| Course Unit Code | Course Unit Title | Number of ECTS Credits Allocated |
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| 337-0903/01 | Finite Element Method in Mechanics | 10 ECTS credits |
| Type of Course Unit | Choice-compulsory |
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| Level of Course Unit | Third Cycle |
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| Year of Study | First Year |
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| Semester when the Course Unit is delivered | Winter, Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech, English |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| HOR80 | prof. Ing. Petr Horyl, CSc., dr.h.c. |
| Learning Outcomes of the Course Unit |
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Students will extend and make deeper their theoretical knowledge of the
background of FEM and the numerical procedures that lead to the practical use
of the method. Especially the problematics of solving nonlinear tasks will be
deepen. |
| Recommended Optional Programme Components |
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| Common optional components are not offered, students of special interest can participate in departmental activities or can arrange consulting hours with lecturer. |
| Course Contents |
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Variational Methods. Principle of stationary potential energy. Problems having many degrees of freedom (DOF). Potential energy of an elastic body. The Rayleigh-Ritz method. Galerkin and other weighted residual methods (MWR). Examples: Uniform bar, Beam dynamics. Galerkin FEM in two dimensions.
Bar and Beam Elements. Displacement-based elements. Shape functions. Stiffness matrix. Properties of stiffness matrices. Timoshenko beam element. Boundary conditions. Applied mechanical loads. Equilibrium equations. Stresses.
FEM Concepts. Elements of arbitrary orientation – local and global matrices. Assembly of elements ( assembly and structure node numbers ). Exploiting sparsity, numbering and sparsity. Solution of equations. Structural symmetry. Connecting dissimilar elements. Eccentric stiffeners. Rigid elements.
Basic Elements. Preliminaries: Strain-displacement relations, Stress-strain relations. Interpolation and shape functions. Formulas for element matrices. Linear triangle ( constant-strain triangle CST ). Quadratic triangle ( LST ). Bilinear rectangle
( Q4 ). Quadratic rectangle ( Q8, Q9 ). Rectangular solid elements. Choice of interpolation functions. Nature of a finite element solution.
Isoparametric Elements. Example- bar element. Bilinear quadrilateral ( Q4 ). Transformation. [B] matrix and stiffness matrix. Numerical integration and Gauss quadrature. One, two and three dimensions. Stiffness matrix integration. Static condensation. Stress calculation.
Analysis of axisymmetric solids. Elasticity relations. Axisymmetric solid elements. Loads without axial symmetry.
FEM in Structural Dynamics. Dynamic equation. Mass and damping matrices. Consistent and lumped (diagonal) mass matrix. Proportional damping, Eigenfrequencies (natural frequencies), eigenmodes (mode shapes) and solutions method. Reduction of the number of DOF.
Response History. Modal methods. Harmonic response. Direct integration methods-explicit or implicit. Central differences-stability conditions. Newmark family of methods.
Heat Transfer and Selected Fluid Problems. Heat transfer: introduction. Finite element formulation. Transient thermal analysis – Modal method and direct integration. Acoustics and FE formulation. Boundary absorption. Fluid - structure interaction.
Buckling. Geometric nonlinearity-Green strain. Energy considerations. Initial stress stiffness matrix ( geometric stiffness matrix ). Linear buckling. Imperfection. Nonlinear buckling.
Nonlinearity. Newton-Raphson method. Arc-length method. Convergence criteria. Problems of gaps and contact.
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| Recommended or Required Reading |
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| Required Reading: |
|---|
Cook R. D., Malkus D.S., Plesha M.E., Witt R.J. CONCEPTS AND APPLICATIONS OF
FINITE ELEMENT ANALYSIS. 4th edition. J. Wiley & Sons, Inc. NY, 2002, p. 719,
ISBN 0-471-35605-0
Examples for ANSYS solutions: http://www.mece.ualberta.ca/tutorials/ansys/
REDDY, J.N., An Introduction Nonlinear Finite Element Analysis, Oxford
University Press, 2004, p. 463, ISBN 0-19-852529-X
BHATTI,M.A., Advanced Topics in Finite Element Analysis of Structures: with
Mathematica and Matlab Computations, Wiley, 2006, p.590, ISBN-13 978-0-471-
64807-9
|
Cook R. D., Malkus D.S., Plesha M.E., Witt R.J. CONCEPTS AND APPLICATIONS OF
FINITE ELEMENT ANALYSIS. 4th edition. J. Wiley & Sons, Inc. NY, 2002, p. 719,
ISBN 0-471-35605-0
Crisfield M. A. Non-linear Finite Element Analysis of Solids and Structures,
Vol. 1: Essentials. J. Wiley & Sons, Inc. Chichester, UK. 1991
Crisfield M. A. Non-linear Finite Element Analysis of Solids and Structures,
Vol. 2: Advanced Topics. J. Wiley & Sons, Inc. Chichester, UK. 1997
Zhi-Hua Zhong. Finite Element Procedures for Contact-Impact Problems. Oxford
University Press, 1993, p. 371, ISBN 0-19 856383-3
REDDY, J.N., An Introduction Nonlinear Finite Element Analysis, Oxford
University Press, 2004, p. 463, ISBN 0-19-852529-X
WRIGGERS, P., Nichtlineare Finite-Element Metoden, Springer, 2005, p. 495, ISBN
3-540-67747
BHATTI,M.A., Advanced Topics in Finite Element Analysis of Structures: with
Mathematica and Matlab Computations, Wiley, 2006, p.590, ISBN-13 978-0-471-
64807-9
Examples for ANSYS solutions: http://www.mece.ualberta.ca/tutorials/ansys/
|
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Project work |
| Assesment methods and criteria |
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| Tasks are not Defined |
| Work placement(s) |
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| Course does not contain work placement. |
