More Info on

Finite Element

Method

Finite Element Method

Finite element method (FEM) is a numerical

technique for finding approximate solutions

to boundary valued problems for partial differential

equations. It uses subdivision of a whole problem

domain into simpler parts, called finite elements,

and variational methods to solve the problem by

minimizing an associated error function. FEM

encompasses methods for connecting many simple

element equations over many small subdomains,

named finite elements, to approximate a more

complex equation over a larger domain.

Technologies That Compete With the FEM

• Other numerical solution methods:

Finite-Difference Methods (FDM) are numerical

methods for solving differential equations by

approximating them with difference equations, in

which finite differences approximate the

derivatives. FDMs are thus discretization methods.

» Useful for solving heat transfer and fluid

mechanics problems.

» Works well for two-dimensional regions with

boundaries parallel to the coordinate axes.

» Cumbersome when regions have curved

boundaries.

• Other numerical solution methods:

The Boundary Element Method (BEM) is a

numerical computational method of solving

linear partial differential equations which

have been formulated as integral equations

(i.e. in boundary integral form). It can be

applied in many areas of engineering and

science including fluid mechanics, acoustics,

electromagnetics, and fracture mechanics.

Technologies that Compete With the FEM …

Technologies that Compete With the FEM …

• Prototype Testing

» Reliable. Well-understood.

» Trusted by regulatory agencies.

» Results are essential for calibration of

simulation software.

» Results are essential to verify modeled results

from simulation.

» Non destructive testing (NDT) is lowering costs

of testing in general.

» Expensive, compared to simulation.

Technologies that Compete With the FEM …

• Prototype Testing

» Time consuming.

» Development programs that rely too much on

testing are increasingly less competitive in

today’s market. » Faster product development schedules are

pressuring the quality of development test

efforts.

» Data integrity is more difficult to maintain,

compared to simulation.

Future Trends in the FEM and Simulation

• Enhanced multi-physics capabilities are coming:

– Coupling between numerous physical

phenomena.

» Ex: Fluid-structural interaction is the most

common example.

» Ex: Semiconductor circuits, EMI and

thermal buildup vary with current densities.

• Improved life predictors, improved service

estimations.

•Decreasing reliance on testing.

Future Trends in the FEM and Simulation…

•Increasing use of non-deterministic analysis and

design methods:

– Statistical modeling of material properties,

tolerances, and anticipated loads.

– Sensitivity analyses.

• Faster and more powerful computer hardware.

Massively parallel processing.

• FEM and simulation software available via Internet

subscription.

Finite Element Method

Software Packages

Name Description Operating System

Agros2D

Multiplatform open source application for

the solution of physical problems based on

the Hermes library

Linux, Windows

CalculiX

It is an Open Source FEA project. The solver

uses a partially compatible ABAQUS file

format. The pre/post-processor generates

input data for many FEA and CFD

applications

Linux, Windows

Code Aster

is an Open Source software package for

Civil and Structural Engineering finite

element analysis and numeric simulation in

structural mechanics which is written in

Python and Fortran

Linux, FreeBSD

deal.II

Comprehensive set of tools for finite element

codes, scaling from laptops to clusters with

10,000+ cores. Written in C++.

Linux, Unix, Mac OS

X,Windows

DUNE Distributed and Unified Numerics

Environment, written in C++

Linux, Unix, Mac OS

X

Free/Open source

Name Description Operating System

Elmer

Open source multiphysical simulation software

developed by Finnish Ministry of Education's

CSC, written primarily in Fortran (written in

Fortran90, C and C++)

Linux, Mac OS

X,Windows

FEATool Easy to Use Matlab and Octave Multiphysics

FEM Solver and GUI Toolbox

Linux, Unix, Mac

OS X,Windows

FEBio Finite Elements for Biomechanics Linux, Mac OS

X,Windows

FEniCS Project

Software package developed by American and

European researchers with the goal to enable

automated solution of differential equations

Linux, Unix, Mac

OS X,Windows

FreeFem++

Software written in C++ for rapid testing and

finite element simulations. The problem is

defined in terms of its variational formulation

Linux, Mac OS

X,Windows, Solaris

GetFEM++

A generic finite element library written

in C++ with interfaces

for Python, Matlab and Scilab. It focuses on

modeling of contact mechanics and

discontinuities (e.g. cracks).

Unix, Mac OS

X, Windows

Name Description Operating System

Hermes

Project

Modular C/C++ library for rapid development of

space- and space-time adaptive hp-FEM solvers

Linux, Unix, Mac

OS X,Windows

jFEM 2D/3D open source C++ FEM codes developed

for nanophotonics by Jeffrey M. McMahon [1][2]

Linux, Unix, Mac

OS X, (Windows,

but unsupported)

Kratos Framework for building multi-disciplinary finite

element programs Linux, Windows

MaxFEM Electromagnetic simulation software based on the

finite element method

Linux, Mac OS

X,Windows

MoFEM

JosePH

MoFEM (JosePH) is a finite element analysis

code tailored for the solution of multi-physics

problems

Unix, Linux, Mac

OS X

MOOSE

Multiphysics Object Oriented Simulation

Environment - an object oriented C++ finite

element framework for rapid development of

tightly coupled multiphysics solvers

Unix, Linux, Mac

OS X

OOFEM Object Oriented Finite EleMent solver, written in

C++ Unix, Windows

Name Description Operating System

OpenSees is an Open System for Earthquake Engineering

Simulation

Unix, Linux,

Windows

Z88/Z88Aurora

Freeware finite element package; The present version

Z88Aurora V3 offers, in addition to static strength

analysis modules such as non-linear strength

calculations (large displacements), simulations with

non-linear materials, natural frequency and static

thermal analysis.

