|
Lecturer(s)
|
-
Paščenko Petr, prof. Ing. Ph.D.
|
|
Course content
|
Analytical methods versus numerical methods ? advantages, disadvantages, basis definitions of matrix calculus and calculus of variation. Energy principals (Lagrange, Castiglian), Ritz?s variation method. Principal of FEM, duality (deformation variant, force variant), element stiffness matrix. The overall stiffness matrix, load (mechanical, thermal), boundary conditions, system of linear equations and its solution. Finite elements and their usage ? beam elements. Finite elements and their usage ? plane elements, shell elements. Finite elements and their usage ? solid elements, special elements (MASS, GAP, STRING, axially-symmetric element). Linear statics, displacements, strains, stresses. Result evaluation of linear statics, stress categories, strength, fatigue. Presentation of some real technical problems, usage of various types of elements. Stability, eigenproblems, eigenvalues, eigenmodes. Natural frequencies and natural modes, signification of particular natural frequencies and modes, modal mass. Natural frequencies and modes - methods of solution. Summary of the subject.
|
|
Learning activities and teaching methods
|
|
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Demonstration
|
|
Learning outcomes
|
The aim of this subject is to introduce students into the finite element method (FEM) applied to problems of linear statics and natural vibration of structures. The students will learn a theoretical bases of the method and to solve individually practical tasks by means of the computer program COSMOS/M, COSMOSWorks, as well.
Graduating the subject, the student can solve individually simpler tasks of linear statics and natural vibration by means of the computer program ANSYS. Based on the achieved results of the analysis, the student is able to evaluate strength and fatigue according to valid norms and standards or according to modern scientific and technical knowledge, respectively.
|
|
Prerequisites
|
Basic knowledge of mathematics (linear algebra ? matrix calculus, eigenproblems), numerical mathematics (solution of linear equation system, interpolation), mechanics (statics, kinematics, dynamics, strength of material, thermo-mechanics, eventually) is supposed.
|
|
Assessment methods and criteria
|
Oral examination
The requirements will be defined by lecturer.
|
|
Recommended literature
|
-
Bitnar, Řeřicha. Metoda konečných prvků v dynamice konstrukcí, SNTL Praha 1981. SNTL Praha, 1981.
-
Kolář,V., Kratochvíl,J.,Leitner,F.,Ženíšek,A. Výpočet plošných a prostorových konstrukcí metodou konečných prvků.. SNTL Praha, 1979.
-
Nakasone,Y., Yoshimoto, S. Engineering Analysis with ANSYS Software.. Elsevier, 2006. ISBN 0-7506-6875-X.
-
Servít,R., Drahoňovský,Z., Šejnoha,J.,Kufner,V. Teorie pružnosti a plasticity I,II, SNTL Praha, 1984.. SNTL Praha, 1984.
-
Zienkiewicz, O. C. The finite element method for solid and structural mechanics Amsterdam: Elsevier Butterworth-Heinemann, 2005. ISBN 0-7506-6321-9. Amsterdam: Elsevier Butterworth-Heinemann, 2005. ISBN 0-7506-6321-9.
-
Zienkiewicz,O.C. The Finite Element Method in Engineering Science. N.Y.,London,McGraw Hill, 1971.
|