fem for engineering applications se1025 · engineering applications? •solid mechanics and heat...
TRANSCRIPT
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FEM for engineering applications SE1025
Erik Olsson
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Teachers
• Erik Olsson, Lecturer and course organizer ([email protected]) Room 6380
• MohammadAli Asgharzadeh, Tutorials and computer labs ([email protected])
• Elsiddig Elmukashfi, computer labs, ([email protected])
• Artem Kulachenko, examiner, ([email protected])
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Schedule
• One change: Tutorial 5 and Lecture 14 are switched
T5: 1/10 10-12
L14: 2/10 13-15
• Note that Lecture 13 starts at 14
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Literature
• Course compendium – pdf on the web site
• Compendium with example problems – Buy at course expedition for 80 SEK
• Course book The Finite Element Method E-book
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What is the finite element method?
And why use it?
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FEM
• An approximate method for solving differential equations
• “Invented” in 1943
• Development of FEM codes in 1960
• Development Today: Large deformations, fracture, solid-fluid interaction etc.
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FEM – basic idea
• Divide the problem in small domains (elements)
• Simple approximation of the fields in the elements
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What can we do?
• Accurately compute deformations, stresses, temperature distribution…
• If we now the material behavior
• Predicting if it will fail – difficult problem
• FEM is a tool for when solving problems but does not solve the problem!
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Engineering applications?
• Solid Mechanics and Heat conduction
• Applicable to: - Electrostatics - Diffusion - Piezo-electricity - …
• Every physical phenomena controlled by differential equations
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Contents
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Energy methods
• 2 Lectures 1/2 tutorial and 1/2 home assignment
• Elastic problems with point loads
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Matrix formulated Structure/Solid Mechanics
• 2 Lectures 1/2 tutorial and 1/2 home assignment
• FEM ”light”
• Network of springs
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Deriving FEM equations
• Lecture 5 and part of tutorial 2
• From equilibrium + compatibility + material to matrix equations
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FEM for 1D elements
• Trusses and beams
• Lecture 6-10 and tutorial 2-3
• Home assignment 2.1
• One workshop
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FEM for 2D/3D elements
• Mostly 2D, 3D requires 24x24 matrices
• Lecture 11-15 and tutorial 4-6
• Home assignment 2.2 and 3
• Evaluating results
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FEM for heat conduction
• Lecture 16-17 and tutorial 7
• One workshop
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What is the course about then?
• Methods for solving problems in the computer - Algorithms
• Interpret and knowing if the results are useful!
• Understand what is going on in the program
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Don’t forget to register for the course
KTH homepage-> my pages