Numerical Analysis of Structures

Garant předmětu:

Bořek Patzák

Lecturer:

Bořek Patzák

Tutor:

Tomáš Krejčí, Bořek Patzák, Jan Voříšek

Supervisor:

Department of Mechanics

Synopsis:

Variational principles of mechanics. Method of weighted residuals, conditions of convergence (continuity, integrity). Principles of FEM. Isoparametric elements, area coordinates, numerical integration. Application of method to selected 1D and 2D problems (Elasticity, heat transfer, consolidation). Algorithmic aspects of the method.

Requirements:

Successful completion of a credit test during the semester (written form, must obtain at least 50% of points), written examination test, optional oral test. The points obtained in the credit test and the points obtained in the examination are added together and the final grade is determined on the basis of the points obtained.

Syllabus of lectures:

Introduction, direct solution by the deformation method for 1D elasticity

Strong and weak solutions in 1D

Approximation and integration in 1D

FEM for elastic problem in 1D

FEM for stationary heat conduction in 1D

Non-stationary heat conduction in 1D

Interpolation and approximation in 2D

Two-dimensional heat conduction problem

Two-dimensional elasticity problem

Analysis of beams in 2D, shear locking

Numerical aspects of FEA, aposterior error estimation.

Syllabus of tutorials:

Study Objective:

Students will understand the algorithm of finite element method and will be able to apply it to solution of frames, trusses, and heat conduction problems.

Study materials:

!Z.Bittnar, J.Šejnoha: Numerické metody mechaniky 1, Vydavatelství ČVUT, 1992

!Z.Bittnar, J.Šejnoha: Numerické metody mechaniky 2, Vydavatelství ČVUT, 1992

!B. Patzák, Studijní pomůcky k předmětu Numerická analýza konstrukcí, https://mech.fsv.cvut.cz/student/, 2021

!J. Fish, T. Belytschko: A First Course in Finite Elements, Wiley, 2007

:https://mech.fsv.cvut.cz/web/?page=podpora-vyuky

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Stavební inženýrství, obor Konstrukce pozemních staveb (compulsory course)
• obor Konstrukce a dopravní stavby, zaměření Inženýrské konstrukce (compulsory course)
• obor Konstrukce a dopravní stavby, zaměření Dopravní stavby (compulsory course)
• Stavební Inženýrství - konstrukce a dopravní stavby, specializace Inženýrské konstrukce (compulsory course)
• Stavební Inženýrství - konstrukce a dopravní stavby, specializace Dopravní stavby a geotechnika (compulsory course)
• Stavební inženýrství - pozemní stavby, specializace Statika pozemních staveb (compulsory course)