Finite Element Analysis (FEA) is a computer simulation technique used in engineering analysis. It uses a numerical technique called the finite element method (FEM). In this, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions — 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.
FEA has become a solution to the task of predicting failure due to unknown stresses by showing problem areas in a material and allowing designers to see all of the theoretical stresses within. This method of product design and testing is far superior to the manufacturing costs which would accrue if each sample was actually built and tested.
There are generally two types of analysis: 2D modeling, and 3D modeling. While 2D modeling conserves simplicity and allows the analysis to be run on a relatively normal computer, it tends to yield less accurate results. 3D modeling, produces more accurate results while it can only be run satisfactorily on a faster computer effectively. Within each of these modeling schemes, the programmer can insert numerous algorithms (functions) which may make the system behave linearly or nonlinearly. Linear systems are far less complex and generally do not take into account plastic deformation. Nonlinear systems do account for plastic deformation, and many also are capable of testing a material all the way to fracture.
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, though this will retard the process of converging.
Uses
A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. It is used in new product design, and also in existing product refinement. A company is able to verify whether a proposed design will be able to perform to the client’s specifications prior to manufacturing or construction. Modifying an existing product or structure is utilized to qualify the product or structure for a new service condition. In case of structural failure, FEA may be used to help determine the design modifications to meet the new condition. 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 closedform analytical solutions.
Some FEA Software’s
Free/Open Source

ALBERTA
An adaptive hierarchical finite element toolbox
CalculiX
 is an Open Source FEA project. The solver uses a partially compatible ABAQUS file format. The pre/postprocessor generates input data for many FEA and CFD applications.
Code Aster:
French software written in Python and Fortran, GPL license.
Deal.II
is a finite element differential equation library
DUNE,
Distributed and Unified Numerics Environment GPL Version 2 with RunTime Exception, written in C++
Elmer FEM solver:
Open source multiphysical simulation software developed by Finnish Ministry of Education’s CSC, written in C, C++ and Fortran
FEAPpv
A general purpose finite element analysis program
FEBio
Finite Elements for Biomechanics
FEMM
is a Windows finite element solver for 2D and axisymmetric magnetic, electrostatic, heat flow, and current flow problems
FEMPACK
– Finite Element Routines
FEniCS
Project: a LGPLlicensed software package developed by American and European researchers
FETK
is an adaptive finite element method (AFEM) software libraries and tools for solving coupled systems of nonlinear geometric partial differential equations (PDE)
FRANC2D and FRANC3D:
is a two/three dimensional, finite element based program for simulating curvilinear crack propagation in planar (plane stress, plane strain, and axisymmetric) structures developed by Cornell Fracture Group US. software available for Windows and Linux/UNIX
Freefem++
is an implementation of a language dedicated to the finite element method
GetFEM++
An opensource finite element library
Hermes Project:
Modular C/C++ library for rapid development of space and spacetime adaptive hpFEM solvers.
Impact:
Dynamic Finite Element Program Suite, for dynamic events like crashes, written in Java, GNU license
libMesh
a framework for the numerical simulation of partial differential equations
OFELI :
(Object Finite Element LIbrary)a library of finite element C++ classes for multipurpose development of finite element software
OOF:
finite element modeling for material science
OOFEM:
Object Oriented Finite EleMent solver, written in C++, GPL v2 license
OpenFOAM
(Field Operation And Manipulation). Originally for CFD only, but now includes finite element analysis through tetrahedral decomposition of arbitrary grids.
OpenSees
is an Open System for Earthquake Engineering Simulation
ParaFEM
is a freely available, portable library of subroutines for parallel finite element analysis. The subroutines are written in FORTRAN90/95 and use MPI for message passing.
WARP3D
Static and Dynamic Nonlinear Analysis of Fracture in Solids
Z88:
FEMsoftware available for Windows and Linux/UNIX, written in C, GPL license
Proprietary/Commercial

Abaqus:
FrancoAmerican software from SIMULIA, owned by Dassault Systemes

ADINA

Advance Design BIM
software for FEM structural analysis, including international design eurocodes, a solution developed by GRAITEC

ALGOR
Incorporated

Altair HyperWorks
Altair Engineering’s HyperWorks is a computeraided engineering (CAE) simulation software platform that allows businesses to create superior, marketleading products efficiently and cost effectively.

ANSA:
An advanced CAE preprocessing software for complete model build up.

