Instructor:                   Professor Simona Socrate, 
                                     Room 3-334, 
                                     Ext. 2-2689, 
                                     Office Hours : Fri 3:30 - 5:00
                                     E-mail :  ssocrate@mit.edu 

Units:                            3-3-6 

Lectures:                     Monday, Wednesday, 
                                     9:30 a.m. - 11 a.m.; 
                                     Room 1-371 

Textbooks:

1-  Concepts and Applications of Finite Element Analysis; 4th Edition, Cook, Malken,       Plesha and Witt - Required.  (Not available until Oct 15.  Xerox copies of

      the proofs will be distributed until then) 

2-  Notes on pertinent material will be provided throughout the term. 

Prerequisites:            2.001 Mechanics and Materials I. 
                                   2.002 Mechanics and Materials II. 

ME Distribution:       Discliplinary: 6; 
                                    Design:          3;
                                    Lab:               3; 
 

Subject Summary 

This introductory class focuses on the more practical aspects of structural finite element (FE) modeling, and provides a working knowledge of how to effectively incorporate FE techniques into the design process.The course material will be organized into a sequence of modules relating to topics of increasing computational complexity. For each module, a presentation of the relevant FE  theory (Monday) will be followed by a workshop (Wednesday) designed to discuss and reinforce the concepts presented during the lecture and to provide the students with the experience of running and trouble-shooting actual FE analyses. Weekly or biweekly projects will be assigned where the students will conduct finite element analyses and write concise reports outlining modeling choices and their implications in terms of the FE predictions.  

Modules will cover FE procedures relevant to design and manufacturing applications including: (i) linear statics using continuum and structural elements;  (ii) nonlinear statics with geometric, material, and contact-induced nonlinearities;  (iii) thermomechanical analysis;  (iv) linear and nonlinear dynamics,  
 

Modules Outline 

1.     Overview of Structural Finite Element Analysis 
 

2.     Review of Preliminaries:  

• Stress-Strain Relations  
• Equilibrium  
• Compatibility  
• Implicit and Explicit Formulations  

3.     Linear Static Analysis: Model and Element Types  

• Plane Stress, Plane Strain and Axisymmetric Models  
• Continuum Elements  
• Structural Elements  
• Special Elements  

4.     Nonlinear Static Analysis 

• Sources of Nonlinearity  
• Geometric Nonlinearities: the Solution of Nonlinear Problems  
• Material Properties: Nonlinear Constitutive Relations  
• Contact Modeling  

5.      Analysis Procedures for Implicit Formulation 

• Thermo-mechanical Analysis 
• Buckling  
• Modal Analysis  

6.     Analysis Procedures for Explicit Formulation 

• Overview of Explicit Dynamics 
• High-Speed Dynamic Problems (Crash Simulations)  
• Higly Nonlinear Quasi-Static Problems (Manufacturing Applications)  

Assignments 

Computational projects will be assigned every Wednesday and they will be due on the following Monday before class.
Late assignments will not be accepted. Two oral presentations will be scheduled for each student during the course of the semester. There will be no quizzes and no final exam.  
 

Grading 

The final grade will be weighted as follows: 

• Attendance and Class Participation    15% 
• Computational Assignments                65% 
• Oral Presentations                               20% 

Teaching Assistant

There will be a teaching assistant for this course: 

Eun Suk Suh 
Room 3-455D
Office Hours: Fri 3:30-5:00
E-mail:  essuh@mit.edu 
 

Reference Books 

Below are listed several reference books which cover various special topics of the course in more detail. 
 

Continuum Mechanics

An Introduction to Continuum Mechanics, M.E. Gurtin, Academic Press, 1987. 
Introduction to Mechanics of Continua, W. Prager, Dover, New York. 
Foundations of Solid Mechanics, Fung, Y.C., Prentice-Hall, Englewood Cliffs, NJ, 1965. 
 

Mechanical Behavior of Materials 

Mechanical Behavior of Materials, McClintock, F. A. and Argon, A. S., Addison-Wesley, Reading, MA, 1966. 
Introduction to Composite Materials, Hull, D., Cambridge U. Press, Cambridge, 1981. 
Mechanical Behavior of Materials, Courtney, T. H., McGraw-Hill, New York, 1990. 
Engineering Materials, 4th Ed., Budinski, K. G., Prentice-Hall,Englewood Cliffs, NJ, 1992. 
 

Theory of Elasticity 

Advanced Strength and Applied Elasticity, Ugural and Fenster 
Theory of Elasticity, 3rd Ed., Timoshenko, S. P. and Goodier, J. N., McGraw-Hill, New York, 1970. 
Theory of Thermal Stresses, Boley, B. A. and Weiner, J. H., Wiley, New York, 1960. 
 

Finite Element Methods

Concepts and Applications of Finite Element Analysis, Third Ed.,Cook, R. D., Malkus, D. S., and Plesha, M. E., John Wiley, New York, 1989. 
The Finite Element Method : Linear Static and Dynamic Finite Element Analysis, Hughes, T. J. R., Prentice-Hall, Englewood Cliffs, NJ,1987. 
 

Plasticity

Engineering Plasticity, W. Johnson and P. B. Mellor, Van Nostrand Reinhold, London, 1973. 
Plasticity Theory, Lubliner, J.,Macmillan, New York, 1990. 
 

Structural Mechanics 

Theory of Plates and Shells, 2nd Ed., Timoshenko, S. P. and Woinowsky-Krieger, S., McGraw-Hill, New York, 1959.