چكيده لاتين
The static and dynamic analysis of single-layer and multi-layer composite nanoplates, as well as the buckling and free vibration analysis of piezoelectric nanoplates, based on classical theory using the semi-analytical high-order finite strip method, have been investigated in this dissertation. In the final chapter, the static and dynamic analysis of multi-layer plates with a piezoelectric layer, along with the derivation of relations that allow for the examination of results based on various plate deformation theories, is presented using the semi-analytical finite strip method .In this method, trigonometric functions are used in the longitudinal direction of the strips to satisfy various boundary conditions, including simply supported, clamped, and free edges, while Lagrangian and Hermitian polynomial functions are employed in the transverse direction. This combination is designed in such a way that it allows the modeling of various boundary conditions in the transverse direction by adjusting the degrees of freedom. Initially, a semi-analytical solution method is developed for the analysis of buckling, free vibration, and deflection of nanoplates using the nonlocal strain gradient theory and classical plate theory. The effects of strain gradients in the governing equations are examined, and the results are presented using the Navier method and the finte strip method according to the nonlocal strain gradient theory. Furthermore, a higher-order semi-analytical analysis based on the finite strip method is presented for the investigation of buckling, free vibration, and deflection of orthotropic layered composite nanoplates, as well as time-dependent dynamic analysis for isotropic and orthotropic single-layer and multi-layer macro and nanoplates. In this section, the nonlocal strain gradient theory is first introduced, and the governing equations for the mechanical behavior of nanoplates are derived. Then, the deformation kinematics are applied based on the classical plate theory and the size-dependent theory, and using virtual work and Hamiltonʹs principle, the stiffness, geometric, mass matrices, and force vector are extracted. The Newmark method is employed for temporal discretization in dynamic analysis. Finally, buckling and free vibration analysis of piezoelectric nanoplates based on the nonlocal strain gradient theory and classical plate theory are investigated using the Navier method and the strip method, as well as static and dynamic analysis of piezoelectric layered plates based on first-order and third-order shear deformation theories using the strip method. The examined parameters include the effects of dimensions, elastic modulus, boundary conditions, size effects in small-scale plates, fiber influence in layered plates, various mechanical and dynamic loadings, and the effects of electric potential and piezoelectric properties.
For the first time, buckling, free vibration, and deflection of nanoplates have been analyzed using the finite strip method based on the nonlocal strain gradient theory. This approach combines the simplicity and reduced computational effort of the finite strip method with the comprehensiveness of the nonlocal strain gradient theory, which incorporates both the nonlocal Eringen theory and strain gradients. Additionally, based on this method and theory, the dissertation presents buckling and free vibration analyses, as well as static and dynamic analyses of layered nanoplates, buckling and free vibration analysis of piezoelectric nanoplates, and static and dynamic analysis of piezoelectric composite layered plates.
