The foundation shape effects on the stress distribution induced in the soil. Moreover, it has influence on the failure mechanism of the soil. For these reasons, it plays an important role in the ultimate load capacity of the foundation. Due to lack of materials, the new design methods attempts to utilize the least amount of material and achieve the maximum efficiency. If shell elements are employed in foundations, and the interaction effects are considered, their required cost can be reduced. This paper aims to compare the performance of the composite Annular shell foundation with that of the Annular one. For this purpose, the ultimate load capacity and the settlement of these foundations are experimentally modeled for various shell angles. Findings prove that the ultimate load capacity of the composite foundations are more than that of the Annular one. Furthermore, it is observed that increasing the shell angle reduces the ultimate load capacity. Moreover, the shell efficiency factor is decreased by increasing the soil relative density. This phenomenon shows that the shells perform more appropriately in low-density soils. Additionally, a novel relation is proposed for predicting the ultimate load capacity of the composite shell. It is worth emphasizing that adding the edge beam to composite foundations improve its performance in settlements during failure. Moreover, the efficiency of foundations with edge beams is more than the ones without beam in soils with any density. Hence, usage of shells in Annular foundation enhance its ultimate load capacity.

In this study, the vibration behavior of circular and Annular graphene sheet embedded in a Visco-Pasternak foundation and coupled with temperature change and under in-plane pre-load is studied. The single-layered Annular graphene sheet is coupled by an enclosing viscoelastic medium which is simulated as a Visco- Pasternak foundation. By using the nonlocal elasticity theory and classical plate theory, the governing equation is derived for single-layered graphene sheets (SLGSs). The closed-form solution for frequency vibration of circular graphene sheets has been obtained and nonlocal parameter, in-plane pre-load, the parameters of elastic medium and temperature change appears into arguments of Bessel functions. To verify the accuracy of the present results, the new version differential quadrature method (DQM) is also developed. Closed-form results are successfully verified with those of the DQM results. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, mode number, temperature change, elastic medium and boundary conditions on natural frequencies are investigated. The non-dimensional frequency decreases at high temperature case with increasing the temperature change for all boundary conditions. The effect of temperature change on the non-dimensional frequency vibration becomes the opposite at high temperature case in compression with the low temperature case. The present research work thus reveals that the nonlocal parameter, boundary conditions, temperature change and initial pre-load have significant effects on vibration response of the circular nanoplates. The present analysis results can be used for the design of the next generation of Nano devices that make use of the thermal vibration properties of the graphene.

In this study, the vibration behavior of functional graded (FG) circular and Annular nanoplate embedded in a Visco-Pasternak foundation and coupled with temperature change is studied. The effect of in-plane pre-load and temperature change are investigated on the vibration frequencies of FG circular and Annular nanoplate. To obtain the vibration frequencies of the FG circular and Annular nanoplate, two different size dependent theories are utilized. The material properties of the FGM nanoplates are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The FG circular and Annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a Visco- Pasternak foundation. By using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST), the governing equation is derived for FG circular and Annular nanoplate. The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and Annular nanoplate. The results are subsequently compared with valid result reported in the literature. The effects of the size dependent, the in-plane pre-load, the temperature change, the power index parameter, the elastic medium and the boundary conditions on the natural frequencies are investigated. The results show that the size dependent parameter has an increasing effect on the vibration response of circular and Annular nanoplate. The temperature change also play an important role in the mechanical behavior of the FG circular and Annular nanoplate. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplate.

In this paper, free vibration of functionally graded carbon nanotube Annular sector plates is studied. Distribution of carbon nanotubes is continuous and meaningful and gradual changes of materials in the direction of thickness are in the form of volume fraction. Annular sector plate is placed on the Winkler-Pasternak two parameters elastic foundation. The motion equations of plate are derived using the Hamilton principle and the refined plate theory. These coupled differential equations are transformed to ordinary equations using the trigonometric series expansion of space variation functions and then are solved with the help of differential quadrature method. The obtained results are compared with the other researcher’ s results and an excellent agreement can be observed between them. Finally, the effects of different geometric parameters, different distributions of carbon nanotubes in the thickness direction, elastic foundation, and also different boundary conditions on the natural frequencies are investigated.

In this paper, an attempt is made for solution of free vibration analysis of Annular plate reinforced with carbon nanotubes for Uniformly Distribution (UD), resting on an elastic foundation using a refined theory presented. In this theory, a parabolic distribution of shear stress and strain in the thickness direction and satisfies the boundary conditions of zero shear stress on the upper and lower crust cut without using a correction factor to be considered. The equations of motion are obtained using Hamilton's principle. And then these equations are solved by GDQ method.Factors affecting the frequency such large radius to small radius, the ratio of thickness to the radius of the Annular plate, the length of the radius is obtained. To check the compatibility equations and solving method is used, a comparison between the present work has been done with papers.

In this paper, free vibration of two-dimensional functionally graded (2D-FG) Annular sectorial plate surrounded by Winkler-Pasternak elastic foundation has been investigated. It is assumed that the plate properties vary continuously through its both circumference and thickness according to power law distribution of the volume fraction. Primarily, we calculate the forces and resultant moments and then the total potential energy of system. Then, by applying the Hamilton’s principal any by regarding the first order shear deformation plate theory (FSDT) the governing differential equations have been derived. The numerical differential quadrature method, (DQM), has been employed for solving the motion equations. Two different boundary conditions such as simply supported and clamp supported are considered. Initially, the obtained results were verified against those given in the literature and by ANSYS software and we confident from the obtain results. The effects of geometrical and elastic foundation parameters along with FG power indices effects on the natural frequencies have been studied. The study of results shows that, elastic foundation and FG parameters have significant effects on natural frequencies. By doing this research for 2D-FG materials the characteristic vibration of structure can be controlled by more parameters than 1D-FG materials.

In this paper, the bending analysis of a thin circular sector plate (with inner and outer radius) made of homogeneous material with various boundary conditions including simply support and clamped edges under the act of uniformly and non-uniformly loadings resting on a nonlinear Winkler foundations (elastic) is studied. To do this, for bending analysis of sector thin plate subjected to uniform and nonuniform loading a combination of the Extended Kantorovich Method (EKM) along with weighted residual method was employed to solve the fourth-order governinig bending partial differential equation (PDE) of the plate in the polar coordinates of r and θ . The obtained results for bending deflection of the plate are compared with those from finite element method (FEM) and also with the literature in special cases. Also, the effect of changes in different parameters including geometry of the plate, linear and nonlinear stiffnesses of Winkler foundation, types of various boundary conditions and uniform and nonuniform loading in the bending response of the plate is investigated.