Document Details
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Document Type |
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Thesis |
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Document Title |
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ON THE MIXED NONLOCAL THEORY OF ELASTICITY FOR BENDING OF FUNCTIONALLY GRADED PIEZOELECTRIC NANOPLATES حول نظرية المرونة غير المحلية المختلطة لانحناء صفائح نانوية كهروضغطية متدرجة الخواص |
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Subject |
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faculty of science |
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Document Language |
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Arabic |
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Abstract |
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The current article deals with the bending for the FGPM plates. An attempt is made to obtain the bending analysis of an FGPM based on the simple quasi-3D sinusoidal shear deformation theory, simple two-variable shear deformation theory and mixed nonlocal first order theory. A comparison study with published results acquired by other investigators is presented showing an excellent agreement. The effects of different parameters on the range of validity are investigated for the FGPM plates.
This thesis consists of nine chapters which are summarized as follows:
Chapter 1: is an introduction to the following:
• Elasticity theory: some basic concepts of the elasticity and governing equations have been presented such as; Hooke's law, equilibrium equation, their boundary conditions, engineering constants of elasticity and the different characteristics of elastic body. A brief on the classical plate theory, first order shear theory is presented in addition to the nonlocal elasticity theory.
• Piezoelectric theory: a general introduction to the piezoelectric, its equations and its basic concepts as well as the piezoelectric engineering constants was presented.
• Functionally graded materials: a general introduction to FGMs, their applications and their various characteristics.
Chapter 2: includes a reference survey of the subject of the study.
Chapter 3: concerns with formulation the problem of bending analysis of FGP plate by using a simple quasi-3D sinusoidal shear deformation theory under simply-supported. The exponential law is presented to describe the effective materials properties of FGP plate. Basic definitions of displacement, strain and stress of an FGP plate under mechanical and piezoelectric loadings were presented. The governing equations are obtained and solved. To check the accuracy and validity of bending results obtained from the present analysis of FGP plates, results are compared with the analytical solution obtained by 3D, quasi-3D and higher-order shear deformation theories.
Chapter 4: presents the whole details about the mathematical treatment for hygro-thermo-mechanical bending of FGP plates. We will be supposed that the material properties such as Young's modulus, moisture expansions and thermal expansions to vary continuously according to a power law (FGP). Also, the material properties of the exponentially graded piezoelectric (EGP) plates are assumed to follow the exponential law. The effect of mechanical loadings, temperature loadings, moisture loadings and piezoelectric loadings on the EGP and FGP plates has been studied using quasi-3D sinusoidal plate theory. The displacement field, strains and stresses are given. Applying the analytical solutions of FGP plate by using Navier's method and the principle of virtual work, both the boundary conditions and the governing equations are derived. Numerical analysis is presented to explain the validity and efficiency of the theory by comparing the obtained results with those computed using several other theories available in the literature.
Chapter 5: devotes to the bending analysis for FGP plate through utilizing a simple two-variable shear deformation plate theory under simply-supported edge conditions. The power law of FGP plate is presented to describe the effective materials properties of FGP plate. Basic definitions of displacement, strain and stress of an FGP plate under mechanical and piezoelectric loadings were presented. The governing equations are obtained and solved. Results are compared with the analytical solution obtained by using several other theories available in the literature.
Chapter 6: concerns with formulation the problem of a simply-supported bending of FG and FGP nanoplate, also its solution by using the mixed nonlocal first order theory. General analysis of the problem was presented as follows:
The definitions of the problem under discussion, basic definitions of displacement, strain and stress of an FG and FGP nanoplate were presented. The governing equations are obtained and solved for nanoplates subjected to simply-supported boundary conditions. Furthermore, we presented the mathematical expressions of the bending of FG and FGP nanoplates under mechanical loads in mixed nonlocal elastic theory. We also presented analytic solutions for the FG and FGP nanoplates.
Chapter 7: reports the numerical results of FG nanoplate by two models as follows:
In the first model, we assumed that the FG nanoplate was an isotropic, while in the second model we assumed that the FG nanoplate was an orthotropic. As an example of verification, we compare a sample of current findings with those available in the literature.
Chapters 8: reports the numerical results of FGP nanoplate by two models used in Chapter 7 under the influence of mechanical and voltage loads.
Finally, we present in Chapter 9 summary of the subject of this study as well as the objectives and future outlooks.
It is noteworthy that, one article is published form this thesis and additional two articles are in press in ISI journals. |
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Supervisor |
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Prof. Dr. Ashraf M. Zenkour |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1441 AH
2020 AD |
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Added Date |
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Wednesday, March 11, 2020 |
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Researchers
| زهرة صالح حافظ | Hafed, Zahra Saleh | Researcher | Doctorate | |
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