Functionally Graded Structures Modelling and Computation of Static and Dynamical Problems
This book explores the static and dynamical behaviours such as bending, buckling, and vibration of functionally graded structures using existing and new theories. The text presents a holistic examination of functionally graded structures, providing invaluable knowledge for professionals, researchers...
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| Hlavní autori: | , , |
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| Médium: | E-kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Bristol
Institute of Physics Publishing
2023
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| Vydanie: | 1 |
| Predmet: | |
| ISBN: | 9780750353021, 0750353023 |
| On-line prístup: | Získať plný text |
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- Chapter 13 Analysis of Lamb wave propagation in a generalized thermoelastic functionally graded plate -- 13.1 Introduction -- 13.2 Fundamental equation -- 13.3 The formulation of the problem and its solution -- 13.4 Numerical results -- 13.5 Conclusions -- Appendix -- References
- Intro -- Preface -- Acknowledgements -- Editor biographies -- Professor S Chakraverty -- Dr Subrat Kumar Jena -- Professor Ömer Civalek -- List of contributors -- Chapter 1 The static behavior of functionally graded beams -- 1.1 Introduction -- 1.2 Mathematical formulations -- 1.2.1 Constitutive equations -- 1.2.2 The nonlocal strain gradient continuum beam model -- 1.2.3 The nonlocal couple stress continuum beam model -- 1.3 Isogeometric analysis -- 1.4 Numerical results and discussion -- 1.5 Concluding remarks -- References -- Chapter 2 The static behavior of functionally graded sandwich beams -- 2.1 Introduction -- 2.2 Theory and formulation -- 2.3 Navier's solution technique -- 2.4 Results and discussion -- 2.5 Conclusions -- References -- Chapter 3 The static behavior of functionally graded plates -- 3.1 Introduction -- 3.2 Deriving the governing equations -- 3.3 Planar FGM structures -- 3.3.1 FGM sector sheet -- 3.3.2 Strain tensor -- 3.3.3 FGMs -- 3.3.4 The static governing equations for the FGM sectorial sheet -- 3.3.5 Two-dimensional static equations -- 3.3.6 Static equations for quasi-three-dimensional sectorial FGM sheets -- 3.4 Shell-type FGM structures -- 3.4.1 The spherical FGM structure -- 3.4.2 Conical and cylindrical FGM structures -- 3.5 The solution method -- 3.6 Numerical results and discussion -- 3.6.1 Validation -- 3.6.2 Discussion -- 3.7 Conclusions and remarks -- References -- Chapter 4 The static bending analysis of porous functionally graded sandwich beams -- 4.1 Introduction -- 4.2 The basic relations of FGSBs -- 4.3 The basic equations of FGSBs -- 4.4 An analytical solution -- 4.5 Numerical results and discussion -- 4.6 Conclusions -- References -- Chapter 5 Dynamic analysis of porous functionally graded shell structures using the generalized differential quadrature method -- 5.1 Introduction
- 5.2 A geometrical description of the shell -- 5.3 Kinematic relations -- 5.4 The higher-order constitutive relation -- 5.5 Fundamental governing equations -- 5.6 Numerical implementation -- 5.7 Application and results -- 5.8 Conclusions -- References -- Chapter 6 Assessing the effects of porosity on the buckling of functionally graded beams -- List of symbols -- 6.1 Introduction -- 6.2 Theoretical formulation -- 6.3 Kinematics -- 6.4 Equilibrium equations -- 6.4.1 Boundary conditions -- 6.5 Numerical results and discussion -- 6.6 Conclusions -- References -- Chapter 7 Vibration and buckling problems of functionally graded structures -- List of abbreviations -- 7.1 Functionally graded materials and homogenization -- 7.2 The vibration and buckling problems of functionally graded beams -- 7.2.1 The development of a model for functionally graded beams -- 7.2.2 Solutions of FGM beams -- 7.2.3 FGM beam vibration -- 7.2.4 FGM beam buckling -- 7.3 The vibration and buckling problems of functionally graded plates -- 7.3.1 The development of models for functionally graded plates -- 7.3.2 Solutions for FGM plates -- 7.3.3 FGM plate vibrations -- 7.3.4 FGM plate buckling -- 7.4 Summary and prospects -- References -- Chapter 8 Free vibration analysis of porous functionally graded sandwich beams -- 8.1 Introduction -- 8.2 The fundamental relations of FGSBs -- 8.3 The governing equations of FGSBs -- 8.4 An analytical solution -- 8.5 Numerical results and discussion -- 8.6 Conclusions -- References -- Chapter 9 The torsional vibration of functionally graded nanobeams -- 9.1 Introduction -- 9.2 Theory and mathematical formulation -- 9.2.1 The FGM model -- 9.3 The solution methodology -- 9.3.1 The nondimensional form -- 9.3.2 The Adomian decomposition method -- 9.4 Numerical results and discussion -- 9.4.1 Validation of the presented model
- 9.4.2 The convergence of the ADM -- 9.4.3 The effects of the magnetic field coefficient and the elastic media parameter -- 9.4.4 FGM effects -- 9.5 Conclusions -- References -- Chapter 10 Determining the accurate free vibration response of thin functionally graded plates using the dynamic stiffness method -- 10.1 Introduction -- 10.2 Mathematical modeling and theoretical formulations -- 10.2.1 A geometric description of an FGM plate -- 10.2.2 Material property description of an FGM plate -- 10.3 Classical plate theory and the physical neutral surface -- 10.4 The governing differential equation for FGM plates based on CPT -- 10.5 The Levy-type closed-form solution -- 10.6 The development of the dynamic stiffness matrix -- 10.7 The computation of the natural frequencies using the Wittrick-Williams algorithm -- 10.8 Results and discussion -- 10.8.1 Comparisons with published results -- 10.8.2 Frequency results obtained using the DSM for square FGM plates -- 10.8.3 Frequency results obtained using the DSM for rectangular FGM plates -- 10.8.4 The effects of Erat and ρrat on the DSM results -- 10.9 Conclusions -- References and further reading -- Chapter 11 Effect of functionally graded magneto-electro-elastic facings on the damped nonlinear transient response of a sandwich plate with agglomerated CNT core -- 11.1 Introduction -- 11.2 Problem description -- 11.3 Materials and methods -- 11.4 Results and discussion -- 11.5 Conclusions -- Acknowledgments -- References -- Chapter 12 Lamb-type waves in functionally graded orthotropic piezoelectric plates -- 12.1 Introduction -- 12.2 Statement and solution to the problem -- 12.3 Boundary conditions -- 12.4 The dispersion relation -- 12.5 Numerical results and discussion -- 12.6 Conclusions -- Appendix A -- Acknowledgments -- References