Finite Element Analysis of Structures through Unified Formulation

The finite element method (FEM) is a computational tool widely
used to design and analyse complex structures. Currently,
there are a number of different approaches to analysis using the
FEM that vary according to the type of structure being analysed:
beams and plates may use 1D or 2D approaches, shells and solids 2D
or 3D approaches, and methods that work for one structure are
typically not optimized to work for another.

Finite Element Analysis of Structures Through Unified
Formulation deals with the FEM used for the analysis of the
mechanics of structures in the case of linear elasticity. The
novelty of this book is that the finite elements (FEs) are
formulated on the basis of a class of theories of structures known
as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and
3D FEs on the basis of the same 'fundamental nucleus' that comes
from geometrical relations and Hooke's law, and presents both 1D
and 2D refined FEs that only have displacement variables as in 3D
elements. It also covers 1D and 2D FEs that make use of 'real'
physical surfaces rather than 'artificial' mathematical
surfaces which are difficult to interface in CAD/CAE software.

Key features:

• Covers how the refined formulation can be easily and
  conveniently used to analyse laminated structures, such as sandwich
  and composite structures, and to deal with multifield problems

• Shows the performance of different FE models through the 'best
  theory diagram' which allows different models to be compared in
  terms of accuracy and computational cost

• Introduces an axiomatic/asymptotic approach that reduces the
  computational cost of the structural analysis without affecting the
  accuracy

• Introduces an innovative 'component-wise' approach to deal with
  complex structures

• Accompanied by a website hosting the dedicated software package
  MUL2 (www.mul2.com)

Finite Element Analysis of Structures Through Unified
Formulation is a valuable reference for researchers and
practitioners, and is also a useful source of information for
graduate students in civil, mechanical and aerospace
engineering.

Auteur

Erasmo Carrera is currently a full professor at the
Department of Mechanical and Aerospace Engineering at Politecnico
di Torino. He is the founder and leader of the MUL2 group at
the university, which has acquired a significant international
reputation in the field of multilayered structures subjected to
multifield loadings, see also www.mul2.com. He has introduced the
Unified Formulation, or CUF (Carrera Unified Formulation), as a
tool to establish a new framework in which beam, plate and shell
theories can be developed for metallic and composite multilayered
structures under mechanical, thermal electrical and magnetic
loadings. CUF has been applied extensively to both strong and weak
forms (FE and meshless solutions). Carrera has been author and
co-author of about 500 papers on structural mechanics and aerospace
engineering topics. Most of these works have been published in
first rate international journals, as well as of two recent books
published by J Wiley & Sons. Carrera's papers have had
about 500 citations with h-index=34 (data taken from Scopus).

Maria Cinefra is currently a research assistant at the
Politecnico di Torino. Since 2010, she has worked as a teaching
assistant on the "Non-linear analysis of structures", "Structures
for spatial vehicles" and "Fundamentals of structural mechanics"
courses. She is currently collaborating with the Department of
Mathematics at Pavia University in order to develop a mixed shell
finite element based on the Carrera Unified Formulation for the
analysis of composite structures. She is currently working in the
STEPS regional project, in collaboration with Thales Alenia Space.
M. Cinefra is also working on the extension of the shell finite
element, based on the CUF, to the analysis of multi-field
problems.

Marco Petrolo is a Post-Doc fellow at the Politecnico di Torino
(Italy). He works in Professor Carrera's research group on various
research topics related to the development of refined structural
models of composite structures. His research activity is connected
to the structural analysis of composite lifting surfaces; refined
beam, plate and shell models; component-wise approaches and
axiomatic/asymptotic analyses. He is author and coauthor of some 50
publications, including 2 books and 25 articles that have been
published in peer-reviewed journals. Marco has recently been
appointed Adjunct Professor in Fundamentals of Strength of
Materials (BSc in Mechanical Engineering at the Turin Polytechnic
University in Tashkent, Uzbekistan).

Enrico Zappino is a Ph.D student at the Politecnico di
Torino (Italy). He has worked in Professor Erasmo Carrera's
research group since 2010. His research activities concern
structural analysis using classical and advanced models,
multi-field analysis, composite materials and FEM advanced models.
He is co-author of many works that have been published in
international peer-reviewed journals. Enrico was employed as a
research assistant in Professor Erasmo Carrera's group from
September 2010 to January 2011, where his research, in cooperation
with Tales Alenia Space (TASI), was about the panel flutter
phenomena of composite panels in supersonic flows.

Résumé

The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another.

Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same 'fundamental nucleus' that comes from geometrical relations and Hooke's law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D and 2D FEs that make use of 'real' physical surfaces rather than 'artificial' mathematical surfaces which are difficult to interface in CAD/CAE software.

Key features:

• Covers how the refined formulation can be easily and conveniently used to analyse laminated structures, such as sandwich and composite structures, and to deal with multifield problems
• Shows the performance of different FE models through the 'best theory diagram' which allows different models to be compared in terms of accuracy and computational cost
• Introduces an axiomatic/asymptotic approach that reduces the computational cost of the structural analysis without affecting the accuracy
• Introduces an innovative 'component-wise' approach to deal with complex structures
• Accompanied by a website hosting the dedicated software package MUL2 (www.mul2.com)
  Finite Element Analysis of Structures Through Unified Formulation is a valuable reference for researchers and practitioners, and is also a useful source of information for graduate students in civil, mechanical and aerospace engineering.

Contenu
Preface xiii List of symbols and acronyms xvii

1 Introduction 1

1.1 What is in this book 1

1.2 The finite element method 2

1.2.1 Approximation of the domain 2

1.2.2 The numerical approximation 4

1.3 Calculation of the area of a surfac…