Fall 2006

I would like to recommend "Elasticity: Theory, Applications, and Numerics" by Prof. Martin H. Sadd as a reference for ES240. The book, as its name indicated, is mainly focused on elasticity theory and its applications, but also discusses numerical methods such as finite element method and boundary element method.

Prof. Martin H. Sadd, organized the book into two parts: I. foundations, and II Advanced topics. In part I, the book clearly outlines the basic equations of elasticity, i.e. strain/displacement relation, Hooke's law, and equilibrium equation. The other context of part I is devoted to the formulation and solution of two-dimensional problems. This structure matches the progress of our class very well.

The second part of the book begins with the discussion of anisotropic elasticity, thermo-elasticity, and micromechanics. These topics are complementary to the notes of ES240, and helpful in solving homework problems. In its last chapter, the book introduced finite element method and boundary element method.

Book Title: Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue (Second Edition, Third Edition released earlier this year)

Author: Norman E. Dowling

Amazon.com Review Link

The book starts with a general overview and introduction to the mechanics of materials, but later emphasizes deformation, fracture and fatigue of materials. The following is a list of the chapters in the second edition:

(1) Introduction- Discusses types of material failure, design and materials selection, technological challenges, and the economic importance of fracture.

A word file is attached.

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“An Introduction to the Mechanics of Solids” by S. H. Crandall, N.C. Dahl, and T. J. Lardner

As the title explains, this book shows very basics of the solid mechanics. The book has a good coverage of the concepts of primary elements of mechanics, the three equations, some environmental effect, and examples of torsion, bending, and buckling. This book elaborately explains/proofs several important equations, whose procedures tend to be skipped in many courses due to time limitation. Various case studies/problems accompanied with suitable figures have always helped me to get better senses. It is also easy to find what I am looking for in the book with neatly sorted tables and index. And most importantly, I like this book since the book discusses engineering applications and the limitations of these models.

The materials given in ES240 exceed the range that this book can cover, but this book still is a good resource to go back to when I forget the basics since my sophomore year when I used as our textbook for the materials and structures.

26. Stress-strain relations under the plane strain conditions

27. Getting weak: derive weak statements from differential equations

28. Potential energy and Rayleigh -Ritz method

29. Constant strain triangle

30. Gaussian quadrature

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So besides using Timoshenko (which is basically the bible of solid mechanics), I have been using Slaughter's The Linearized Theory of Elasticity which I came across in the Gordon McKay Library.

Unlike some of the other textbooks, there is a big focus put on the theory and the idea behind the examples while still having many worked out problems. The first few chapters give a big refresher course on mathematics and lay the groundwork for what is to be taught later on.

I came across this book in particular for the in depth coverage of Airy Stress Functions.

The book is broken into 11 chapters:

Review of Mechanics of Materials
Mathematical Preliminaries
Kinematics
Forces and Stress
Constitutive Equations
Linearized Elasticity Problems
2D Problems
Torsion of Noncircular Cylinders
3D Problems
Variational Methods
Complex Variable Methods

The notes are attached. Return to the outline of the course.

If you prefer to learn tensors in solid mechanics, Nye's book is recommended.

A word file is attached.

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21. A fiber in an infinite matrix

22. Anti-plane shear

23. Saint-Venant's principle for orthotropic materials

24. Plane problems with no length scales

25. More scaling relations: a half space filled with a power-law material

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