Carnegie Mellon

Mechanical Engineering

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Finite Element Method
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To obtain the best results from ANSYS, or for that matter any Finite Element program it is important to understand the basic concepts and limitations of the Finite Element Method. 

The Finite Element Method is a technique for approximating the governing differential equations for a continuous system  with a set of algebraic equations relating a finite number of variables. These methods are popular because they can be easily programmed. The FE techniques were initially developed for structural problems but they have been extended to numerous field problems.

The basic steps involved in any FE Analysis consist of the following.


bulletCreate and discretize the solution domain into finite elements. This involves dividing up the domain into sub-domains, called 'elements', and selecting points, called nodes, on the inter-element boundaries or in the interior of the elements.
bulletAssume a function to represent the behavior of the element. This function is approximate and continuous and is called the "shape function".
bulletDevelop equations for an element.
bulletAssemble the elements to represent the complete problem.
bulletApply boundary conditions, initial conditions, and the loading.


bulletSolve a set of linear or nonlinear algebraic equations simultaneously to obtain nodal results, such as displacement values, or temperature values, depending on the type of problem.


bulletThis stage involves processing the nodal data to get other information such as values of principal stresses, heat fluxes, etc.
bulletMathematics of the Finite Element Method
bulletFinite Element Method: A Prototype Hypermedia Course - Finite Element Method THEORY & PROGRAMMING & MODELLING & RECENT DEVELOPMENTS
bulletFinite Element Method Universal Resource - FEMur
bulletIntroduction to the Finite Element Method for Computer Aided Engineering - Introduction to the Finite Element Method for Computer Aided Engineering.
bulletThe Finite Element Method - The Finite Element Method.
bulletMecE 563: The Finite Element Method - University of Alberta Mechanical Engineering MecE 563
bulletAn Introduction to the Finite Element Method (McGraw-Hill Series in Mechanical Engineering) - J. N. Reddy
bulletConcepts and Applications of Finite Element Analysis - Robert D. Cook, et al
bulletFinite Element Procedures - Klaus-Jurgen Bathe
bulletIntroduction to Finite Elements in Engineering - Tirupathi R. Chandrupatla, A. D. Belegundu
bulletThe Finite Element Method : Basic Formulation and Linear Problems, Vol. 1  -  O.C.C. Zienkiewicz,R.L. Taylor
bulletThe Finite Element Method in Heat Transfer and Fluid Dynamics - J. N. Reddy, David K. Gartling (Contributor)

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