Plates and shells for smart structures : classical and advanced theories for modelling and analysis

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Title:

Personal Author:

Carrera, Erasmo

Edition:

1st ed.

Publication Information:

Hoboken, NJ. : Wiley, 2011.

Physical Description:

x, 309 p. : ill. ; 24 cm.

ISBN:

9780470971208

Abstract:

"Plates and Shells for Smart Structures firstly gives an overview of classical plate and shell theories for piezoelectric elasticity, demonstrating their limitations in static and dynamic analysis with a number of example problems. The authors then go on to explain how these limitations can be overcome with the use of the more advanced models that have been developed in recent years; introducing theories able to consider electromechanical couplings as well as those that provide appropriate interface continuity conditions for both electrical and mechanical variables. They provide both analytical and finite element solutions, thus enabling the reader to compare the strong and weak solutions to problems.Plates and Shells for Smart Structures is accompanied by dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given in the book as well as to solve other problems of their own"-- Provided by publisher.

Subject Term:

Shells (Engineering)

Plates (Engineering)

Smart structures

Added Author:

Brischetto, Salvatore

Nali, Pietro

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010283136	TA660.S5 C276 2011	Open Access Book	Book	Searching... Unknown

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Summary

Smart structures that contain embedded piezoelectric patches are loaded by both mechanical and electrical fields. Traditional plate and shell theories were developed to analyze structures subject to mechanical loads. However, these often fail when tasked with the evaluation of both electrical and mechanical fields and loads. In recent years more advanced models have been developed that overcome these limitations.

Plates and Shells for Smart Structures offers a complete guide and reference to smart structures under both mechanical and electrical loads, starting with the basic principles and working right up to the most advanced models. It provides an overview of classical plate and shell theories for piezoelectric elasticity and demonstrates their limitations in static and dynamic analysis with a number of example problems. This book also provides both analytical and finite element solutions, thus enabling the reader to compare strong and weak solutions to the problems.

Key features:

compares a large variety of classical and modern approaches to plates and shells, such as Kirchhoff-Love , Reissner-Mindlin assumptions and higher order, layer-wise and mixed theories introduces theories able to consider electromechanical couplings as well as those that provide appropriate interface continuity conditions for both electrical and mechanical variables considers both static and dynamic analysis accompanied by a companion website hosting dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given as well as solve problems of their own

The models currently used have a wide range of applications in civil, automotive, marine and aerospace engineering. Researchers of smart structures, and structural analysts in industry, will find all they need to know in this concise reference. Graduate and postgraduate students of mechanical, civil and aerospace engineering can also use this book in their studies.

www.mul2.com

Author Notes

Erasmo Carrera, Politecnico di Torino, Italy
Erasmo Carrera is Professor of Aerospace Structures and Computational Aeroelasticity and Deputy Director of Department of Aerospace Engineering at the Politecnico di Torino, Torino, Italy. He has authored circa 200 journal and conference papers. His research has concentrated on composite materials, buckling and postbuckling of multilayered structures, non-linear analysis and stability, FEM; nonlinear analysis by FEM; development of efficient and reliable FE formulations for layered structures, contact mechanics, smart structures, nonlinear dynamics and flutter, and classical and mixed methods for multilayered plates and shells.

Salvatore Brischetto, Politecnico di Torino, Italy
Dr Salavatore Brischetto is a research assistant in the Aeronautics and Space Engineering Department, Politecnico di Torino.

Petro Nali, Politecnico di Torino, Italy
Marco Petrolo is a research scientist in the Department of Aeronautics and Space Engineering at the Politecnico di Torino.

