Finite Element Analysis

Course Name - Finite Element Analysis                                   Course Code: AEC603

Contents of Module 1- Introduction of FEA 

1. Introductory Concepts: Introduction to FEM, Historical Background, 
2. General FEM procedure. 
3. Applications of FEM in various fields. 
4. Advantages and disadvantages of FEM. 
5. Mathematical Modelling of field problems in Engineering,
6. Governing Equations, 
7. Differential Equations in different fields. 
8. Approximate solution of differential equations– 
9. Weighted residual techniques, 
10. Least squares, 
11. Galerkin methods, 
12. Boundary Value problems. 

Introduction to FEM

Finite Element Method (F.E.M) in plain language, can be said to be a numerical method to solve differential equations. We Know that in general engineering problem are analysed by forming differential equations for different processes and solving The same applying suitable boundary conditions.

However the problem arise when the differential equation become complex or the domain over which they are to be solved are complex. In such case use of numerical methods becomes very handy

There are many numerical methods which are used predominant of which are 

(a). Finite difference Method (F.D.M.)

(b). Weighted Residue Method (W.R.M)

(c). Finite Element Method (F.E.M)

The finite element method is a computational scheme to solve field problems in  engineering and science.  The technique has very wide application, and has been used on problems involving stress analysis, fluid mechanics, heat transfer, diffusion, vibrations, electrical and magnetic fields, etc.

 Historical Background

• The term Finite Element was first coined by Clough in 1960. During this period methods of approximation were usually used to solve problems on stress analysis, fluid flow, heat transfer, etc.
• The first book on the Finite Element Method was written by Zienkiewicz and Chung published in 1967

Finite Element Analysis Process

In general, a finite element solution may be broken into the following three stages. This is a general guideline that can be used for setting up any finite element analysis.

1. Pre-processing: Defining the problem; the major steps in pre-processing are given below: Define key points/lines/areas/volumes, Define element type and material/geometric properties, Mesh lines /areas/volumes as requiredThe amount of detail required will depend on the dimensionality of the analysis:(i.e. 1D, 2D, axisymmetric, 3D).

2. Processing/Solution: assigning loads, constraints, and solving; here we specify the loads (point or pressure), constraints (translational and rotational) and finally solve the resulting set of equations.

3. Post-processing: further processing and viewing of the results; in this stage one may wish to see: Lists of nodal displacement, Element forces and moments, Deflection plots, Stress contour diagrams

Applications of FEM in various fields. 

FEM has a number of applications in the engineering industry in the fields of 

• solid mechanics, 
• fluid mechanics,
• heat transfers, and so on.

Structural Analysis: Getting 

• stresses and strains, 
• deflections, 
• bending moments, etc. at specific points in the system.

Thermal Analysis: to find the 

• temperature values, 
• heat flow, 
• thermal stresses in critical areas.

Fluid Analysis: to get 

• pressures,
• velocities,
• discharge at the required point.

Vibration  Analysis:  to get the 

• natural frequencies,
• resonant frequencies and dynamic response of the system to time-varying loads.

Nuclear Engineering: to get 

• temperature, 
• temperature gradients, 
• heat flow rates etc.

Electrical Circuits: Determination of 

• charge, 
• current, 
• voltage, 
• power etc.

Nonlinear Analysis: Which include advance material behaviour such as plastic yielding buckling or failure.

Area of FEA: It depends on the types of industry and its requirements.

For Example

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Further Modules to be continue