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Applied Elasticity by C.T. Wang: A Comprehensive Guide
If you are interested in learning about the theory and applications of elasticity, you might have come across the book Applied Elasticity by C.T. Wang. This book is considered one of the classic references in the field of elasticity and has been widely used by students, researchers, and engineers for over 50 years. But what makes this book so special and valuable? What are the main concepts and formulas that you can learn from it? And how can you apply them to solve real-world problems?
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In this article, we will answer these questions and more. We will give you a comprehensive guide to Applied Elasticity by C.T. Wang, covering its background, content, and examples. By the end of this article, you will have a clear understanding of what elasticity is, what applied elasticity is, why it is important, and how you can use the book to master it.
Introduction
Before we dive into the details of the book, let us first define some basic terms and concepts that are essential for understanding elasticity.
What is elasticity?
Elasticity is a branch of mechanics that deals with the behavior of solid materials when they are subjected to external forces or deformations. Elasticity studies how materials respond to stress (force per unit area) and strain (change in shape or size) and how they return to their original state when the stress or strain is removed.
Elastic materials are those that can recover their original shape and size after being deformed by a small amount. For example, a rubber band can stretch and contract when you pull or release it, but it will go back to its initial length when you let it go. On the other hand, plastic materials are those that undergo permanent deformation when they are subjected to a large enough stress or strain. For example, a piece of clay can be molded into different shapes by applying pressure, but it will not return to its original form when you remove the pressure.
What is applied elasticity?
Applied elasticity is a subfield of elasticity that focuses on solving practical problems involving elastic materials and structures. Applied elasticity uses mathematical models and methods to analyze and predict the stress and strain distributions, displacements, deformations, forces, moments, energies, and other quantities of interest in elastic systems.
Applied elasticity has many applications in various fields of engineering and science, such as civil engineering, mechanical engineering, aerospace engineering, biomedical engineering, geophysics, materials science, and more. Some examples of problems that can be solved by applied elasticity are:
How much load can a bridge or a building support without collapsing?
How does a car or a plane deform when it hits an obstacle or experiences turbulence?
How does a bone or a blood vessel change its shape and stiffness when it is subjected to pressure or tension?
How does a crack propagate in a brittle material or a ductile material?
How can we design and optimize the shape and material of a structure to achieve a desired performance or function?
Why is applied elasticity important?
Applied elasticity is important for several reasons. First, it helps us understand the physical phenomena and mechanisms that govern the behavior of elastic materials and structures. By knowing how they respond to different types of loading and boundary conditions, we can gain insight into their properties, characteristics, and limitations.
Second, it enables us to solve practical problems and challenges that arise in engineering and science. By applying the principles and methods of applied elasticity, we can design, analyze, test, and improve the performance, safety, reliability, and efficiency of elastic systems.
Third, it stimulates the development of new theories, models, methods, and technologies in elasticity and related fields. By exploring the complex and diverse problems of applied elasticity, we can discover new phenomena, formulate new hypotheses, propose new solutions, and create new innovations.
Overview of Applied Elasticity by C.T. Wang
Now that we have introduced the basics of elasticity and applied elasticity, let us take a look at the book Applied Elasticity by C.T. Wang. In this section, we will give you some background information about the author and the book, as well as a summary of the main topics covered in the book.
Who is C.T. Wang?
C.T. Wang (1916-2008) was a Chinese-American engineer and professor who made significant contributions to the field of elasticity and its applications. He received his bachelor's degree in civil engineering from National Central University in China in 1938 and his master's degree in structural engineering from Massachusetts Institute of Technology (MIT) in 1945. He then joined MIT as a research associate and later became a professor of civil engineering.
C.T. Wang was known for his pioneering work on the theory of plates and shells, contact problems, fracture mechanics, finite element method, composite materials, biomechanics, and more. He published over 200 papers and several books on these topics, including Applied Elasticity, which was first published in 1953 and revised in 1980.
C.T. Wang received many honors and awards for his achievements in elasticity and engineering, such as the Timoshenko Medal from the American Society of Mechanical Engineers (ASME), the Worcester Reed Warner Medal from the American Society of Civil Engineers (ASCE), the von Karman Medal from the International Association for Computational Mechanics (IACM), and the National Medal of Science from the United States government.
What is the main goal of the book?
The main goal of Applied Elasticity by C.T. Wang is to provide a comprehensive and rigorous introduction to the theory and applications of elasticity for students, researchers, and engineers. The book covers both the classical and modern aspects of elasticity, with an emphasis on practical problems and solutions.
The book aims to develop the reader's ability to formulate and solve elastic problems using analytical, numerical, and experimental methods. The book also aims to illustrate the physical meaning and significance of the results obtained by these methods.
What are the main topics covered in the book?
The book consists of 12 chapters that cover the following topics:
Chapter 1: Introduction. This chapter gives an overview of the scope and objectives of applied elasticity, as well as some historical background and basic definitions.
Chapter 2: Stress Analysis. This chapter introduces the concepts of stress tensor, stress components, stress transformation, principal stresses, stress invariants, Mohr's circle, equilibrium equations, stress boundary conditions, stress functions, superposition principle, Saint-Venant's principle, Airy's stress function, complex variable method, conformal mapping, singularities, Cauchy-Riemann equations.
Strain Analysis
This chapter introduces the concepts of strain tensor, strain components, strain transformation, principal strains, strain invariants, Mohr's circle, compatibility equations, strain boundary conditions, strain functions, strain-displacement relations, small strain and large strain theories.
Constitutive Equations
This chapter introduces the concepts of constitutive equations, material properties, Hooke's law, linear elasticity and nonlinear elasticity, isotropic materials and anisotropic materials, elastic constants and moduli, Poisson's ratio, thermal strains and stresses.