Linux, Windows,

Mac OS X

Proprietary/Commercial Abaqus: Advanced Franco-USA software from SIMULIA, owned by Dassault

Systemes.

ADINA: finite element software for structural, fluid, heat transfer, electromagnetic,

and multiphysics problems, including fluid-structure interaction and thermo-

mechanical coupling

Advance Design: BIM software for FEM structural analysis, including international

design eurocodes, a solution developed by GRAITEC.

ALGOR: USA software from Autodesk. (Renamed to Simulation Multiphysics.)

Altair HyperWorks: A full CAE program suite (including pre/post-processor, Solvers,

Optimization solver, parameter study solver)

ANSA: An advanced CAE pre-processing software for complete model build up.

ANSYS: USA software

AutoForm: Swiss origin German software for Sheet metal forming process chain

CFD-FASTRAN: A commercial Computational Fluid Dynamics (CFD) software package

developed by ESI Group for aerodynamic and aerothermodynamic applications. It

employs multiple moving body capability for simulating problems such as missile

launch, maneuvering and staging, and aircraft flight dynamics and store separation.

Computers and Structures: Berkeley, California-based producers of SAP2000,

CSiBridge, ETABS, SAFE, PERFORM-3D, and CSiCOL

COMSOL Multiphysics COMSOL Multiphysics Finite Element Analysis Software

formerly Femlab

CosmosWorks

CST Studio Suite

DIANA_FEA: designed by TNO DIANA BV in the Netherlands, linear and non-linear

analysis of engineering structures such as dams, bridges, tunnels and underground

structures, oil and gas installations.

Diffpack Software for finite element analysis and partial differential equations

Extreme Loading for Structures: Software made by Applied Science International for

non-linear dynamic structural analysis, progressive collapse, blast, seismic, impact

and other loading.

FEDEM: FEDEM is a simulation software for mechanical multibody systems[3]

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

media

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

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.

Flexcom, Finite element package used in the offshore oil and gas industry.

Developed by MCS Kenny.

FlexPDE

GTSTRUDL, INTEGRAPH System: Structural Design and Analysis Language FEM

System developed by MIT and GATECH, used in Energy and Offshore structural

designs

HydroGeoSphere: A 3D control-volume finite element hydrologic model, simulating

surface and subsurface water flow and solute and thermal energy transport

HyperSizer, design software specializing in composite materials; integrates with

other software

IMPETUS Afea Solver: An explicit general purpose simulation software from

IMPETUS Afea[4]

Jupiter Designer developed by TechnoStar Co. Ltd., headquatered in Tokyo, Japan.

Jupiter designer is a FEA software developed for CAE engineers. [5]

JMAG, Japanese software

LS-DYNA, LSTC - Livermore Software Technology Corporation

LUSAS: UK Software

MADYMO: TASS - TNO Automotive Safety Solutions

MSC Marc: Advanced, nonlinear FEA solver from MSC Software

MultiMech: Multiscale Structural Finite Element Analysis

Nastran: USA software, from MSC Software

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

NEi Nastran, NEi Software: General purpose Finite Element Analysis

NEi Works: Embedded Nastran for SolidWorks users

Pam-Crash: Used for crash simulation and the design of occupant safety systems,

primarily in the automotive industry

PLAXIS 2D and PLAXIS 3D: developed and marketed by Plaxis BV; specially designed

for soil and rock mechanics with emphasis on analysis, design and simulation of

underground constructions and the soil-structure interaction. Special modules

available for dynamics (earthquake), groundwater flow and temperature flow. [6]

PZFlex: USA software for wave propagation and piezoelectric devices

Quickfield : Physics simulating software

Radioss: A linear and nonlinear solver owned by Altair Engineering

RAM Elements: Bentley software available mainly for the use of analysis of

structural systems for civil engineers

Range Software: Multiphysics simulation software

RFEM: BIM software for structural analysis and design according to various

international standards including eurocodes and USA codes

S-FRAME: Software for civil and structural engineers

SAMCEF: CAE package developed by the Belgian company

SAP2000: USA software

Sesam: Norwegian software, developed by DNV GL for the offshore and maritime

industries.

Sherlock Automated Design Analysis: Software is a Physics of Failure-based tool for

analyzing, grading and certifying the expected reliability of products at the circuit

card assembly level, Developed by DfR Solutions. Sherlock interfaces with other FEA

tools such as Abaqus and Ansys software

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

Italy.

StressCheck developed by ESRD, Inc (USA) emphasizing solution accuracy by

utilizing high order elements

TSV developed by TechnoStar Co. Ltd., headquatered in Tokyo, Japan. TSV software

suite includes pre-processor, solver as well as post-processor. [7]

Vflo: Physics-based distributed hydrologic modeling software, developed by Vieux &

Associates, Inc.

VisualFEA, Korean software for structural and geotechnical analysis