Finite element analysis
From Free net encyclopedia
Image:FAE visualization.jpg Finite element analysis (FEA) is a computer simulation technique used in engineering analysis. It uses a numerical technique called the finite element method (FEM).
It was first developed in 1943 by Richard Courant, who utilized the Ritz method of numerical analysis and minimization of variational calculus to obtain approximate solutions to vibration systems. Shortly thereafter, a paper published in 1956 by M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp established a broader definition of numerical analysis. The paper centered on the "stiffness and deflection of complex structures". Development of the finite element method in structural mechanics is usually based on an energy principle such as the virtual work principle or the minimum total potential energy principle.
In its application, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions—i.e., finite elements. Equations of equilibrium, in conjunction with applicable physical considerations such as compatibility and constitutive relations, are applied to each element, and a system of simultaneous equations is constructed. The system of equations is solved for unknown values using the techniques of linear algebra or nonlinear numerical schemes, as appropriate. While being an approximate method, the accuracy of the FEA method can be improved by refining the mesh in the model using more elements and nodes.
A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. However, it is also routinely used in the analysis of many other types of problems, including those in heat transfer, fluid dynamics and electromagnetism. FEA is able to handle complex systems that defy closed-form analytical solutions.
See also
External links
Open-source finite element software include Z88, SLFFEA, YADE, FEniCS, deal.II, libMesh, freeFEM, Elmer, Code-Aster and FElt.
- Z88
- SLFFEA
- YADE
- FEniCS
- deal.II
- libMesh
- freeFEM
- Code-Aster
- Impact
- IMTEK Mathematica Supplement (IMS)
- Calculix
- OFELI
- Elmer
- FElt
- OpenSees -- an object oriented program
- OOFEM -- a free, object oriented, general purpose FEM code
There are many commercially available FEA software packages, including ABAQUS, Ansys, Nastran, Marc and COMSOL Multiphysics.
- NEiNastran FEA
- ABAQUS, Inc.
- FEMPRO (Algor)
- NAFEMS - The International Association for the Engineering Analysis Community
- ANSYS, Inc.
- MSC Software (Nastran and Marc)
- LSTC (provide LS-Dyna)
- COMSOL, Inc. (provide COMSOL Multiphysics (formerly FEMLAB))
- VisualFEA
- GLView Inova
- MEGA (electromagnetics)
- Pro/MECHANICA
- Plaxis (finite element code for soil and rock analyses)
- SOFiSTiK: FEA software based on AutoCAD. (structural engineering)
- Strand7 (also known as Straus7 in Europe outside the U.K)
- UGS NX Nastran
- CUBIT Hex/Tet meshing tool (Sandia National Laboratories)
Other links
- "Early Masters of the Mesh" - Mechanical Engineering Magazine Online (ASME).
- ASME Eyewitness Series: Finite Element Method (FEM) - Historical Timeline
- A Historical Outline of Matrix Structural Analysis: A Play in Three Acts
- Mini-FEA - This is a free web-based package that teaches students and other newbies how to "do FEA."ca:Anàlisi d'Elements Finits