Course: Continuum Mechanics 1

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Course title Continuum Mechanics 1
Course code KMA/MK1M
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Fürst Tomáš, RNDr. Ph.D.
  • Vodák Rostislav, RNDr. Ph.D.
Course content
A. Elasticity primer: Elasticity in single space dimension Lame equations will be derived from physical principles in 1D Existence, uniqueness and stability of the solution several methods for numerical solution B. Linear elasticity in 3D Lame equations in 3D virtual work principle and the weak formulation proof of the existence, uniqueness and stability of the weak solution in 3D

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Semestral Work - 25 hours per semester
  • Preparation for the Exam - 45 hours per semester
Learning outcomes
Understand the mathematical tools for continuum description
Application Apply differential and intergral calculus of functions of several variables to flow modeling and elasticity.
Prerequisites
Classical calculus

Assessment methods and criteria
Oral exam, Seminar Work

Credit: course work. Exam (combined): written test - examples, oral exam.
Recommended literature
  • C. Truesdell. (1975). A first course in rational mechanics (v ruštině). Izdatelstvo Mir, Moskva.
  • D. E. Carlson. (1972). Linear Thermoelasticity Encyclopedia of Physics VIa/2. Springer-Verlag Berlin.
  • Feynmann R.P. (2003). Feynmannovy přednášky z fyziky I.-III.. Fragment.
  • G. Duvaut, J. L. Lions. (1976). Inequalities in Mechanics and Physics. Springer, Berlin.
  • J. Haslinger, I. Hlaváček, J. Nečas, J. Lovíšek. (1982). Riešenie variačných nerovností v mechanike. ALFA Bratislava.
  • J. Kopáček. (2001). Matematická analýza pro fyziky III. Matfyzpress.
  • J. Nečas, I. Hlaváček. (1983). Úvod do matematické teorie pružných a pružně plastických těles. SNTL, Praha.
  • M. E. Gurtin. (1981). An Introduction to Continuum mechanics. Academic Press, New York.
  • M. E. Gurtin. (1972). The linear theory of elasticity, Encyclopedia of Physics, VIa. Springer-Verlag, Berlin.
  • P. G. Ciarlet. (1986). Mathematical Elasticity, Volume I.: Three-dimensional elasticity. Elsevier Amsterdam.
  • P. G. Ciarlet. (1997). Mathematical Elasticity, Volume II.: Theory of plates. Elsevier Amsterdam.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses - Summer
Faculty of Science Mathematics and Applications (1) Mathematics courses 3 Summer