Finite element analysis

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Visualization of how a car deforms in an asymmetrical crash using finite element analysis.

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

• Finite element method
• Rayleigh-Ritz method
• Computational fluid dynamics
• Computer representation of surfaces
• Stress (physics)

External links

Open-source FEA software packages include Z88, SLFFEA, YADE, FEniCS, deal.II, libMesh, freeFEM, Elmer, Code-Aster, and FElt.

• [Calculix]
• [Code-Aster]
• [deal.II]
• [Elmer]
• [FElt]
• [FEniCS]
• [freeFEM]
• [Impact]
• [IMTEK Mathematica Supplement (IMS)]
• [libMesh]
• [OFELI]
• [OOFEM] - Free, object oriented, general purpose FEM code
• [OpenSees] - An object oriented program
• [SLFFEA]
• [YADE]
• [Z88]

Commercial FEA software packages include ABAQUS, ANSYS, LS-DYNA, Nastran, Marc, and COMSOL Multiphysics.

• [ABAQUS, Inc.]
• [Analysis for Windows]
• [ANSYS, Inc.]
• [COMSOL, Inc.] - Provide COMSOL Multiphysics (formerly FEMLAB)
• [COSMOS/M and COSMOSWorks] - Integrated Design Validation in SolidWorks
• [CUBIT] - Hex/Tet meshing tool (Sandia National Laboratories)
• [ESI Pam-Crash] - Advanced crash simultion software
• [FEMPRO] - Provide Algor
• [GLView Inova]
• [Infolytica Corp.]
• [Livermore Software Technology Corporation, LSTC] - Provide LS-DYNA and [LS-PrePost]
• [MEGA] - Electromagnetics
• [Moldflow] - Provide [Moldflow Plastics Insight] flow analysis software
• [MSC Software] - Provide Nastran and Marc
• [NAFEMS] - The International Association for the Engineering Analysis Community
• [NEiNastran]
• [NISA] Cranes Software International Ltd.
• [Plaxis] - Finite element code for soil and rock analysis
• [Pro/MECHANICA]
• [Quickfield] - Free Demo (limited to 255 mesh nodes)
• [SOFiSTiK] - Structural FEA software based on AutoCAD
• [Strand7] (aka Straus7 in Europe outside the UK)
• [StressCheck] - P-version FEA software
• [UGS NX Nastran]
• [VisualFEA]
• [Visual-Mesh] - Advanced meshing tool for crash, thermal and magnetic applications

Other links

• [ASME Eyewitness Series: Finite Element Method (FEM)] - Historical Timeline
• [A Historical Outline of Matrix Structural Analysis: A Play in Three Acts]
• [FEAinformation] - Industry leaders in software and hardware
• ["Early Masters of the Mesh"] - Mechanical Engineering Magazine Online (ASME)
• [Mini-FEA] - Free web-based package that teaches students and other beginners how to "do FEA"
• [IFER] - Internet Finite Element Resources - an annotated list of FEA links and programs
• [FEA in the Semiconductor Industry] - www.SiliconFarEast.com
• [FEAdomain] - Finite Element Analysis Resources

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