FEM-in-SE

Finite Element Methods in Structural engineering

MST-102 Finite Element Method in Structural Engineering

Credits 3, L:T:P 3:0:0

Teaching Scheme

Lectures: 3 hrs/week

Course Outcomes:

On completion of the course, the student will have the ability to:

1. Learn elemental stiffness technique
2. Formulate finite element equation, equilibrium equation.
3. Apply the concepts of Finite Element Formulation and loads
4. Learn computer applications of FEM.

Pre-requisites / Skills

1. Basic understanding of Matrix Algebra
2. Numerical Methods
3. Solid Mechanics
4. Fundamental Structural Analysis concepts
   • Deflection of beams
   • Bending moments
   • Shear forces

Syllabus Content:

• Introduction: History and Applications. Spring and Bar Elements, Minimum Potential Energy Principle, Direct Stiffness Method, Nodal Equilibrium equations, Assembly of Global Stiffness Matrix, Element Strain and Stress
• Beam Elements: Flexure Element, Element Stiffness Matrix, Element Load Vector.
• Method of Weighted Residuals: GalerkinFinite Element Method, Application to Structural Elements, Interpolation Functions, Compatibility and Completeness Requirements, Polynomial Forms, Applications.
• Types:Triangular Elements, Rectangular Elements, Three-Dimensional Elements, Isoparametric Formulation, Axi-Symmetric Elements, Numerical Integration, Gaussian Quadrature.
• Application to Solid Mechanics: Plane Stress, CST Element, Plane Strain Rectangular Element, Isoparametric Formulation of the Plane Quadrilateral Element, Axi- Symmetric Stress Analysis, Strain and Stress Computations.
• Computer Implementation of FEM procedure, Pre-Processing, Solution, Post-Processing, Use of Commercial FEA Software.

Reference Books:

1. A first course in the finite element method by Daryl L. Logan, ISBN:9780534552985, Publisher:Thomson
2. Finite Element Procedures by Klaus-Jürgen Bathe, ISBN 0979004950
3. Finite Element Analysis, Seshu P., Prentice-Hall of India
4. Concepts and Applications of Finite Element Analysis, Cook R. D., Wiley J., New York
5. Fundamentals of Finite Element Analysis, Hutton David, Mc-Graw Hill
6. Finite Element Analysis, Buchanan G.R., McGraw Hill Publications, New York
7. Finite Element Method, Zienkiewicz O.C. & Taylor R.L. Vol. I, II & III, Elsevier
8. Finite Element Methods in Engineering, Belegundu A.D., Chandrupatla, T.R., Prentice Hall India
9. Finite Element Analysis, NPTEL Web Course by IIT Kharagpur, Dr. D. Maity, Prof. S.K. Bhattacharyya
10. Finite Element Analysis, NPTEL Video Course by IIT Madras, Dr. B.N. Rao

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