School of Engineering and Technology, (SET)
The objective of this course is to introduce the fundamental concepts and background of finite element methods along with the implementation on computer platform. Finite element methods (FEM) of standard structural elements, e.g. rod, beam, plane element (two-dimensional problem), plate and shell element, and three-dimensional solid element, will be presented. Major factors that affect the accuracy of finite element solution and error estimation will be discussed.
The student on completion of this course would be able to:
-          Construct governing differential equations and weak formulations for structural mechanics problems
-          Apply numerical techniques to solve problems in FEM on computer platforms
-          Perform finite element analysis for elastic continua
-          Construct finite element analysis programs for different structural elements
-          Post-processand interpret finite element solutions for engineering practice

CE72.11 Computer Methods in Structural Analysis

I.          Fundamentals of FEM – Illustrated by St. Venant Torsion Problem
1.    Theory of elasticity
2.    Total potential energy
3.    Ritz method
4.    Finite element solution
.
II.         Development of Finite Elements
1.    Discretization
2.    Element geometry
3.    Interpolation function
4.    Numerical integration scheme

III.        General Structure of a FE Computer Implementation
1.    Pre-processor module
2.    Solver module
3.    Post-processor module

IV.       Application of FEM to 1D/2D/3D Problems
1.    Dimensional elements: bar, Euler’s beam, Timoshenko’s beam
2.    Dimensional elements: plane stress, plane strain, plates, and shells
3.    Dimensional elements: 3D elasticity
 
VI.       Nonlinear Problems and Solution Techniques
1.    General nonlinear elasto-dynamic problems
2.    Time discretization
3.    Newton-Raphson iteration techniques

VII.      Time Discretization
1.    Hamilton principle
2.    Lagrange’s equation of motion
3.    Galerkin’s weighted residual method

None.

No designated textbook, but class notes and handouts will be provided.
1.    O. C. Zienkiewicz, R. L. Taylor, and J.Z. Zhu (2013):
The Finite Element Method: Its Basis and Fundamentals, 7th Edition, Butterworth-Heinemann, Oxford.
 
2.    T.J. Hughes (2000)
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, 1st Edition, Courier Corporation.

3.    K.J. Bathe (2013)

Finite Element Procedures, 2nd Edition, Klaus-Jürgen Bathe

1.    International Journal for Numerical Methods in Engineering, John Wiley & Sons
2.    Computers and Structures, Elsevier

Others:.

1.    S. Chapra (2017)
Applied Numerical Methods with MATLAB for Engineers and Scientists, 4th Edition, McGraw-Hill Education.
·         Lectures:                    45 hours
·         Self-study:                 135 hours

Class lectures and weekly homework assignment.

Mid-semester examination (30%), Final examination (30%),and Homework assignment (40%). Both mid-semester and final examinations are open book.

An “A” would be awarded if the student fully understand concepts of finite element methods and be able to implement FEM by computer programming to solve structural mechanics problems accurately. Those who achieve the “A” grade are considered strong enough to continue his/her research in computational mechanics.
A “B” would be awarded if the student understand major concepts in finite element methods and aware of factors that affect accuracy of finite element solution. The student is expected to be able to use commercial finite element program to produce accurate solution.
A “C” would be assigned if the student knows major concepts in finite element methods.
SECTION NAME
A Dr. Chaitanya Krishna