Computational Mechanics

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Materials

Synopsis:

Abstract:

Theory and application of the finite element method in the mechanics of deformable bodies. Lectures are accompanied by model examples which aims to demonstrate the basic principles of building the correct numerical models.

Requirements:

Syllabus of lectures:

Outline:

Basic terms and concepts (discrete vs. continuous system, set of algebraic vs differential equations, direct vs variational approach), formulation of the displacement-based finite element method, classification of tasks and finite elements, boundary conditions, linear and nonlinear analyses, material nonlinearities, geometric nonlinearities (large displacements and strains, strain and stress quantities), contact (Lagrange multiplier and penalty method, friction), static analysis, dynamic analysis (implicit and explicit techniques), eigenvalue problem, good practice (modelling assumptions, meshing strategy, convergence, sources of errors), advanced modelling techniques.

Keywords:

Solid continuum mechanics, numerical methods, finite element method

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1]Bathe, K.-J.: Finite Element Procedures, 2nd edition 4th printing, K.J. Bathe, Watertown, MA, 2016, 1065 p.,

ISBN 978-0-9790049-5-7 (available online: http://web.mit.edu/kjb/www/Books/FEP_2nd_Edition_4th_Printing.pdf)

Recommended references:

[2]Zienkiewicz, O.C. –Taylor, R.I. – Zhu, J.Z.: The Finite Element Method: Its Basis and Fundamentals, 7th edition, Butterworth-Heinemann, 2013, 756 p., ISBN: 978-1856176330.

[3]Belytschko, T. – Liu, W.K. – Moran, B. – Elkhodary, K.: Nonlinear Finite Elements for Continua and Structures, 2nd edition, Wiley, 2014, 830 s., ISBN: 978-1118632703.

[4]Reddy, J.: Introduction to the Finite Element Method, 4th ed. McGraw-Hill Education, 2018, 816 s., ISBN: 978-1259861901.

Media and tools:

General purpose FE codes, e.g. MSC.Marc (in PC lab), Calculix, Code_Aster, Cast3M (available for free)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Fyzikální inženýrství materiálů (compulsory course in the program)