semester graduate course on elasticity. Graduate students interested in this topic will appreciate the author’s accessible approach. Instructors will find the comprehensive coverage uniquely suited to providing an overview of the area. Readers are assumed to have some experience at the undergraduate level of the mechanics of materials.

By: Jiashi Yang
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Volume: 54
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031861178
ISBN 10: 3031861175
Series: Advances in Mechanics and Mathematics
Pages: 200
Publication Date: 08 April 2025
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

Preface.- Review of Mechanics of Materials.- Cartesian Tensors.- Kinematics.- Nonlinear Theory for Large Deformation.- Linear Theory for Small Deformation.- Saint-Venant’s Problem.- Some Simple Problems.- Antiplane Problems.- Plane Strain and Plane Stress.- Waves and Vibrations.- Appendices.

Jiashi Yang is a Professor at the Department of Mechanical and Materials Engineering of University of Nebraska-Lincoln. He received his bachelor's and master's degrees from Tsinghua University, Beijing, China in 1982 and 1985, respectively, and his Ph.D. from Princeton University in 1994. Then he did postdoctoral research at University of Missouri-Rolla and Rensselaer Polytechnic Institute. He worked as an engineer with Motorola, Inc. prior to joining University of Nebraska-Lincoln in 1997. His research area is the mechanics of electromagnetoelastic structures and devices. He has coauthored over 400 papers in refereed journals. His previous books include “Mechanics of Piezoelectric Structures”, “Mechanics of Functional Materials” and “Theory of Electromagnetoelasticity” with World Scientific, as well as “An Introduction to the Theory of Piezoelectricity” and “Analysis of Piezoelectric Semiconductor Structures” with Springer.