Método dos Elementos Finitos


Vá para o link desejado:




Imagens de modelos

Provas resolvidas

Freewares com código fonte

Visualização de resultados de EF


Qualquer material que você queira colocar na página, mande para  amiranda@tecgraf.puc-rio.br




Método dos Elementos Finitos - Disponível pelo Prof. Álvaro F. M. Azevedo (bom livro).


        Retorna ao topo da página


Ansys Exercícios de EF.pdf - Obtido da Internet.

Barras em Traçao e Compressão.pdf - Obtido da Internet.

Elementos Finitos Isoparamétricos.pdf - Obtido da Internet.

Formulação do MEF.pdf - Obtido da Internet.

Integração Numérica 01.pdf - Obtido da Internet.

Integração Numérica 02.pdf - Obtido da Internet.

Introdução ao MEF 02.pdf - Obtido da Internet.

Introdução ao MEF.zip - Obtido da Internet.

Cap_1_2_metodos.zip - Obtido da Internet.

        Retorna ao topo da página


Basic Analysis Reference - SAP.pdf

Analysis Reference 01 - SAP.pdf

Analysis Reference 02 - SAP.pdf


Manuais Online do Ansys Release 5.5


        Retorna ao topo da página

Imagens de modelos


        Retorna ao topo da página

Provas resolvidas


        Retorna ao topo da página

Freewares com Código Fonte

ALADDIN - Aladdin is a computational toolkit for the interactive matrix and finite element analysis of large engineering structures, particularly building and highway bridge structures. Aladdin views finite element computations as a specialized form of matrix computations, matrices as rectangular arrays of physical quantities, and numbers as dimensionless physical quantities.

ALBERT - ALBERT is an Adaptive multiLevel finite element toolbox using Bisectioning refinement and Error control by Residual Techniques.

BASIN - BASIN is a finite-element program, that simulates the filling of a sedimentary basin and includes transport, erosion and consolidation of sediment, tectonic processes like isostatic compensation, consolidational fluid flow,topography driven fluid flow, heat flow including advection, solute transport.

CalculiX - CalculiX is a package designed to solve field problems. The method used is the finite element method. So far only structural problems can be solved but it is planned to extend the capabilities.


Deal.II - Deal.II is a C++ program library targeted at adaptive finite elements and error estimation. It uses state-of-the-art programming techniques of the C++ programming language to offer you a modern interface to the complex data structures and algorithms required for adaptivity and enables you to use a variety of finite elements in one, two, and three space dimensions, as well as time-dependent problems.

DOUG - DOUG is a black box parallel iterative solver for finite element systems arising from elliptic partial differential equations. Used in conjunction with a finite element discretisation code, DOUG will solve the resulting linear systems using an iterative method and provides a range of powerful domain decomposition preconditioners.

EMAP - EMAP (ElectroMagnetic Analysis Program) is a family of three-dimensional finite element modeling codes that can be used to analyze simple 3-dimensional geometries. The EMAP codes are relatively easy to learn to use and are distributed in source code form.

EXPDE - Expression Templates for Partial Differential Equations.

FEATFLOW - Solver package for incompressible flow in 2D and 3D. "AMiranda recomenda".

FeaTure - FeaTure is a framework for C++ programming of finite element codes. It provides a number of base classes such as element, node, degree of freedom and material classes, but also utility classes as matrix and vector classes, shape function classes and more.

FELIB - The Finite Element Library (FELIB) is a program subroutine library for the numerical solution of partial differential equations using the finite element method. It has been designed to meet the needs of the algorithm developer and is a set of software tools, rather than a package addressing one particular area. As a result the library is very flexible and enables its users to apply the finite element technique to any new research area in mathematical physics where packages do not exist, e.g. in free-surface flows and non-Newtonian mixing.

FELT - FElt is an open source system for finite element analysis. The current version of FElt knows how to solve linear static and dynamic structural and thermal analysis problems; it can also do modal and spectral analysis for dynamic problems. FElt's element library currently contains fourteen elements.

FEM - FEM is a C++ Object Oriented Finite Element Code Demonstrator. The source code contains C++ classes that represent Finite Element objects such as nodes, elements, connectivities, and degrees of freedom as well as Mathematical objects such as vectors, matrices, and sparse matrices. These C++ objects can be (and are) used to construct specific problem description classes for linear statics, linear dynamics, and modal analysis.  The source code also contains three different equation solvers: a skyline, a frontal, and a Preconditioned Conjugate Gradient (PCG) solver.

FEM_Object - FEM_Object 001 in Smalltalk V offers a user-friendly object-oriented finite element development environment; it includes truss and plain-strain elements in statics and dynamics. Extensive tutorials explain how to expand the existing package. FEM_Object 001 in C++ can be used to solve large problems; it retains most pleasant features of its Smalltalk version without the drawbacks (limited problem size, slow execution speed).

FEMM - A free magnetics finite element package.

FEMSET - Der Finite-Elemente-"Baukasten" FEMSET stellt die Routinen des Finite-Elemente-Algorithmus im Quellcode zur Verfügung (es ist ein “Baukasten” für die Lehre und für Experimente, keine Konkurrenz für kommerzielle Systeme). Vom Benutzer können beliebige Routinen für spezielle finite Elemente ergänzt werden.

FreeFem+ - FreeFem+ is an implementation of a language dedicated to the finite element method. It provides you a way to solve Partial Differential Equations (PDE) simply.  Problems involving partial differential equations (pde) of  several branches of physics such as fluid-structure interactions require interpolations of data on several meshes and their manipulation within one program.

