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2021 | Book

Nonlinear Analysis of Thin-Walled Smart Structures

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About this book

This book focuses on nonlinear finite element analysis of thin-walled smart structures integrated with piezoelectric materials. Two types of nonlinear phenomena are presented in the book, namely geometrical nonlinearity and material nonlinearity. Geometrical nonlinearity mainly results from large deformations and large rotations of structures. The book discusses various geometrically nonlinear theories including von Kármán type nonlinear theory, moderate rotation nonlinear theory, fully geometrically nonlinear theory with moderate rotations and large rotation nonlinear theory. The material nonlinearity mainly considered in this book is electroelastic coupled nonlinearity resulting from large driving electric field. This book will be a good reference for students and researchers in the field of structural mechanics.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
The chapter first discusses the application background of smart structures and the definition of smart structures. Later, the history of smart structures, including various programs, is introduced. Finally, the objectives of the report and the outlines are addressed.
Shun-Qi Zhang
Chapter 2. Literature Review
Abstract
This chapter gives an overview of modeling and simulation techniques for smart structures. First, the chapter starts with various through thickness hypotheses for beam, plate and shell structures. Later, the development history of geometrically nonlinear theories in composite thin-walled structures are discussed, which is followed by the implementation of those nonlinear shell theories in smart structures. For the case of smart structures under strong electric fields, electroelastic materially nonlinear modeling methods are presented. In order to give a deep understanding of the multi-physics coupled phenomenon, the modeling techniques for many recently developed types of smart structures are presented, including functionally graded smart structures, electro-thermo-mechanically coupled structures, magneto-electro-elastic composites, and macro-fiber composites. Finally, a literature survey on vibration control of piezoelectric structures is discussed for the applications of vibration and noise reduction.
Shun-Qi Zhang
Chapter 3. Geometrically Nonlinear Theories
Abstract
This chapter starts with discussing various hypotheses, and the differences between these hypotheses are outlined. Afterwards, the mathematical preliminaries, including position vectors, covariant and contravariant base vectors, Christoffel symbols, shifter tensor, curvature tensor, etc., will be defined and discussed. Based on the FOSD hypothesis, through-thickness displacement distribution is assumed, where six parameters are introduced. Using these predefined quantities, Green-Lagrange strain tensor with fully geometrically nonlinear strain-displacement relations is developed in terms of six parameters for geometrically nonlinear theory with unrestricted finite rotations (LRT56). Imposing different assumptions, various simplified nonlinear strain-displacement relations are developed for the theories of von Kármán type nonlinear (RVK5), moderate rotation nonlinear (MRT5), fully geometrically nonlinear with moderate rotations (LRT5).
Shun-Qi Zhang
Chapter 4. Nonlinear Constitutive Relations
Abstract
This chapter deals with constitutive relations for piezoelectric materials with isotropy or orthotropy. Firstly, piezoelectricity is introduced for brief understanding of piezoelectric materials. To deep understand the basic principles of piezo materials, the fundamental theory of piezoelectricity is discussed in the three-dimensional case. In order to deal with fiber based piezo materials or fiber reinforced composites, coordinate transformation law between fiber coordinates (material coordinates) and convective coordinates (structural coordinates) is introduced. Afterwards, the constitutive relations for two typical configurations of macro-fiber composite piezo materials are developed, where multi-layered structures are considered. Finally, an electro-mechanically coupled nonlinear constitutive relations for piezoelectric with either isotropy or orthotropy are constructed.
Shun-Qi Zhang
Chapter 5. Finite Element Formulations
Abstract
In this chapter, resultant strain and stress are introduced, such that the volume integration can be treat as surface integration. In order to describe the unrestricted finite rotations in thin-walled smart structures, five mechanical nodal DOFs are defined to represent the six kinematic parameters in strain-displacement relations by using Euler angles. Furthermore, an eight-node elements with five mechanical nodal DOFs and additionally integrated with one electrical DOF using full integration or uniformly reduced integration scheme are developed for both composite and smart structures. Implementing both linear constitutive equations and electroelastic nonlinear constitutive equations, one obtains nonlinear FE models by Hamilton’s principle and the principle of virtual work, in which various geometrically nonlinear phenomena discussed in Chap. 3 are considered. In the last part of this chapter, several numerical algorithms are developed for solving the nonlinear equilibrium equations and the equations of motion.
Shun-Qi Zhang
Chapter 6. Nonlinear Analysis of Piezoceramic Laminated Structures
Abstract
In this chapter, geometrically nonlinear FE models, including RVK5, MRT5, LRT5 and LRT56, are validated by static analysis of composite laminated thin-walled structures. Later, the geometrically nonlinear FE models are test by buckling and post-buckling analysis of cylindrical composite panels. Afterwards, the geometrically nonlinear FE models are implemented into static and dynamic analysis of piezolaminated beam, plate and shell structures. In the last part, the simulations of nonlinear phenomena including both geometrically and electroelastic materially nonlinear effects are performed through piezo structures undergoing large displacement and under strong electric field.
Shun-Qi Zhang
Chapter 7. Numerical Analysis of Macro-fiber Composite Structures
Abstract
This chapter deals with the simulation of MFC bonded structures using the numerical models developed in previous chapters. First the model is validated by MFC bonded plate structure, in which two typical types of MFCs are considered, MFC-d31 and MFC-d33. Then, various geometrically nonlinear models are applied to compute multi-MFC integrated pate and cylindrical shell structures. In both linear and nonlinear analysis, various piezo-fiber orientation angles are considered, to demonstrate the influences on structural response.
Shun-Qi Zhang
Chapter 8. Conclusion and Future Work
Abstract
Due to the excellent properties of smart structures, a wide applications can be found in aerospace, civil and automotive engineering. Smart structures are usually appearing with beam-, plate- and shell-shaped structures. There is a great concern about the appropriate computation approaches for smart structures undergo large displacement and under strong electric filed. This report dealt with geometrically nonlinear and electroelastic materially nonlinear modeling techniques for both composite laminated and piezoelectric integrated thin-walled structures.
Shun-Qi Zhang
Backmatter
Metadata
Title
Nonlinear Analysis of Thin-Walled Smart Structures
Author
Dr. Shun-Qi Zhang
Copyright Year
2021
Publisher
Springer Singapore
Electronic ISBN
978-981-15-9857-9
Print ISBN
978-981-15-9856-2
DOI
https://doi.org/10.1007/978-981-15-9857-9