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Finite element analysis - Essay Example

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Summary
Finite element analysis is an approximate method that involves discretising the entire problem domain into finite elements and later combining the element properties to obtain a global solution. The global system is analyzed by incorporating the boundary conditions to get the required solution (Cooks et al, 1989)…
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Finite element analysis Essay
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Finite element analysis

Download file to see previous pages... The distribution of meshes is based on the type of the problem. If a location requires very refined analysis this region could have very fine meshes (Widas, 1997). A typical finite element application is shown as below. Here, the finite element model of the problem is shown in figure 1. The material is divided into small triangle shaped elements and hence it can be said that the body is meshed using triangular elements.
The FEA software consists of different type of elements that could be used in the analysis. The element refers to the geometrical shapes that are used to mesh the system. Some of the types of elements used usually used are rod elements, beam elements, plate/shell/composite elements and Solid elements
The process of dividing the problem element into the fine grids is known as meshing. The mesh would consist of similar elements or combination of different elements. Like for a irregular body the using square or rectangular elements might be useful in proper division of the domain space into small elements. This disadvantage shall be overcome by different type of elements like triangular elements to wards the boundary or irregular side for proper geometrical matching between the finite element model and the actual physical body. ...
This disadvantage shall be overcome by different type of elements like triangular elements to wards the boundary or irregular side for proper geometrical matching between the finite element model and the actual physical body. Another important aspect that need to be considered is the size of meshes that are used for the process of discretisation. The size of meshes could be course , large and well spread, or fine , small size and closer placed. The choice of the size depends on variery of factors. The type of the element chosen for a particular problem, nature of the variation of the unknowns, computational efficiency etc. For example, the choice between linear bar element and quadratic bar element is based on the experience of the analyst. Problems might require few number of complex elements or larger number of simpler element no strict guideline exist in this aspect. The experience gained from analysis would be the prime factor that would help in the proper choice of elements for a particular type of problem (Chandrupatla and Belegundu, 2007)
Results
All finite element computations would result in the be The element stiffness matrix in all cases would be of the form


The equation is used to construct the element level matrices for the particular problem. The size of the matrix would depend on the type of the element chosen. For linear bar element with one unknown at each node the size of the matrix is 2 2. While for a bilinear element like rectangle with two unknowns at each node the size of the matrix would be 8 8. The element matrices hence formed shall be combined to get the global equations with appropriate boundary conditions incorporated in it. The equations are hence solved using any standard solver. The results obtained as ...Download file to see next pagesRead More
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