Gurantor department | Department of Mechanics | Credits | 10 |

Subject guarantor | prof. Ing. Petr Horyl, CSc., dr.h.c. | Subject version guarantor | prof. Ing. Petr Horyl, CSc., dr.h.c. |

Study level | postgraduate | Requirement | Choice-compulsory |

Year | Semester | winter + summer | |

Web link | Study language | Czech | |

Year of introduction | 2012/2013 | Year of cancellation | 2014/2015 |

Intended for the faculties | FS | Intended for study types | Doctoral |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

HOR80 | prof. Ing. Petr Horyl, CSc., dr.h.c. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Examination | 2+2 |

Combined | Examination | 18+10 |

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.

Lectures

Individual consultations

Project work

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.

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
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

Examples for ANSYS solutions: http://www.mece.ualberta.ca/tutorials/ansys/

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Subject has no prerequisities.

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Examination | Examination |

Show history

Academic year | Programme | Field of study | Spec. | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|

2014/2015 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (2301V013) Robotics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (2301V013) Robotics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2301) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2301) Mechanical Engineering | (3901V003) Applied Mechanics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2301) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P2301) Mechanical Engineering | (3901V003) Applied Mechanics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2301) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2301) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2301) Mechanical Engineering | (3901V003) Applied Mechanics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2301) Mechanical Engineering | (3901V003) Applied Mechanics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2301V013) Robotics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2301V013) Robotics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2301V013) Robotics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2301V013) Robotics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2301) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2301) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2301) Mechanical Engineering | (3901V003) Applied Mechanics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P2301) Mechanical Engineering | (3901V003) Applied Mechanics | K | Czech | Ostrava | Choice-compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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