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Lecturer(s)
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Paščenko Petr, prof. Ing. Ph.D.
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Tomek Petr, doc. Ing. Ph.D.
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Course content
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Analytical methods versus numerical methods - advantages, disadvantages, basic 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 (critical loads), eigenmodes. Natural frequencies and natural modes, signification of particular natural frequencies and modes, modal mass. Natural frequencies and modes - methods of solution. Course summary.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The aim of this course is to introduce students to the Finite Element Method (FEM) applied to problems of linear statics, loss of stability and natural vibration of structures. The students will acquire the theoretical basis of the method and they will also solve practical tasks by means of the computer programs COSMOS/M and COSMOSWorks individually.
On completing the FEM-I course, the student can solve simple tasks of linear statics and natural vibration by means of the computer program COSMOS/M, COSMOSWorks individually. Based on the achieved results of the analysis, the student is able to evaluate strength and fatigue according to valid norms and standards or more precisely according to modern scientific and technical knowledge.
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Prerequisites
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The following basic knowledge is expected: mathematics (linear algebra - matrix calculus, eigenproblems), numerical mathematics (solution of linear equation system, interpolation), mechanics (statics, kinematics, dynamics, strength of material, thermo-mechanics).
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Assessment methods and criteria
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unspecified
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Recommended literature
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BATHE, WILSON. Numerical Methods in Finite Element Analysis..
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BITNAR , ŘEŘICHA. Metoda konečných prvků v dynamice konstrukcí..
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HORYL, P. Inženýrské základy MKP. Studijní materiál..
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HORYL, P. MKP jako nástroj řešení problematiky ztráty stability tvaru. Studijní materiál..
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Kolář,V., Kratochvíl,J.,Leitner,F.,Ženíšek,A. Výpočet plošných a prostorových konstrukcí metodou konečných prvků.. SNTL Praha, 1979.
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Servít,R., Drahoňovský,Z., Šejnoha,J.,Kufner,V. Teorie pružnosti a plasticity I,II, SNTL Praha, 1984.. SNTL Praha, 1984.
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ZIENKIEWICZ O. C., Taylor, R. L. The Finite Element Method for Solid and Structural Mechanics.
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Zienkiewicz,O.C. The Finite Element Method in Engineering Science NY, London,MCGRAW Hill 1971. N.Y.,London,McGraw Hill, 1971.
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