Continuum Mechanics and Linear Elasticity - An Applied Mathematics Introduction

✍ Scribed by Ciprian D. Coman

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 528
• Category: Library

✦ Synopsis

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).

✦ Table of Contents

Front Matter ....Pages i-xv
Front Matter ....Pages 1-1
Vector, Tensors, and Related Matters (Ciprian D. Coman)....Pages 3-120
Kinematics (Ciprian D. Coman)....Pages 121-160
Balance Laws (Ciprian D. Coman)....Pages 161-196
Constitutive Relationships (Ciprian D. Coman)....Pages 197-240
Front Matter ....Pages 241-241
Linear Elasticity: General Considerations and Boundary-Value Problems (Ciprian D. Coman)....Pages 243-280
Compatibility of the Infinitesimal Deformation Tensor (Ciprian D. Coman)....Pages 281-318
Torsion (Ciprian D. Coman)....Pages 319-370
Two-Dimensional Approximations (Ciprian D. Coman)....Pages 371-418
Special Two-Dimensional Problems: Unbounded Domains (Ciprian D. Coman)....Pages 419-458
Back Matter ....Pages 459-519