In this research, the thermal buckling analysis of a truncated conical SHELL made of porous materials on elastic FOUNDATION is investigated. The equilibrium equations and the conical SHELL`s stability equations are obtained by using the Euler`s and the Trefftz equations. Properties of the materials used in the conical SHELL are considered as porous foam made of steel, which is characterized by its non-uniform distribution of porous materials along the thickness direction. Initially, the displacement field relation based on the classical model for double-curved SHELL is expressed in terms of the Donnell`s assumptions. Non-linear straindisplacement relations are obtained according to the von Ká rmá n assumptions by applying the Green-Lagrange strain relationship. Then, performing the Euler equations leads obtaining nonlinear equilibrium equations of cylindrical SHELL. The stability equations of conical SHELL are obtained based on neighboring equilibrium benchmark (adjacent state). In order to solve the stability equations, primarily, due to the existence of axial symmetry, we consider the cone crust displacement as a sinusoidal geometry, and then, using the generalized differential quadrature method, we solve them to obtain the critical temperature values of the buckling Future. In order to validate the results, they compare with the results of other published articles. At the end of the experiment, various parameters such as dimensions, boundary conditions, cone angle, porosity parameter and elastic bed coefficients are investigated on the critical temperature of the buckling.

In this paper, Free Vibration analysis of truncated conical SHELL Reinforced with single-walled carbon nanotubes for Uniformly Distribution (UD), resting on Pasternak elastic FOUNDATION, based on the first order shear deformation plate theory is investigated. The rule of mixture is used to effect of the properties of nanotubes in the mentioned structure. Based on the displacement field according to the first order shear deformation theory, after determining the strain components in the curvilinear coordinates and simplifying derived relation, we compute the strain components in conical coordinate. Then, the stress components are derived by the Hook’s law. In the next stage, by computing the total potential energy of system by regarding the effect of Pasternak elastic FOUNDATION and regarding the suitable functions for displacements, by applying the Ritz method the natural frequency of system have been derived. At the end, the effect of volume fraction of nanotubes, ratio of thickness to radius of cone, elastic constants and other parameters, on the natural frequency of structure have been investigated. Also, it can be observe close agreements between present results and other papers.

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.

This paper is focused on the study of nonlinear vibration of rotating laminated composite cross-ply cylindrical SHELLs on a nonlinear rotating elastic FOUNDATION. In this study, FSDT is employed while the geometrical nonlinearity of the cylindrical SHELL is modeled considering the von Karman approach. It should be mentioned that this study is accomplished considering the influences of initial hoop tension as well as Coriolis and Centrifugal accelerations. The nonlinear equation of the rotating laminated composite cross-ply cylindrical SHELL is extracted via the Ritz method and then is written in the state space form. Then, modal analysis and the multiple scales method are applied to the nonlinear vibration equation in the state space form to obtain relations for nonlinear forward and backward frequency ratios. Validation of the results of this study is investigated considering some results published in the literature and good agreement is observed. Finally, the effects of the nonlinear and linear constants of the rotating FOUNDATION, radius, total thickness, length, and rotation speed on the linear frequencies, nonlinear parameters, and the curves of nonlinear frequency ratios versus amplitude parameters are acquired. The results show that the increase of the nonlinear constant of the rotating FOUNDATION doesn’t influence the linear frequencies. Besides, linear frequencies increase with increase of the linear constants of the rotating elastic FOUNDATION and decrease with increase of the radius or total thickness. Furthermore, the increase of the nonlinear constant of the rotating elastic FOUNDATION or total thickness leads to an increase in nonlinear parameters and nonlinear frequency ratios. Conversely, the increase of the linear constants of the rotating FOUNDATION or the radius leads to a decrease in nonlinear parameters and frequency ratios. Moreover, the increase in amplitude parameters leads to an increase in the nonlinear frequency ratios.