ANSYS:
American software

COMSOL Multiphysics
COMSOL Multiphysics Finite Element Analysis Software formerly Femlab

Creo Elements / Pro Mechanica:
A pversion finite element program that is embedded in the MCAD application Creo Elements Pro, from PTC (Parametric Technology Corporation)

Diffpack
Software for finite element analysis and partial differential equations

Diana
(software) a multipurpose finite element program (threedimensional and nonlinear) by TNO

Falcon2.0 :
Lightweight FEM POST Processor and Viewer for 3D UNV and NASTRAN files

FEFLOW:
simulates groundwater flow, mass transfer and heat transfer in porous media

Femap,
Siemens PLM Software: A pre and post processor for Windows

FEM
Design Structural analysis software from StruSoft (Swedish company).

FEMtools,
Dynamic Design Solutions: A toolbox for static and dynamic simulation, verification, validation and updating of finite element models. Includes also modules for structural optimization and for obtaining experimental reference data.

FENSAPICE
(Finite Element Navier–Stokes Package) the fullyintegrated 3D inflight CFD icing simulation system developed by Newmerical Technologies Intl.

FlexPDE

Flux :
American electromagnetic and thermal FEA

Genie:
DNV (Det Norske Veritas) Software

HydroGeoSphere:
A 3D controlvolume finite element hydrologic model, simulating surface and subsurface water flow and solute and thermal energy transport

HyperSizer:
Software for composite material analysis

Infolytica MagNet :
North American electromagnetic, electric and thermal FEA software

JMAG:
Japanese software Actran: Belgian Software (Acoustic)

LINKpipe:
from LINKftr AS (Norwegian company). Special purpose non linear FE program for pipelines

LSDYNA
LSTC – Livermore Software Technology Corporation

LUSAS:
UK Software

MADYMO:
TASS – TNO Automotive Safety Solutions

MSC.Marc:
from MSC Software

Nastran:
American software, from MSC Software

Nautics 3D Beam:
DNV (Det Norske Veritas) Software

Nastran/EM
Nastran Suit for highly advanced Durability & NVH Analyses of Engines; born from the AK32 Benchmark of Audi, BMW, Daimler, Porsche & VW; Source Code available

NEi Fusion, NEi Software:
3D CAD modeler + Nastran FEA

NEi Nastran, NEi Software:
General purpose Finite Element Analysis

NEi Works, NEi Software:
Embedded Nastran for SolidWorks users

NISA:
Indian software

PAK:
Serbian software for linear and nonlinear structural analysis, heat conduction, fluid mechanics with heat transfer, coupled problems, biomechanics, fracture mechanics and fatigue.

Plaxis:
Geotechnical 2D/3D FE suites, with support for stresses, deformations, groundwater flow and dynamics.

PZFlex:
American software for wave propagation and piezoelectric devices

Quickfield :
Physics simulating software

Radioss:
A linear and nonlinear solver owned by Altair Engineering

Range Software:
Multi physics simulation software

RFEM

SAMCEF:
CAE package developed by the Belgian company

SAP2000:
American software

STRAND7:
Developed in Sydney Australia by Strand7 Pty. Ltd. Marketed as Straus7 in Europe.

StressCheck
developed by ESRD, Inc (USA) emphasizing solution accuracy by utilizing high order elements

Vector Fields Concerto:
UK 2d/3d RF and microwave electromagnetic design software

Vector Fields Opera:
UK 2d/3d Electromagnetic and multiphysics finite element design software

Vflo:
Physicsbased distributed hydrologic modeling software, developed by Vieux & Associates, Inc.

Zébulon:
French software
The site is devoted to AutoFEM Analysis, the FEA software, which is oriented
towards a broad community of engineers. The important feature of the system is its close relationship with the wellknown system of designing, i.e.,‑ AutoCAD. The most popular graphic system AutoCAD 20072010, 2012 is used as a geometric modeling kernel for the preparation of the finite element model in AutoFEM Analysis. There is a free version AutoFEM Lite for educational purposes, which allows to solve various FEA problems without any limitations in quantities of degrees of freedom.
Is not a comment but a question about the FEM code for heat conduction in solids. which one of the source free codes is best fitted to my problem in heat conduction in solids? I am using a laser to heat a metalic surface and need the temperature profile along the surface as well as inside?
Alexander do you feel that FEA software like AutoFEM analysis will be able to compete with software like Ansys in the future?