finite element methods (in solid and structural … · k.-j. bathe (1995) finite element procedures...
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Finite Element Methods
(in Solid and Structural Mechanics)
Spring 2014
Prof. Glaucio H. Paulino Donald Biggar Willett Professor of Engineering
Acknowledgements:
J. Kim, Z. Zhang, S. Song, C. Le and K. Park
Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
CEE570 / CSE 551 Class #1
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The slide series for this class has been developed with the help from the following people.
Acknowledgements
Chau Le J. Kim S. Song Z. Zhang
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K. Park
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Content
Teaching Team
Prerequisites
Course Logistics
Course Outline (See Handout)
Course Information (See Handout)
Course Schedule (See Handout)
Course Objectives
Text books
FEM: The big picture
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Paper Handouts
Course outline
Course information
Course schedule
Electronic Handouts
MATLAB
Review of elasticity (CEE471)
This ppt presentation
Handouts
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Note: These
handouts are
clipped together.
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CEE570/CSE551 Teaching Team
Prof. Paulino
Professor
Willett Prof.
of Eng.
Faculty:
CEE, CSE
Instructor TA TA TA TA TA
Sofie Leon Tomas
Zegard
Junho
Chun
Heng Chi Xiaojia
(Shelly)
Zhang
Ph.D.
Student
CEE
Ph.D.
Student
CEE
Ph.D.
Student
CEE
Ph.D.
Student
CEE
Ph.D.
Student
CEE
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CEE 471 (Structural Mechanics)
Hjelmstad, Keith D. Fundamentals of Structural Mechanics 2nd ed., 2005, XIV, 480 p., Hardcover ISBN: 0-387-23330-X
This course is an introduction to basic continuum
mechanics that emphasizes variational formulations and
some basic theoretical/numerical aspects. It provides the
prerequisite information for finite elements for graduate and
advanced undergraduate students in engineering.
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Pre-requisites for CEE570/CSE551: FEM
CEE 471 (Structural Mechanics) Tensors; geometry of deformation; constitutive relations;
energy principles; boundary value problem; beam theory; plate theory; static stability theory; computational methods.
OR
TAM 551 (Solid Mechanics I) Mechanics of elastic deformable bodies, based on the
fundamental concepts of modern continuum mechanics: kinematics, balance laws, constitutive equations; classical small-deformation theory; formulation of initial boundary-value problems of linear elastodynamics and boundary-value problems of linear elastostatics; variational formulations, minimum principles; applications of theory to engineering problems
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Course Logistics
URL:
http://paulino.cee.illinois.edu/fem_login.html
Computer Labs.:
EWS: http://www.ews.uiuc.edu
Software Required (available at EWS)
MATLAB
PATRAN
ABAQUS
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CEE570/CSE551: FEM Class Description
Theory and applications of the finite element method;
General procedure for solving a structural problem using FEM;
Variational Methods; Weighted Residual (WR) Methods
Review of one-dimensional elements;
Techniques for constructing element stiffness matrices;
Various two- and three-dimensional solid elements;
Isoparametric formulation;
Plates and shells elements;
Stress recovery and post processing;
Other topics: error, convergence, solving linear system of equations…
Textbook
Concepts and Applications of Finite
Element Analysis, R.D. Cook, D.S.
Malkus, M.E. Plesha, R.J. Witt., 4th
edition, John Wiley & Sons, Inc. 2002.
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1. Introduction
2. One-Dimensional Elements and Computational Procedures
3. Basic Elements
4. Formulation Techniques: Variational Methods
5. Formulation Techniques: Galerkin and Other Weighted Residual Methods
6. Isoparametric Elements
7. Isoparametric Triangles and Tetrahedra
8. Coordinate Transformation and Selected Analysis Options
9. Error, Error Estimation, and Convergence
10. Modeling Consideration and Software Use
11. Finite Elements in Structural Dynamics and Vibrations
12. Heat Transfer and Selected Fluid Problems
13. Constraints: Penalty Forms, Locking, and Constraint Counting
14. Solids of Revolution
15. Plate Bending
16. Shells
17. Nonlinearity: An Introduction
18. Stress Stiffness and Buckling
Concepts and Applications of Finite Element Analysis; Cook, Malkus, Plesha, Witt., 4th Ed, John Wiley, 2002.
Our book has something for everyone …
Practical
Application
Very
Important Theoretical
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Recommended Textbooks
K.-J. Bathe (1995)
Finite Element Procedures Prentice Hall
R. D. Cook (1995)
Finite Element Modeling for Stress Analysis
John Wiley and Sons
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Recommended Textbooks T. J. Hughes (2000)
The Finite Element Method: Linear Static
and Dynamic Finite Element Analysis
Dover Publications
J. N. Reddy (2005)
An Introduction to the Finite Element
Method
3nd Edition, McGraw Hill
J. N. Reddy (2004)
An Introduction to Nonlinear Finite
Element Analysis
Oxford University Publication
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Recommended Textbooks M. Asghar Bhatti (2005)
Fundamental Finite Element Analysis and
Applications: with Mathematica and
Matlab Computations
John Wiley and Sons
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Recommended Textbooks
Vol 1: The Basis Vol 2: Solid Mechanics Vol 3: Fluid Mechanics
O. C. Zienkiewicz and R. L. Taylor (2000)
The Finite Element Method
4th Edition, John Wiley and Sons
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Recommended Textbooks
Vol 1: The Basis Vol 2: Solid Mechanics Vol 3: Fluid Mechanics
O. C. Zienkiewicz, et. al (2005)
The Finite Element Method
6th Edition, Butterworth-Heinemann
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We want to know the states (displacement, strains, stresses…) throughout the structure.
FEM: The big picture
General Structural Analysis Problem
Structure
Geometry Material properties
Boundary conditions: Essential BCs (prescribed
displacement) Natural BCs (tractions)
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(1) Constitutive relations: relation between stresses and strains (determined by material properties) (2) Kinematic relations: relation between displacement and strains (usually in the form of differential equations) (3) Equilibrium of forces (usually in the weak form of the Principle of Virtual Work, the Principle of Stationary Potential Energy, or the vanishing of weighted residuals)
Governing relations to be satisfied:
Closed form solution is not possible for a general case. Approximate numerical solution is employed: the FEA.
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Simulation process (broad view)
Mathematical system
Discrete Model
Discrete Solution
Physical system
SOLUTION IDEALIZATION DISCRETIZATION
Solution error
Discretization + solution error
Modeling + discretization + solution error
Beam theory Plate theory
…
change models (e.g.
beam solid)
e.g. iterative
refinement
e.g. adaptive re-
meshing
The above flowchart is based on the one given in Felippa’s book
Finite element
methods …
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Finite Element Analysis Procedure
Discretization (divide the structure into small,
simple elements)
Localization (obtain the behavior of each element)
Globalization (Assembly) (relate all elements
based on the connectivity)
Solution and post processing (solve for state variables and
recover quantities of interest, such as stress)
y
x
z
efuK ee
fKu
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Introduction to FEM
History of FEM
Advantages and shortcomings of FEM
Misuses of FEA programs
Next Class
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