Finite Element Formulation of
Boundary Value Problems
Fundamental Concepts of Engineering analysis
Objectives
The analyst needs certain requirements while designing and
assembling the parts of the product. Those requirements are mentioned below.
To calculate,
A.
Displacement at certain points
B.
Stress distribution
C.
Natural frequencies
D.
Critical buckling loads
E.
Vibrations
F.
Pressure, Velocity and temperature distribution
G.
Crack growth, residual strength and fatigue
life.
Methods of Engineering Analysis
There are three different approaches to achieve the above
mentioned objectives. They are
1.
Experimental methods
2.
Analytical methods
3.
Numerical methods or approximate methods
1.Experimental Methods
In this methods, prototypes can be used. If we want to
change the dimensions of the prototype, we have to diassemble the entire
prototype and reassemble it and then testing should be carried out. It needs
man power and materials. So, it is time consuming and costly process.
2. Analytical Methods or Theoretical Analysis
In these methods, problems are expressed by mathematical
differential equations. It gives quick and closed form soluitions. It is used
only for simple geometries and idealized support and loading conditions.
3.Numerical Methods
Analytical solutions can be obtained only for certain
simplified situations. For problems involving complex material properties and
boundary conditions, the engineer prefers numerical methods that gives
approximate but acceptable solutions.
