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Lecturer(s)
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Vodák Rostislav, RNDr. Ph.D.
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Course content
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Introduction: Thermodynamics laws, derivation of non-linear field theory, coupled thermoelasticity, linearization. Kinematics: bodies, deformations, motions, transport theorems, mass, conservation laws of mass, momentum. Force, stress, Cauchy stress theorem, Finite elasticity: The Piola - Kirchhoff stress, hyperelastic bodies. Linear elasticity, Korn inequality, special 2D cases. Contact problems and inequalities, inclusion and hemivariational inequalities.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Gain knowledge of continuum mechanics problems and realize their essence and principles.
Knowledge Gain knowledge required in order to study and solve continuum mechanics problems.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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D.E. Carlson. (1972). Linear Thermoelasticity, Encyclopedia of Physics, VIa/2. Springer-Verlag, Berlin.
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G. Duvaut, J. L. Lions. (1976). Inequalities in Mechanics and Physics. Springer, Berlin.
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J. Haslinger, I., Hlaváček, J. Nečas, J. Lovíšek. (1982). Riešenie variačných nerovností v mechanike. ALFA, Bratislava.
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J. Haslinger, M. Miettinen, P.D. Panagiotopoulos. (1999). Finite Element Method for Hemivariational Inequalities. Theory, Methods and Applications. Kluwer, Dordrecht.
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J. Nečas, I. Hlaváček. (1983). Úvod do matematické teorie pružných a pružně plastických těles. SNTL, Praha.
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M. E. Gurtin. (1981). An Introduction to Continuum mechanics. Academic Press, New York.
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M. E. Gurtin. (1972). The linear theory of elasticity, Encyclopedia of Physics, VIa. Springer-Verlag, Berlin.
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P.G. Ciarlet. Mathematical Elasticity, Volume I.: Three-dimensional elasticity, II.: Theory of plates. Elsevier, Amsterdam 1986, 1997.
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