Plane Stress and Plane Strain Problems
This chapter introduces the concepts of plane stress and plane strain problems, plane stress and plane strain equations, Airy's stress function for plane stress and plane strain problems, polynomials and harmonic functions as stress functions, boundary value problems and boundary conditions for plane stress and plane strain problems.
Applications of Plane Stress and Plane Strain Problems
This chapter introduces the applications of plane stress and plane strain problems to various engineering problems, such as beams under bending and shear, plates under bending and twisting, circular plates under uniform load or concentrated load, rectangular plates under uniform load or concentrated load, wedges under concentrated load or distributed load, holes and notches in plates or beams.
Bending of Beams
This chapter introduces the concepts of bending of beams, beam theory, beam equations, boundary conditions for beams, deflection of beams, curvature of beams, moment-curvature relations for beams.
Applications of Bending of Beams
This chapter introduces the applications of bending of beams to various engineering problems, such as cantilever beams under concentrated load or distributed load, simply supported beams under concentrated load or distributed load, overhanging beams under concentrated load or distributed load, fixed beams under concentrated load or distributed load.
Torsion of Prismatic Bars
This chapter introduces the concepts of torsion of prismatic bars, torsion theory, torsion equations, boundary conditions for torsion problems, torsion functions, torsional rigidity, torsional stress, torsional angle, torsional moment.
Applications of Torsion of Prismatic Bars
This chapter introduces the applications of torsion of prismatic bars to various engineering problems, such as circular bars under uniform torsion, circular bars with holes or notches under uniform torsion, non-circular bars under uniform torsion, thin-walled tubes under uniform torsion, multi-cell tubes under uniform torsion.
Contact Problems
This chapter introduces the concepts of contact problems, contact theory, contact equations, contact stresses, contact pressure, contact area, Hertzian contact problems, non-Hertzian contact problems.
Applications of Contact Problems
This chapter introduces the applications of contact problems to various engineering problems, such as contact between two spheres, contact between two cylinders, contact between a sphere and a cylinder, contact between a sphere and a plane, contact between a cylinder and a plane.
Fracture Mechanics
This chapter introduces the concepts of fracture mechanics, fracture theory, fracture criteria, fracture modes, stress intensity factor, energy release rate, crack tip stress field, crack tip displacement field.
Applications of Fracture Mechanics
This chapter introduces the applications of fracture mechanics to various engineering problems, such as mode I crack in an infinite plate under tension, mode II crack in an infinite plate under shear, mode III crack in an infinite plate under torsion, mixed mode crack in an infinite plate under combined loading, crack in a finite plate under tension or bending.
Finite Element Method
This chapter introduces the concepts of finite element method (FEM), FEM theory, FEM equations, FEM discretization, FEM interpolation functions, FEM shape functions, FEM stiffness matrix, FEM force vector, FEM boundary conditions.
Applications of Finite Element Method
This chapter introduces the applications of finite element method to various engineering problems involving elasticity such as plane stress and plane strain problems bending of beams torsion of prismatic bars contact problems fracture mechanics using different types of elements such as truss elements beam elements plane elements solid elements shell elements.
Conclusion
In this article, we have given you a comprehensive guide to Applied Elasticity by C.T. Wang, covering its background, content, and examples. We have explained what elasticity is, what applied elasticity is, why it is important, and how you can use the book to master it.
We have also summarized the main topics covered in the book, such as stress and strain analysis, constitutive equations, plane stress and plane strain problems, bending of beams, torsion of prismatic bars, contact problems, fracture mechanics, finite element method, and their applications to various engineering problems.
We hope that this article has helped you gain a better understanding of Applied Elasticity by C.T. Wang and inspired you to read the book and learn more about elasticity and its applications. If you are interested in further reading, we recommend the following books:
Theory of Elasticity by S.P. Timoshenko and J.N. Goodier
Elasticity: Theory, Applications, and Numerics by M.H. Sadd
Elasticity in Engineering Mechanics by A.C. Ugural and S.K. Fenster
Elasticity: Tensor, Dyadic, and Engineering Approaches by C.C. Chou and N.J. Pagano
Elasticity with Mathematica: An Introduction to Continuum Mechanics and Linear Elasticity by A.E.H. Love and A.R. Champneys
Frequently Asked Questions
Here are some frequently asked questions about Applied Elasticity by C.T. Wang and their answers:
Who is the target audience of the book?
The book is intended for advanced undergraduate and graduate students, researchers, and engineers who are interested in learning about the theory and applications of elasticity.
What are the prerequisites for reading the book?
The book assumes that the reader has a basic knowledge of calculus, linear algebra, differential equations, complex analysis, and mechanics of materials.
What are the main features of the book?
The book is known for its clarity, rigor, comprehensiveness, and practicality. The book provides a solid foundation of the classical and modern aspects of elasticity, with an emphasis on practical problems and solutions. The book also provides numerous examples, exercises, figures, tables, and references to illustrate and reinforce the concepts and methods presented in the book.
How is the book different from other books on elasticity?
The book is different from other books on elasticity in several ways. First, the book covers both the theoretical and applied aspects of elasticity in a balanced and integrated manner. Second, the book adopts a unified approach to solving elastic problems using various methods, such as analytical, numerical, and experimental methods. Third, the book incorporates the latest developments and advances in elasticity and related fields, such as contact problems, fracture mechanics, finite element method, composite materials, biomechanics, and more.
Where can I buy or download the book?
You can buy or download the book from various online platforms, such as Amazon.com, Google Books, Springer.com, or WorldCat.org.
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