ME 6124: Finite-Element Method:
Theory and Practice
Offered Every Spring
| Credit Hours: | 3-0-3 |
| Prerequisites: | Graduate standing in engineering or related discipline |
| Catalog Description: | Line, plane, solid, plate, and shell-elements theory; practical aspects of modeling; applications in mechanical engineering; final project. |
| Textbooks: | J. N. Reddy, An Introduction to the Finite-Element Method, 2nd, McGraw-Hill, 1993. |
| Instructors: | Suresh Sitaraman (Spring 2004) |
| References: | K.
J. Bathe, Finite-Element Procedures, Prentice Hall, Inc., 1996
O. C. Zienkiewicz and R. L. Taylor, The Finite-Element Method, McGraw Hill, 1989 F. L. Stasa, Applied Finite-Element Analysis for Engineers, Saunders/HBJ Publishers, 1985 E. Zahavi, The Finite-Element Method in Machine Design, Prentice-Hall, Inc., 1992 |
Goals:
To provide an in-depth understanding of the theory and formulation behind various finite elements with exposure to applications in Mechanical Engineering. To gain hands-on experience with practical aspects of Finite-Element Modeling.
Topics:
| I. | Introduction | |
| A. | Basic concepts | |
| B. | Variational Formulations | |
| C.
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Weighted-Residual
Methods
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| II. |
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| A. |
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| B. |
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| C. |
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| D. |
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| E. |
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| F.
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Solution
of Equations
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| III. | Theoretical Formulation of Plane Elements | |
| A. |
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| B. | Weak Formulation | |
| C. | Derivation of Element Equations/ Interpolation Functions | |
| D. | Assembly of Element Equations | |
| E. | Imposition of Boundary Conditions and Assembly Reduction | |
| F. | Plane Stress, Plane Strain Analysis | |
MIDTERM TEST I
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| IV. | Theoretical Formulation of Solid Elements | |
| A. | Governing Differential Equation | |
| B. | Weak Formulation | |
| C. | Derivation of Element Equations and Interpolation Functions | |
| D.
|
Imposition
of Boundary Conditions
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| V. | Theoretical Formulation of Plate and Shell Elements | |
| A. | Governing Differential Equation | |
| B. | Interpolation Functions and Degrees of Freedom | |
| C.
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Imposition
of Boundary Conditions
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| VI. |
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| A. |
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| B. | Material Modeling | |
| C. | Model Simplification - Symmetry/Antisymmetry, Plane Strain, Plane Stress | |
| D. | Imposition of Boundary Conditions | |
| E. | Element Aspect ratios/biasing of elements | |
| F. | Convergence/Mesh Refinement | |
| G. | Submodeling | |
| H. | Substructuring | |
| I.
|
Validation
of Results
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| VII. | Applications in Mechanical Engineering | |
| A. | Heat Transfer | |
| B. | Solid Mechanics | |
MIDTERM TEST II
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| VIII. |
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| A. | Gap Elements | |
| B. | Contact Elements | |
| C. | Fracture Elements | |
| FINAL
PROJECT AND PRESENTATION |
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Delivery Mode
|
Lecture |
85% |
|
Supervised Lab |
15% |
Grading Scheme
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Homework |
20% |
|
Midterm |
25% |
|
Midterm II |
25% |
|
Final Project and Presentation |
30% |
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Revised June 2004