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Finite Elements Analysis

Finite element analysis was developed by R. Courant in the year 1943, by utilizing the Ritz method of numerical analysis and by minimizing the variation calculus for obtaining approximate solutions for vibrations systems. Later, a paper published in the year 1956 by M.J Turner, H.C. Martin and .W. Clough established a somewhat broader definition of numerical analysis. This paper was based on stiffness and deflection of complex structures.

In the early decade of 1970, the FEA was limited to expensive mainframe computers which were generally used by automotive, aeronautics, defense and nuclear industries. Now, with the most of computers on rapid decline along with increase in their computational power, the finite element analysis has gained an incredible position. The present day supercomputers can now produce more accurate results for all kinds of parameters.

Finite element analysis consists of a computer material or design that is analyzed and stressed for achieving specific results. It is also used in new product design and for refining existing products. A company is able to correctly verify a proposed design and is able to accommodate client specifications prior to the actual manufacturing or construction. A product can also be made to qualify for same service condition by modifying its structure. If a design meets structural failure, the finite element analysis can determine design modifications needed for meeting the new condition.

Generally two types of modeling are used in the industry, the 2D modeling and 3D modeling. Though the 2D model helps the model to be run on a relatively normal computer, it gives results which are less accurate. The use of 3D models gives more accurate results, but cannot be run on all computers. In both the modeling schemes the programmers are able to insert numerous functions and algorithms which make the system to behave linearly or non-linearly. The non linear systems can test the materials up to the fracture stages and account for plastic deformation. The linear systems are less complex and do not take into account the plastic formation.

The working of Finite Element Analysis

The finite system analysis uses a complex system of points called nodes. These nodes make a grid which is called a mesh. The mesh is programmed to contain the material and other structural properties associated with it and define how the structure will react to the loading conditions provided. Nodes are then assigned at various densities though out the material. The assigning of the nodes also depends on the anticipated stress level at a given area. Higher node density is provided at the points which have large amount of stress. The point of interest consists of the fracture points of previously tested material, corners, fillers, complex detail and the high stress area. The mesh also acts like a spider web, extending a mesh element to each of the adjacent nodes. The material properties of the objects are carried by this web of vectors.

For minimization and maximization purposes, a wide range of objective functions are present-

1. Mass, temperature, volume.

2. Stress strain, strain energy.

3. Acceleration, velocity, displacement and force.

4. User defined synthetic.

The various loading conditions applied to a system are-

1. Point pressure by thermal gravity as well as centrifugal static loads.

2. Thermal loads from the solution of heat transfer analysis.

3. Enforced displacements.

4. Convection and heat flux

5. Pressure and gravity dynamic loads

6. The element library of the finite element analysis is constructed over time, and some examples are rod elements, beam elements, shear panel, spring elements, rigid elements, mass elements, viscous damping elements etc.

7. Some finite element analysis programs also use capability to use multiple materials within their structure. Some examples are isotropic, orthotropic and general anisotropic materials

Types of engineering analysis in FEA

Structural analysis- consists of linear and non linear models. The linear models use simple parameters and assume that the material is not practically deformed. The non linear models stress the material past its elastic capabilities. The amount of deformation caused is directly proportional to the amount of stress.

The vibration analysis-is used for testing material against impact, shock and vibrations. These incidences also act on the vibration frequency of the material which causes resonance and subsequent failure.

Fatigue analysis-various effects of cyclic loadings are studied on the structure or material and the life of the material is predicted based the study. The analysis shows the areas where the crack propagation is likely to occur. The damage tolerance of the material is displayed by the failure resulting form fatigue.

Heat transfer analysis-it consists of the steady state or transient transfer and the analysis models the conductivity or the thermal fluid dynamics of the structure or material.

Thus FEA helps to predict the causes of failure that may occur in a system and allows the designers to see the theoretical stress within the design. Thus the material can b tested beforehand, thereby avoiding costs involved in actual manufacturing.