This paper is investigated vibration of magneto-electro-elastic (MEE) composite conical SHELL on a nonlinear elastic FOUNDATION and under electric or magnetic potential while the influence of geometrical nonlinearity is taken into account. The conical SHELL is modeled based on the von Karman approach while the influences of shear deformation and rotary inertia are heeded. Coupled relations of MEE material are utilized to derive the vectors of stress, electric displacement as well as magnetic induction. Quasi-static Maxwell equations, Gauss' laws as well as thin SHELL assumptions are used to determine electric and magnetic fields. The nonlinear ordinary differential equation of the SHELL is derived through the Lagrange approach. Lindstedt-Poincare method and modal analysis are hired in order to obtain nonlinear vibration responses of the MEE composite conical SHELL. For validation intention, some results of the literature are compared with some results of this study. The effects of several parameters including nonlinear and linear constants of FOUNDATION, electric and magnetic potentials, thickness as well as length on the values of fundamental linear frequency, nonlinear parameter, and the curves of nonlinear frequency ratio versus amplitude parameter are investigated. The results show that the increase of the nonlinear constant of elastic FOUNDATION or thickness causes the increase of the nonlinear frequency ratio. On the other hand, the nonlinear frequency ratio gets smaller values with an increase in the linear constants of the elastic FOUNDATION or length.

Sea SHELLs are natural-biological objects. They are embedded in geological layers in the form of fossils, but also, to find in archaeological deposits as a result of human activities. Archaeologists can use the provenance of SHELLs in the functional analysis of ancient sites in terms of social archeology and prehistoric trading activities. Aarcheological excavations in several sites of the Iranian Plateau have shown that from the 3rd third millennium B.C. onwards, finds of of sea SHELLs (e.g. Lambis, Dentalium, etc.) rapidely increased. Such SHELLs were for instance discovered from ritual cemetery contexts such as Shahdad, Tepe Hesar, Kale Nisar cemeteries or Bani Surma. These objects are mainly used as natural or polished SHELLs. In some cases, they served as a raw material for making all kinds of beads, buttons, and other ornamental objects.. The main question is to understand the relationship between the use of seaSHELLs and archaeological context, and also, their role in Bronze Age ritual life. In this article, the descriptive, analytical method has been used in the biological recognition of all types of SHELLs. This method is also used based on similar studies on this issue in Mesopotamia's archeology of the Sumerian-Akkadian period. The distribution of recognizable species shows that these objects are concentrated in the settlements from south to southeast of Iran in the coastal strip of the Persian Gulf, and from the Oman Sea to the Zagros intermountain valleys, as well as in the northwest and northeast of Iran. The biological origin can be placed in the northern shores of the Oman Sea to the Gulf of Kutch on the northern coast of the Indian Ocean. It seems that with the growth and development of urbanization in Southwest Asia and especially the development of sea trade, oysters have been traded as valuable goods and other prestige goods. The importance of the SHELL findings is more than the value of the SHELLs themselves because they were used as sacred goods in religious affairs. Analysis of the fields where the SHELLs were discovered is more related to cemeteries and temples as sacred spaces. Also, the significant presence of Lambis SHELLs for the production of specific ritual bowls, placed together with bronze axes in graves, can be seen as the reflection of a patriarchic tradition in the social-political organisiation of the third and second millennia B.C. Despite many excavations and the discovery of many samples of these types of SHELLs, no furthergoing investigation on these specific objects was undertaken so far. This desideratum reveals more valuable findings in the archeology of the Iranian plateau. Therefore, one of this article's final goals is to focus more on analyzing the context of the discovery of seaSHELLs in future Excavation

In this paper، the nonlinear vibration analysis of a symmetric laminated composite cylindrical SHELL on a viscoelastic FOUNDATION under a subsonic external air flow has been investigated. The boundary conditions for both ends of the cylindrical SHELL are clamped conditions. The governing equations of motion in the longitudinal، circumferential and radial directions are derived in conducture with the Donnel’ s nonlinear SHELL theory. Using Galerkin method، three nonlinear partial differential equations of motion are transformed to a nonlinear ordinary equation of motion governing lateral (radial) vibration of the SHELL. Then، the relations for linear and nonlinear natual frequencies and amplitude-dimensionless natural frequency of the SHELL are calculated. The effects of variations in different values of parameters including orientation angles of lamina in layerwise laminate، stiffness and damping of viscoelastic FOUNDATION and the external applied load on the free and forced vibration behavior of the SHELL are all studied in this paper analyses. Moreover، the time history of radial displacement of midpoint of the SHELL using linear and nonlinear analyses. Are also presented.