Perusal of the Finite Element Method

273 Pages·2016·75.848 MB·English

by  Radostina Petrova

Perusal of the Finite Element Method
Edited by Radostina Petrova
Perusal of the Finite Element Method
Edited by Radostina Petrova
Published by ExLi4EvA
Copyright © 2016
All chapters are Open Access distributed under the Creative Commons Attribution
3.0 license, which allows users to download, copy and build upon published articles
even for commercial purposes, as long as the author and publisher are
properly credited, which ensures maximum dissemination and a wider impact of our
publications. After this work has been published, authors have the right to
republish it, in whole or part, in any publication of which they are the author,
and to make other personal use of the work. Any republication, referencing or
personal use of the work must explicitly identify the original source.
As for readers, this license allows users to download, copy and build upon
published chapters even for commercial purposes, as long as the author and publisher
are properly credited, which ensures maximum dissemination and a wider impact of
our publications.
Notice
Statements and opinions expressed in the chapters are these of the individual
contributors and not necessarily those of the editors or publisher. No responsibility is
accepted for the accuracy of information contained in the published chapters. The
publisher assumes no responsibility for any damage or injury to persons or property
arising out of the use of any materials, instructions, methods or ideas contained in the
book.
Publishing Process Manager
Technical Editor AvE4EvA MuViMix Records
Cover Designer
ISBN-10: 953-51-2820-5
ISBN-13: 978-953-51-2820-5
Print
ISBN-10: 953-51-2819-1
ISBN-13: 978-953-51-2819-9

C ontents
Preface
Chapter 1 Problems of Hierarchical Modelling and hp-Adaptive
Finite Element Analysis in Elasticity, Dielectricity and Piezoelectricity
by Grzegorz Zboiński
Chapter 2 The Discontinuous Galerkin Finite Element Method
for Ordinary Differential Equations
by Mahboub Baccouch
Chapter 3 On Finite Element Vibration Analysis of Carbon
Nanotubes
by Ishan Ali Khan and Seyed M. Hashemi
Chapter 4 Micromechanical Analysis of Polymer Fiber
Composites under Tensile Loading by Finite Element Method
by Ezgi Günay
Chapter 5 Estimation of Shallow Water Flow Based on Kalman
Filter FEM
by Takahiko Kurahashi, Taichi Yoshiara and Yasuhide Kobayashi
Chapter 6 Improved Reduced Order Mechanical Model and
Finite Element Analysis of Three-Dimensional Deformations of
Epithelial Tissues
by Ara S. Avetisyan, Asatur Zh. Khurshudyan and Sergey K. Ohanyan
Chapter 7 Simulating Contact Instability in Soft Thin Films
through Finite Element Techniques
by Jayati Sarkar, Hemalatha Annepu and Satish Kumar Mishra
VI Contents
Chapter 8 The Role of Finite Element Analysis in Studying Potential
Failure of Mandibular Reconstruction Methods
by Raymond C.W. Wong, John S.P. Loh and I. Islam
Chapter 9 Evaluation of Adaptive Bone Remodeling after Total Hip
Arthroplasty Using Finite lement Analysis
by Yutaka Inaba, Hiroyuki Ike, Masatoshi Oba and Tomoyuki Saito
Chapter 10 Finite Elements Method in Implant Prosthetics
by Iulia Roateşi

Preface
The finite element method (FEM) is a numerical technique for finding
approximate solutions to different numerical problems. The practical
applications of FEM are known as finite element analysis (FEA). FEA
is a good choice for analyzing problems over complicated domains.
The first three chapters of this book contribute to the development of
new FE techniques by examining a few key hurdles of the FEM and
proposing techniques to mitigate them. The next four chapters focus
on the close connection between the development of a new technique
and its implementation. Current state-of-the-art software packages for
FEA allow the construction, refinement, and optimization of entire
designs before manufacturing. This is convincingly demonstrated in
the last three chapters of the book with examples from the field of
biomechanical engineering.
This book presents a current research by highlighting the vitality and
potential of the finite elements for the future development of more
efficient numerical techniques, new areas of application, and FEA's
important role in practical engineering.

ProvisionaCl hchapaptetre r1
PPrroobblleemmss ooff HHiieerraarrcchhiiccaall MMooddeelllliinngg aanndd hhpp--AAddaappttiivvee
Finite Element Analysis in Elasticity, Dielectricity and
Finite Element Analysis in Elasticity, Dielectricity and
Piezoelectricity
Piezoelectricity
Grzegorz Zboiński
Grzegorz Zboiński
Additional information is available at the end of the chapter
Additional information is available at the end of the chapter
http://dx.doi.org/10.5772/64892
Abstract
In this chapter, we consider theoretical and implementation difficulties in application
of the hierarchical modelling and hp-adaptive finite element approach to elasticity,
dielectricity and piezoelectricity. The main feature of the applied methodology is its
generalizing character which is reflected by application of the same or analogous
algorithms to three mentioned physical problems, including multi-physics problem of
piezoelectricity, simple and complex physical description as well as simple and complex
geometries. In contrast to the most common approaches dealing with a single physical
phenomenon, described by a single physical model, within a single geometrical part,
this chapter presents the ideas which brake and overcome such a simplicity. This
presented chapter generalizes author’s hitherto accomplishments, in hierarchical
models and hp-approximations of linear elasticity, onto dielectricity and piezoelectricity.
The same refers to error estimation and adaptivity control. In this context, the main
similarities and differences of three physical problems are of interest in this work.
Keywords: physical complexity, elasticity, dielectricity, piezoelectricity, geometrical
complexity, model complexity, hierarchical modelling, finite elements, hierarchical ap-
proximations, error estimation, hp-adaptivity
1. Introduction
In this chapter of the book we extend our hitherto propositions concerning 3D-based hier-
archical models of liner elasticity onto 3D-based linear dielectric and piezoelectric media. In
the case of hierarchical models of linear elasticity we apply 3D-elasticity model, hierarchical