GEOCRACK - GEOCRACK is a 2D coupled structural deformation/fluid flow/heat transfer program. It has been primarily developed to calculate fluid flow in jointed rock, such as occurs in a Hot Dry Rock geothermal reservoir. However, it can also be used to solve elasticity problems. All input is interactive, including visualisation of the results.

GeoFEM - A multi-purpose / multi-physics parallel finite element solver for the solid earth. GeoFEM is part of the very ambitious Earth Simulator project begun in 1997. The latter aims at the development of a high performance massively parallel processing computer capable of 40 TFLOPS at peak and 5 TFLOPS effective speed (about 1000 times faster than current super computers). The GeoFEM component aims at the modelling and simulation of solid earth phenomena and development of associated large scale parallel software.

KASKADE - Family of adaptive FEM codes in 2D and 3D for solution of elliptic (KASKADE) or parabolic (KASTIO) pdes.

KFem - KFem stands for Kde Finite Element Method. It is based FreeFEM which is an implementation of the GFem language.

LUGR Project - Adaptive grid solvers for systems of (time-dependent) pdes in 2D and 3D.

MiniFEM - An experimental 2D object oriented FE package for student and academic use.

MODFE - A two-dimensional FE program for groundwater flow under saturated conditions.

MODULEF - A modular FE library which can be installed on workstations, mainframes and supercomputers. The facilities include 2D and 3D mesh generation and visualisation, and a choice of solution methods (direct and iterative). There is an interactive mode and source code is available.

OFELI - An Object Finite Element LIbrary of C++ classes for the development of finite element codes.

PadFEM - PadFEM is an environment supporting parallel adaptive finite element simulations. Besides graphical pre-processing interfaces based on Tcl/Tk and Java, PadFEM includes a quadtree-based mesh generators for 2-dimensional arbitrary domains, mesh partitioning algorithms, different solvers, error estimators, mesh refinement and load balancing algorithms. For monitoring, debugging and post-processing in 2D, the XLib-based graphical interface XFem! is provided.

PARSYS - Solve systems of non-linear parabolic PDE's in one space variable.

PHYSICA - A toolkit for multi-physics computational continuum mechanics modelling based on three dimensional unstructured meshes using finite volume / finite element techniques.

Rheolef - An 1D/2D/3D finite element environment for solving PDEs comprising a set of unix commands and a library of C++ classes.

San Le's Free Finite Element Analysis - It is a package of scientific software and graphical user interfaces for use in finite element analysis. It is written in ANSI C by San Le and distributed under the terms of the GNU license. "AMiranda recomenda".

SOL1D - This is a simple Galerkin finite-element solution of the time-dependent equations governing the state of a plasma confined between two absorbing plates. There are source functions for heat and particles, in the presence of which the plasma approaches a steady state.

TOCHNOG - A comprehensive FE package with a wide range of applications, including fluids, solids, ground water flow, the wave equation, and the convection-diffusion equation. "AMiranda recomenda".

UG - A flexible toolbox for the adaptive multigrid solution of partial differential equations. Problem classes include 3D convection diffusion, linear elasticity, incompressible Navier-Stokes (2D).

VECFEM - VECFEM (VECtorised Finite Element Method) solves nonlinear boundary value problems. It has several components, including the graphical user interface xvem as well as the VECFEM kernel.

WARP3D - A large scale research code for the static and dynamic nonlinear analysis of solids. The code includes such features as ductile fracture, J2 integral computation, finite strain formulation, crack growth modelling, and a selection of non-linear material models. Much of the code is written in Fortran 90.

        Retorna ao topo da página

Visualização de Resultados de EF

GiD - GiD is a pre/post processing environment (including mesh generation) which can be adapted to the requirements of specific finite element/difference/volume/point analysis programs. GiD has been designed as a universal, adaptive and user-friendly graphical user interface for geometrical modelling, data input and visualisation of results for all types of numerical simulation programs. Typical problems that can be successfully tackled with GiD include most situations in solid and structural mechanics, fluid dynamics, electromagnetics, heat transfer, geomechanics, etc. using finite element, finite volume, boundary element, finite difference or point based (meshless) numerical procedures.

FE Visualisation for Silicon Graphics Workstations

Geomview - Geomview is an interactive program written by the staff of the Geometry Center for viewing and manipulating geometric objects. It can be used as a standalone viewer for static objects or as a display engine for other programs which produce dynamically changing geometry.

GMV - GMV is an easy to use, 3-D scientific visualization tool designed to view simulation data from any type of structured or unstructured mesh.


Khoros - A software development environment for scientific visualisation, data exploration and image and signal processing.


OpenDX - OpenDX is an open source (free) port of IBM's Visualization Data Explorer software. This is a set of tools for visualisation, which include isosurface and isocontour generation, volume rendering, and cutting planes. "AMiranda recomenda".


PV-WAVE - PV-WAVE is a visualisation package programmed with a ``fourth generation language''. It can be used for postprocessing output from FEA.

VTK (Visualization Toolkit) - The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics, image processing, and visualization used by thousands of researchers and developers around the world. VTK consists of a C++ class library, and several interpreted interface layers including Tcl/Tk, Java, and Python. "AMiranda recomenda".

VU - VU is a configurable scientific visualisation program for the display and analysis of numerical solutions.


        Retorna ao topo da página



        Retorna ao topo da página


Página sempre em construção.