Introduction to the Finite Element Method (FEM)

Posted by: Admin | Posted on: December 11th, 2012

The finite element method is a process in which approximate solutions are being derived for the complex partial differential equations and the integral equations. With a numerical approach to the issues at hand, this method aims at solving the problems by dividing it into subparts or finite elements among which, some sort of relationship could be established. These established relationships help in finding the accurate and reliable solutions for the complex engineering issues.

Need of Finite Element Method

The partial differential equations are encountered in the mathematical modelling of various chemical, biological and physical phenomena. Some of the concepts such as fluid dynamics, material science and electromagnetism etc. include the partial differential equations. The need of the finite element method originated, when various elasticity and structural analysis related problems emerged in the civil engineering and aeronautical engineering fields. Now, this methodology of solving complex problems has developed a lot and is being implemented in a wide range of engineering disciplines.

Essential Steps of the Finite Element Method

The whole process of finite element methodology or analysis can be distinguished into three basic steps namely pre-processing, analysis and post processing.

Pre-processing phase: In this initial phase, the user develops a particular model of the part to be analyzed. Geometrically, the particular model is divided into various sub regions. Each single element or sub region of the model is connected at discrete points such as the nodes. This method is often referred to as discretization. This is a time consuming stage and proper selection of the displacement models is much necessary for the effective execution of the following steps. This particular process use the computer aided design and drafting software to perform the necessary tasks.

Analysis phase: The data gathered in the pre-processing phase is used as an input data in this particular stage. Depending upon the data being fed to the finite element code, the linear or non-linear numerical equations are being developed and solved. To solve the linear problems, the matrix algebra techniques are being implemented. For the non-linear problems, the force matrix at each iteration strategy is being applied.

Post processing phase: In this final phase, the solutions for unknown displacements are determined and computations for the strains and stresses are being performed. Various principles of solid mechanics are being practically applied in this stage. Finally, photorealistic displays of the models are being developed for representation. The model displays represent the stress levels on the experimented models.

Applications of Finite Element Method

The finite element analysis concepts are being utilized in the design and development of different products in a wide range of industries such as the automotive, aeronautical and the structural sectors. In the structural engineering field, the finite element method is used in the simulation of the buildings in order to know the cause behind any type of deformations or damage to the buildings. The medical field is no exception. The finite element analysis methodology also finds its application in the dental implant research and other researches belonging to the other parts of the human body. The finite element analysis has proved to be a boon for the industries because it has substantially reduced the time and cost for production and has enhanced the design and quality of the products.