Welcome to this open online course on the theory of elasticity. In this course, we will help you to get familiar with the major contents of elasticity theory. As you may already know, elasticity is one of the most important courses in many engineering subjects such as mechanics, civil engineering, mechanical engineering, transportation engineering and materials science and engineering. This course will require some reasonable background knowledge in advanced mathematics, linear algebra, statics and mechanics of materials. The major contents of this course involve the fundamentals of tensor, three and two-dimensional theory of elasticity, governing equations, boundary conditions, typical solution strategy and solution method, as well as many illustrating examples. This course particularly emphasizes on the integration of mathematical knowledge and mechanical principles. Throughout the process, we will go through the origin, development and maturation of the basic equations of elasticity, such that you can get a deep understanding about the logic flow of this theory. If you wish to lay a solid mathematical foundation for the further learning of mechanics courses, taking this course is a wise choice. Upon completion of this course, your abilities of calculating, analyzing and self-learning mechanical knowledge will be enhanced. You will also able to propose some new mechanical models and make some routine analysis by yourself. This course will also prepare you better for more advanced courses in mechanics and engineering, both in terms of theory and engineering practice.

Upon the completion of this course, students are expected to: (1) understand the assumptions, research objects and major topics of elasticity theory; (2) familiarize with the governing equations, boundary conditions, formulations and conventional analytical solution methods; (3) know how to solve simple two and three-dimensional elastic problems. Through these rigorous trainings, students’ capabilities on analyzing, calculating and self-learning mechanics problems can be significantly solidified. As a result, students should be more prepared for mechanics courses at a more advanced level and more capable of conducting research activities on solid mechanics.

Background knowledge in advanced mathematics, linear algebra, statics and mechanics of materials is desired

M.H. Sadd, Elasticity: Theory, Applications, and Numerics, 2005, Elsevier. (A modern textbook, using tensor notation, that is relatively easier to follow.)

Y.C. Fung, Foundations of Solid Mechanics, Prentice Hall, 1965. (A deep explanation on the deformation and motion of solids. Explained and proved many fundamental principles on the subject matter.)

S.P. Timoshenko & J.N. Goodier, 1970, Theory of Elasticity, 3rd ed., McGraw-Hill. (A classic textbook, using older notation, emphasizing practical solution of engineering problems.)

I.S. Sokolnikoff, 1956, Mathematical Theory of Elasticity, McGraw-Hill. (This is also a classic textbook, using extensively tensor notation, more emphasis on mathematical methods.)

R.W. Little, 1973, Elasticity, Prentice Hall. (A good textbook emphasizing series solutions, and 3-D problems, uses modern tensor notation. It hosts many interesting problems.)

A.P. Boresi and K.P. Chong, 1987, Elasticity in Engineering Mechanics, Elsevier. (Solid textbook, good discussion of 2-D and 3-D problems.)

A.H. England, 1971, Complex Variable Methods in Elasticity, Wiley-Interscience. (Good textbook for the application of complex variable methods to the solution of 2-D problems.)

N.I. Muskhelishvili, 1975, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff International Publishing. (A huge book, very detailed, the standard reference on the application of complex variable methods to elasticity problems.)

A.K. Mal and S.J. Singh, 1991, Deformation of Elastic Solids, Prentice Hall. (Good, modern textbook.)

A.S. Saada, 1993, Elasticity: Theory & Applications, 2nd ed., Krieger. (Good, modern textbook, includes problems at end of chapter.)

B.A. Boley and J.H. Weiner, 1960, Theory of Thermal Stresses, John Wiley. (The standard reference on thermal stresses in elastic and plastic solids.)

G.L.M. Gladwell, 1980, Contact Problems in the Classical Theory of Elasticity, Sijthoff and Nordhoff. (Emphasis on contact of elastic solids.)

A.E. Green and W. Zerna, 1968, Theoretical Elasticity, Oxford University Press (also in Dover edition, 1992). (If you can master the notation, the book is very well written. Heavy emphasis on mathematical approach.)

L.D. Landau and E.M. Lifshitz, 1986, Theory of Elasticity, 3rd ed., Pergamon Press.

A.E.H. Love, 1944, The Mathematical Theory of Elasticity, Dover Publications. (Older notation, contains a wealth of solved difficult problems. A standard reference.)

T. Mura, 1987, Micromechanics of Defects in Solids, 2nd ed. Martinus Nijhoff. (Exclusive emphasis on the theory of defects in elastic solids, and on various applications of the Eshelby transforming inclusion problem.)

J.F. Nye, 1957, Physical Properties of Crystals, Oxford University Press. (Superb discussion of crystalline anisotropy effects for many material properties, including compliance and stiffness.)

S.G. Lekhnitskii, 1963, Theory of Elasticity of an Anisotropic Elastic Body, Holden Day.

I. Sneddon, 1951, Fourier Transforms, McGraw-Hill (Recently in Dover edition). (Discusses in detail the application of Fourier and Hankel transforms to elasticity solutions for indentation of half-planes and half-spaces.)

S.P. Timoshenko, 1953, A History of Strength of Materials, McGraw-Hill (Recently in Dover edition). (For historical details.)

A.E.H. Love, 1934, A Treatise of the Mathematical Theory of Elasticity, 4th ed., Cambridge University Press. (For historical details.)

Todhunter and Pearson, 1893, History of the Theory of Elasticity, University Press. (For historical details.)