Finite Element Theory And Its Application With Open Source Codes
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Finite element theory and its application with open source codes
This book combines essential finite element (FE) theory with a set of fourteen tutorials using relatively easy-to-use open source CAD, FE and other numerical analysis codes so a student can undertake practical analysis and self-study. The theory covers fundamentals of the finite element method. Formulation of element stiffness for one dimensional bar and beam, two dimensional and three dimensional continuum elements, plate and shell elements are derived based on energy and variational methods. Linear, nonlinear and transient dynamic solution methods are covered for both mechanical and field analysis problems with a focus on heat transfer. Other important theoretical topics covered include element integration, element assembly, loads, boundary conditions, contact and a chapter devoted to material laws on elasticity, hyperelasticity and plasticity. A brief introduction to Computational Fluid Dynamics (CFD) is also included. The second half of this book presents a chapter on using tutorials containing information on code installation (on Windows) and getting started, and general hints on meshing, modelling and analysis. This is then followed by tutorials and exercises that cover linear, nonlinear and dynamic mechanical analysis, steady state and transient heat analysis, field analysis, fatigue, buckling and frequency analysis, a hydraulic pipe network analysis, and lastly two tutorials on CFD simulation. In each case theory is linked with application and exercises are included for further self-study. For these tutorials open source codes FreeCAD, CalculiX, FreeMAT and OpenFOAM are used. CalculiX is a comprehensive FE package covering linear, nonlinear and transient analysis. One particular benefit is that its format and structure is based on Abaqus, so knowledge gained is relevant to a leading commercial code. FreeCAD is primarily a powerful CAD modelling code, that includes good finite element meshing and modelling capabilities and is fully integrated with CalculiX. FreeMAT is used in three tutorials for numerical analysis demonstrating algorithms for explicit finite element and CFD analysis. And OpenFOAM is used for other CFD flow simulations. The primary aim of this book is to provide a unified text covering theory and practice, so a student can learn and experiment with these versatile and powerful analysis methods. It should be of value to both finite element courses and for student self-study.
Finite Element Theory and Its Application with Open-source Codes
This book combines essential finite element (FE) theory with a set of twelve tutorials using relatively easy-to-use open source CAD, FE and numerical analysis codes so a student can undertake practical analysis and self-study. The theory covers fundamentals of the finite element method. Formulation of element stiffness for one dimensional bar and beam, two dimensional and three dimensional continuum elements, plate and shell elements are derived based on direct, energy and variational methods. Linear, nonlinear and transient dynamic solution methods are covered for both mechanical and field analysis problems with a focus on heat transfer. Other important theoretical topics covered include element integration, element assembly, loads, boundary conditions, contact and a chapter devoted to material laws on elasticity, hyperelasticity and plasticity.The second half of this book presents one chapter on using the tutorials containing information on installing the codes (on Windows) and getting started, and general hints on meshing, modelling and analysis. This is then followed by the tutorials and exercises which cover linear, nonlinear and dynamic mechanical analysis, steady state and transient heat analysis, field analysis, fatigue, buckling and frequency analysis, and lastly a hydraulic pipe network analysis. In each tutorial I have linked theory with application and included exercises for further self-study. For these tutorials open source codes FreeCAD, CalculiX and FreeMAT are used. CalculiX is a comprehensive FE package covering linear, nonlinear, mechanical, fluid and thermal analysis. One particular benefit is its format and structure, which is based on Abaqus and therefore knowledge gained is relevant to a leading commercial code. FreeCAD is primarily a powerful CAD modelling code, that includes good finite element meshing and modelling capabilities and is fully integrated with CalculiX. FreeMAT is used in two tutorials for numerical analysis demonstrating algorithms for explicit finite element analysis.The primary aim of this book is to provide a unified text covering theory and practice, so a student can learn and experiment with this versatile and powerful analysis method. It should be of interest to both finite element courses and for student self-study.Anthony Pickett undertook postgraduate research in composites analysis at the University of Surrey and RAE Farnborough, followed by nearly twenty-five years industrial work as scientific director with ESI GmbH developing and applying FE codes for crash, impact, process and mechanical simulation of metal and composite structures. From 2002 he was a professor at Cranfield University and since 2007 has continued research and teaching of advanced composites and analysis at IFB (Institute of Aircraft Design) at the University of Stuttgart, Germany.
Automated Solution of Differential Equations by the Finite Element Method
Author: Anders Logg
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-02-24
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.