Theory of elasticity

Garant předmětu:

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Department of Mechanics, Biomechanics and Mechatronics

Synopsis:

The objective of this course is an introduction to the theory and applications of linear elasticity.It also provides the foundation for pursuing other solid mechanics courses such as theory of plasticity, fracture mechanics, composite structures, theory of plates and shells or continuum mechanics. This course introduces the basic definitions of stress and strain tensors used in the linear theory of elasticity, determines the principal stress and strain, derives equilibrium equations, compatibility conditions for strain tensor, postulates the constitutive relations for linear elastic material (generalized Hooke's law).The governing differential equations of elasticity are derived including the Navier's equation expressed in terms of the displacement vector and the Beltrami-Michell's equation expressed in terms of the stress tensor. Next, two-dimensional problems in cartesian and cylindrical coordinate systems is considered andthe Airy stress function is introduced for the solution of these problems. A few useful application are studied such as bending of a beam using the Airy stress function in the form of a polynomial, the stress distibution in a plate with small circular hole submitted to a uniform tension, the stress distibution for a concentrated vertical force action on a horizontal straight boundary, the stress distibution in a wedge due to a concentrated force at its apex. Finally, a brief introduction to the energy principles in solid mechanics is presented including the principles of virtual displacements and virtual forces.

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Study materials:

P.Reif. Základy matematické teorie pružnosti, ČVUT, Praha, (1980)

M. Brdička, L. Samek, B. Sopko. Mechanika kontinua, Academia, (2000)

I.S.Sokolnikoff. Mathematical Theory of Elasticity, McGraw-Hill, (2nd edition), (1956)

J. Plešek. Mechanika kontinua, přednášky pro kurs FS ČVUT, Praha, (2012)

F. Kuba. Teorie pružnosti a vybrané aplikace, SNTL, Praha, (1982)

D.S. Chandrasekharaiah, L. Debnath. Continuum Mechanics, Academic Press, (1994)

S.P. Timoshenko, J.N. Goodier. Theory of elasticity, McGraw-Hill, (3rd edition), (1970)

A. Mendelson. Plasticity: Theory and Appplication, The Macmillan Company, (1968)

J. Nečas, I. Hlaváček. Mathematical Theory of Elastic and Elasto-plastic bodies: an Introduction, Elsevier (Studies in Applied Mechanics), (1981)

J. Nečas, I. Hlaváček. Úvod do matematické teorie pružných a pružně plastických těles, SNTL, Praha, (1983)

G.T. Mase, G.E. Mase. Continuum Mechanics for Engineers, CRC Press, (2rd edition), (1999)

J.R. Barber. Elasticity, Kluwer Academic Publishers, (2rd edition), (2002)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• 13 136 NSTI MMT 2012 základ (compulsory course in the program)
• 14 141 NSTI AME 2012 základ (compulsory course in the program)
• 16 151 NSTI BLP 2012 základ (compulsory course in the program)