INTRODUCTION TO 1-D & 2-D
FINITE ELEMENT ANALYSIS
B. N. Rao
Structural Engineering Division
Department of Civil Engineering
Indian Institute of Technology Madras
Chennai 600 036
bnrao@iitm.ac.in
19 December 2006
TEXT BOOKS
http://www.engineering.uiowa.edu/faculty-staff/profile-directory/cee/bhatti_m.html
REFERENCES
• Reddy, J. N., An Introduction to the Finite Element Method, 2nd
Edition, McGraw-Hill Education (ISE Editions), 1993.
• Cook, R. D., Malkus, D. S., and Plesha, M. E., Concepts and
Applications of Finite Element Analysis, 4th Edition, Prentice Hall-
India, New Delhi, 2003.
• Bathe, K-J., Finite Element Procedures, Prentice Hall, 1996.
• Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method, 5th
Ed., Vol. 1, Butterworth-Heinemann, 2000.
• Zienkieewicz, O.C. and Taylor, R.L., The Finite Element Method, 5th
Ed., Vol. 2, Butterworth-Heinemann, 2000.
• Zienkiewicz, O. C., Taylor, R. L., Zhu, J. Z., The Finite Element
Method: Its Basis and Fundamentals, Elsevier, 2005.
• Hughes, T. J. R., The Finite Element Method : Linear Static and
Dynamic Finite Element Analysis, Dover Publications, 2000.
APPROXIMATE METHODS
APPROXIMATE METHODS (Continued)
Weighted Residual Methods
APPROXIMATE METHODS (Continued)
APPROXIMATE METHODS (Continued)
Least Squares Weighted Residuals
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4th Order Polynomial
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BVP with EBC and NBC
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Collocation Method
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Galerkin Method (Basic Formulation)
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APPROXIMATE METHODS (Continued)
Variational Method (Rayleigh-Ritz Method)
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APPROXIMATE METHODS (Continued)
Modified Galerkin Method
APPROXIMATE METHODS (Continued)
APPROXIMATE METHODS (Continued)
Boundary Conditions
BASIC FINITE ELEMENT CONCEPTS
Classical Approx. Solution Techniques Vs. FEM
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Variational Method (Rayleigh-Ritz Method)
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Example
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Advantages of FEM
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Example
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Element Equations Without BCs
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Element Equations With BCs
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Three Element Solution
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Modified Galerkin Method
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Three Element Solution
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Axial Deformation of Bar
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Analysis of 2-D Trusses
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Analysis of 3-D Trusses
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