The Finite Element

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Research Paper
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The finite element method (FEM) is a numerical procedure used for finding approximate solutions of partial differential equations (PDE). Problems which use this method are usually too complicated to be solved by classical analytical methods and require significant computational solving capabilities…

Introduction


One of the main challenges in solving partial differential equations is to use equations which are approximate but numerically stable so that error accumulation does not cause the solution to be meaningless. The finite element method is an excellent technique for solving partial differential equations over complex domains. Application of the finite element method in structural mechanics is based on an energy principle, such as the virtual work principle, which provides a general, intuitive and physical basis.
The finite element method originated as a technique used to solve stress analysis problems, but today it can be applied to a multitude of disciplines ranging from fluid mechanics, to heat transfer to electromagnetism.
The buckle of a standard lap belt used in passenger aircrafts has been designed and is ready to undergo testing. In order to be released into the market, the strap system must be able to withstand a 450 kg tensile load. It is assumed that the weakest point of the design is the flat plate of the buckle. Thus, prior to engaging in a costly test scenario, a simple finite element analysis of the buckle is to be made to insure soundness of design, i.e. the material does not exceed its yield strength and no significant distortion occurs. Preparing the problem for analysis first requires definition of assumptions.
Figure 1 is a schematic drawing of the buckle to be analy ...
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