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YOU ARE HERE: Home >> Analysis Basics >> Finite Element Analysis |
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Finite Element Analysis - a definition |
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WHAT IS FINITE ELEMENT ANALYSIS
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Finite Element Analysis Trends in FEA Computer based numerical stress analysis methods like finite element analysis have permitted calculation of the distributions of stress in engineering components to become routine. Increasingly, engineering design offices are integrating the processes of solid modelling and analysis through what is often called 'designer analyses'. Information about a service we offer to support this kind of analysis is available here. Experimental stress analysis methods describe physical techniques to determine the stresses in models or actual production items, tested under controlled loading conditions. Photo-elasticity is one of these techniques that has been largely superseded by finite element analysis. However, using FEA without independent verification can be dangerous and independent testing and calculation is often important. Strain measurement by the use of strain gauges for example, provides important data to back up finite element results. Unfortunately, there are often difficulties in correlating test results with those from finite element analysis. Some of these are purely technical matters but there are also administrative or communication difficulties that can impede efficient collaboration between test and analysis departments in larger organisations. Consider a body in which the distribution of displacement and stress is required. The first step is to divide the actual geometry of the structure using a collection of discrete portions. These are the finite elements and they are joined together by shared nodes. These jointly are known as the mesh. A simple introduction to the mathematics of FEA is given here. Each element represents the unknown displacements mathematically in a predefined (typically linear or quadratic) manner. This allows relatively simple equations to define this variation. The stress distribution over a complete engineering structure cannot be represented by a single simple equation of course, but over the small distances that each finite element spans, a linear or quadratic variation in displacement can represent the actual displacement that occurs quite well. Thus, the distribution over the whole body is approximated by the connected representation of the many finite elements. Simplistically, there is an equation for each element which has, as unknowns, the displacements at its nodes. Each element shares at least one node with its neighbour. The equations formed and solution obtained must satisfy the physical condition that any nodal displacement must be the same for these neighbouring elements. This is called 'compatibility' and is one of the fundamental mathematical requirements for a valid finite element analysis. After the problem has been divided into finite elements, the whole structure can be represented numerically by the structured formation of the individual equations, identical in form, which defines the behaviour across each finite element. The finite element analysis solution process consists of the formation and subsequent solution of what becomes a very large set of simultaneous equations, and is readily achieved using matrix algebra and computers. |
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