About the Authors	p. ix
Preface	p. xi
1 Introduction	p. 1
1.1 Direct and inverse piezoelectric effects	p. 2
1.2 Some known applications of smart structures	p. 3
References	p. 6
2 Basics of piezoelectricity and related principles	p. 9
2.1 Piezoelectric materials	p. 9
2.2 Constitutive equations for piezoelectric problems	p. 14
2.3 Geometrical relations for piezoelectric problems	p. 18
2.4 Principle of virtual displacements	p. 20
2.4.1 PVD for the pure mechanical case	p. 23
2.5 Reissner mixed variational theorem	p. 23
2.5.1 RMVT(u, , Ïân)	p. 24
2.5.2 RMVT(u, , Dn)	p. 26
2.5.3 RMVT(u, , Ïân, Dn)	p. 28
References	p. 30
3 Classical plate/shell theories	p. 33
3.1 Plate/shell theories	p. 33
3.1.1 Three-dimensional problems	p. 34
3.1.2 Two-dimensional approaches	p. 34
3.2 Complicating effects of layered structures	p. 37
3.2.1 In-plane anisotropy	p. 38
3.2.2 Transverse anisotropy, zigzag effects, and interlaminar continuity	p. 38
3.3 Classical theories	p. 41
3.3.1 Classical lamination theory	p. 41
3.3.2 First-order shear deformation theory	p. 42
3.3.3 VlasovâÇôReddy theory	p. 45
3.4 Classical plate theories extended to smart structures	p. 45
3.4.1 CLT plate theory extended to smart structures	p. 45
3.4.2 FSDT plate theory extended to smart structures	p. 56
3.5 Classical shell theories extended to smart structures	p. 58
3.5.1 CLT and FSDT shell theories extended to smart structures	p. 59
References	p. 60
4 Finite element applications	p. 63
4.1 Preliminaries	p. 63
4.2 Finite element discretization	p. 64
4.3 FSDT finite element plate theory extended to smart structures	p. 68
References	p. 87
5 Numerical evaluation of classical theories and their limitations	p. 89
5.1 Static analysis of piezoelectric plates	p. 90
5.2 Static analysis of piezoelectric shells	p. 92
5.3 Vibration analysis of piezoelectric plates	p. 98
5.4 Vibration analysis of piezoelectric shells	p. 101
References	p. 104
6 Refined and advanced theories for plates	p. 105
6.1 Unified formulation: refined models	p. 105
6.1.1 ESL theories	p. 106
6.1.2 Murakami zigzag function	p. 108
6.1.3 LW theories	p. 110
6.1.4 Refined models for the electromechanical case	p. 113
6.2 Unified formulation: advanced mixed models	p. 113
6.2.1 Transverse shear/normal stress modeling	p. 113
6.2.2 Advanced mixed models for the electromechanical case	p. 115
6.3 PVD(u, ) for the electromechanical plate case	p. 117
6.4 RMVT(u, , Ïân) for the electromechanical plate case	p. 122
6.5 RMVT(u, , Dn) for the electromechanical plate case	p. 130
6.6 RMVT(u, , Ïân, Dn) for the electromechanical plate case	p. 137
6.7 Assembly procedure for fundamental nuclei	p. 148
6.8 Acronyms for refined and advanced models	p. 150
6.9 Pure mechanical problems as particular cases, PVD(u) and RMVT(u, Ïân)	p. 151
6.10 Classical plate theories as particular cases of unified formulation	p. 153
References	p. 154
7 Refined and advanced theories for shells	p. 157
7.1 Unified formulation: refined models	p. 157
7.1.1 ESL theories	p. 158
7.1.2 Murakami zigzag function	p. 160
7.1.3 LW theories	p. 162
7.1.4 Refined models for the electromechanical case	p. 165
7.2 Unified formulation: advanced mixed models	p. 165
7.2.1 Transverse shear/normal stress modeling	p. 166
7.2.2 Advanced mixed models for the electromechanical case	p. 168
7.3 PVD(u, ) for the electromechanical shell case	p. 169
7.4 RMVT(u, , Ïân) for the electromechanical shell case	p. 175
7.5 RMVT(u, , Dn) for the electromechanical shell case	p. 181
7.6 RMVT(u, , Ïân, Dn) for the electromechanical shell case	p. 188
7.7 Assembly procedure for fundamental nuclei	p. 197
7.8 Acronyms for refined and advanced models	p. 200
7.9 Pure mechanical problems as particular cases, PVD(u) and RMVT(u, Ïân)	p. 200
7.10 Classical shell theories as particular cases of unified formulation	p. 202
7.11 Geometry of shells	p. 202
7.11.1 First quadratic form	p. 204
7.11.2 Second quadratic form	p. 204
7.11.3 StrainâÇôdisplacement equations	p. 205
7.12 Plate models as particular cases of shell models	p. 208
References	p. 210
8 Refined and advanced finite elements for plates	p. 213
8.1 Unified formulation: refined models	p. 213
8.1.1 ESL theories	p. 215
8.1.2 Murakami zigzag function	p. 217
8.1.3 LW theories	p. 219
8.1.4 Refined models for the electromechanical case	p. 222
8.2 Unified formulation: advanced mixed models	p. 222
8.2.1 Transverse shear/normal stress modeling	p. 223
8.2.2 Advanced mixed models for the electromechanical case	p. 225
8.3 PVD(u,) for the electromechanical plate case	p. 226
8.4 RMVT(u,, Ïân) for the electromechanical plate case	p. 231
8.5 RMVT(u,,Dn) for the electromechanical plate case	p. 238
8.6 RMVT(u,, Ïân,Dn) for the electromechanical plate case	p. 244
8.7 FE assembly procedure and concluding remarks	p. 252
References	p. 252
9 Numerical evaluation and assessment of classical and advanced theories using MUL2 software	p. 255
9.1 The MUL2 software for plates and shells: analytical closed-form solutions	p. 256
9.1.1 Classical plate/shell theories as particular cases in the MUL2 software	p. 264
9.2 The MUL2 software for plates: FE solutions	p. 269
9.3 Analytical closed-form solution for the electromechanical analysis of plates	p. 276
9.4 Analytical closed-form solution for the electromechanical analysis of shells	p. 283
9.5 FE solution for electromechanical analysis of beams	p. 290
9.6 FE solution for electromechanical analysis of plates	p. 296
References	p. 302
Index	p. 303

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Table of Contents