At the end of this course, the students; 1) To understand the fundamentals of physical and mathematical theory that exist in the background of the finite element method. 2) To learn the basics of variation principles in solid mechanics. 3) To understand the types of elements that exist in the package programs and to select the appropriate element type depending on the analysis method. 4) To be able to do finite element solution in linear and nonlinear material behavior. 5) To learn isoparametric modeling that everyone can easily program on the computer. 6) Modeling the character and behavior of dynamic problems with finite element analysis.
MODE OF DELIVERY
Face to face
PRE-REQUISITES OF THE COURSE
No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT
None
COURSE DEFINITION
Matrix algebra. Potential energy and Rayleigh-Ritz Method. Element interpolation and local coordinates. Elements based on assumed displacement fields in 1-D. Plane stress analysis. Higher order elements. Computer implementation.
COURSE CONTENTS
WEEK
TOPICS
1st Week
Introduction to numerical analysis methods
2nd Week
Finite element types, definition of stiffness and rod elements
3rd Week
Element matrices and the creation of the complete stiffness matrix
4th Week
Truss systems
5th Week
Applications of linear elasticity in Finite Element method
6th Week
Analysis of two-dimensional problems
7th Week
Introduction to variation mathematics
8th Week
MIDTERM
9th Week
Variation techniques used in finite element analysis
10th Week
Galerkin and Ritz methods, interpolation functions
11th Week
Basic elements, high-grade elements
12th Week
Dynamic analysis with finite element method
13th Week
Isoparametric element equation inference
14th Week
Analysis of two dimensional and solid body problems
RECOMENDED OR REQUIRED READING
Reference: Reddy, J.N., An Introduction to the Finite Element Method, McGraw-Hill Education; 3 edition, 2018. Additional Resources: Fish, J., and T. Belytschko. A First Course in Finite Elements, Wiley, 2007. Cook, R. D., Malkus, D.S. and Plesha, M. E., Concepts and Applications of Finite Element Analysis, 3rd ed., Wiley, 1989. McGuire, W., Gallagher, R.H., Ziemian, R.D., Matrix Structural Analysis, 2nd edition, Wiley, 1999. Wasti, T., and M. Utku. Introduction to Finite Elements, METU, 2001.