Introduction to Finite Element Method

1. Dr. A. S. Sayyad
Professor & Head
Department of Structural Engineering
Sanjivani College of Engineering, Kopargaon 423603.
(An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune)
Finite Element Method
In Civil Engineering
What is Finite Element Method?

2. Introduction to FEM
For any structural/Engineering problem two types of solutions are available; (i) Analytical
solution and (ii) Numerical solutions.
• Analytical solutions are accurate for the simple boundary conditions, loading conditions
and linear problems.
• But, for the complex geometry, irregular boundary conditions and geometric non-
linearity, analytical solutions are not effective and accurate.
• Therefore, various numerical methods are developed by the researchers for solving such
complex problems.
• The finite element method (FEM) is a numerical technique used to find out solutions of
complex engineering problems.
• Originally this method was developed for the aerospace engineering but, it is now widely
used in other engineering disciplines such as Civil Engineering, Mechanical Engineering
and Electrical Engineering.
• The first book on finite element method (FEM) was written by O. C. Zienkiewicz in three
volumes.

3. What is Finite Element Analysis (FEA)?
In finite element analysis, solution of complex problem is obtained by dividing domain
(structure) into ‘n’ number of subdomains (elements).
There are two stages in finite element analysis
Element formulation: The study of properties of one element is called as element formulation
System formulation: Assembly of properties of all elements (global study) to obtain solution
of problem is called as system formulation.

4. Principles of FEA
1) The finite element method (FEM) is a computational technique used
to obtain approximate solutions of boundary value problems in
engineering.
2) Boundary value problems are also called field problems. The field is
the domain of interest and most often represents a physical
structure.
3) The field variables are the dependent variables of interest governed
by the differential equation.
4) The boundary conditions are the specified values of the field
variables (or related variables such as derivatives) on the boundaries
of the field.