Tutorial

CHAPTER 2

Applications Of Finite Element Method

With the advent of Computer Aided Design (CAD), the Finite Element Method has been finding wide variety of applications. Some typical applications of FEM are listed below.

PLANE STRESS PROBLEMS :

1. Stress Flow Around Reinforced Opening :

In steel pressure vessel and aircraft structures, openings have to be introduced. These result is stress concentrations in a localized region. The stress analysis can be carried out by simply discretizing the surface near the edge of the hole by very thin triangular element.

2. Dam Subjected To External Pressure :

AXI-SYMMETRIC PROBLEMS :

1. Application Related To Shell :

A shell is a structure which can be derived from a thin plate by initially forming the middle plane to a singly curved surface. In Finite Element Method, it is assumed that the behavior of a continuously curved surface can be adequately represented by the behavior of a surface built up of small, flat elements. In a shell, the element will be subject both to bending and “in-plane” stresses.

One common example of shell is Cooling Tower. The tower is subjected to unsymmetrical wind loading. The tower is divided into small triangular elements for carrying out stress analysis.

2. Belleville Spring :

The Belleville Spring, also called Belleville Washer, is a conical disk spring. The load is applied on the periphery of the circle and supported at the bottom. As load is applied in the axial direction, the supporting edge moves out. Only the rectangular cross-section area needs to be modeled. Load-deflection characteristics and stress distribution can be obtained by dividing the area into elements and using a computer program. In the Belleville spring, the load-deflection curve is non-linear. The stiffness depends on geometry. We can find a good approximate solution by an incremental approach.

APPLICATIONS RELATED TO FLUID FLOW :

1. Aircraft Wing :

FEM can be used to find the lift and drag forces on an aircraft wing in the design stages itself. Given a cross-section of an aerofoil and its relative speed with respect to air, we can find the pressure distribution of air around the aerofoil. Basic idea here is to discretize the region around the aerofoil, thus we can calculate the lift and drag forces on it. The method can also be used to find the optimum cross-section of the aerofoil for a particular speed.

2. Aerodynamics Of A Vehicle :

FEM can be used to compare the Aerodynamics of various proposed vehicle shapes. It is used to calculate the air resistance acting on a particular vehicle shape. Here we discretize region surrounding the vehicle boundary. Thus we can use FEM to get a Sleek body for a vehicle.

APPLICATIONS RELATED TO HEAT TRANSFER :

FEM is a very powerful method for Heat Transfer analysis in the design stages.

1. Engine Piston :

To find out various parameters such as area required for heat transfer, cooling fluid flow, material selection, etc. temperature distribution in a piston must be initially found out.Using FEM the temperature distribution throughout the piston can be found out.

2. Fins :

Fin is an extended surface of a structure used to increase the rate of Heat Transfer. For example, fins are used as extension of cylinder head for heat dissipation in engine. Geometry and arrangement of fins is complex. FEM can be used to find Temperature Distribution and Heat Transfer in the fins.