• Advances in aircraft and spacecraft science
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• 제7권4호
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• pp.335-351
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• 2020

Thermal buckling of functionally graded sandwich cylindrical shells is presented in this study. Material properties and thermal expansion coefficient of FGM layers are assumed to vary continuously through the thickness according to a sigmoid function and simple power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FGM sandwich cylindrical shells with simply supported boundary conditions are derived according to the Donnell theory. The influences of cylindrical shell geometry and the gradient index on the critical buckling temperature of several kinds of FGM sandwich cylindrical shells are investigated. The thermal loads are assumed to be uniform, linear and nonlinear distribution across the thickness direction. An exact simple form of nonlinear temperature rise through its thickness taking into account the thermal conductivity and the inhomogeneity parameter is presented.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.615-631
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• 2016

In this paper, an analytical method for the Post-buckling response of cylindrical shells with spiral stiffeners surrounded by an elastic medium subjected to external pressure is presented. The proposed model is based on two parameters elastic foundation Winkler and Pasternak. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. According to the Von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method is used to solve the nonlinear problem. To valid the formulations, comparisons are made with the available solutions for nonlinear static buckling of stiffened homogeneous and un-stiffened FGM cylindrical shells. The obtained results show the elastic foundation Winkler on the response of buckling is more effective than the elastic foundation Pasternak. Also the ceramic shells buckling strength higher than the metal shells and minimum critical buckling load is occurred, when both of the stiffeners have angle of thirty degrees.

• Geomechanics and Engineering
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• 제36권2호
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• pp.99-109
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• 2024

Studying the dynamic behavior of axially moving cylindrical shells in hygro-thermal environments has important theoretical and engineering value for aircraft design. Therefore, in this paper, considering hygro-thermal effect, the nonlinear forced vibration of an axially moving cylindrical shell made of functionally graded materials (FGM) is studied. It is assumed that the material properties vary continuously along the thickness and contain pores. The Donnell thin shell theory is used to derive the motion equations of FGM cylindrical shells with hygro-thermal loads. Under the four sides clamped (CCCC) boundary conditions, the Gallekin method and multi-scale method are used for nonlinear analysis. The effects of power law index, porosity coefficient, temperature rise, moisture concentration, axial velocity, prestress, damping and external excitation amplitude on nonlinear forced vibration are explored through parametric research. It can be found that, the changes in temperature and humidity have a significant effect. Increasing in temperature and humidity will cause the resonance position to shift to the left and increase the resonance amplitude.

• Steel and Composite Structures
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• 제45권2호
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• pp.175-191
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• 2022

A review of previous studies shows that although there is a considerable difference between buckling loads of structures under follower and non-follower lateral loads, only the buckling load of FGM elliptical cylindrical shell under non-follower lateral load was investigated in the literature. This study is the first to obtain the buckling load of elliptical FGM cylindrical shells under follower lateral load and also make a comparison between buckling loads of elliptical FGM cylindrical shells under follower and non-follower lateral loads. Moreover, this research is the first one to derive the load potential function of elliptical cylindrical shell. In this regard, the FGM cylindrical elliptical shell was modeled using the semi-analytical finite strip method and based on the First Shear Deformation Theory (FSDT). The shell is discretized by strip elements aligned in the longitudinal direction. The Lagrangian and harmonic shape functions were considered in the circumference and longitudinal directions, respectively. The buckling pressure of the shell under follower and non-follower lateral loads was obtained from eigenvalue problem. The results obtained from the model were compared with those presented in the literature to evaluate the validity of the model. A comparison index was defined to compare the buckling loads of the shell under follower and non-follower lateral load. A parametric study was carried out to investigate the effects of material properties and shell geometry characteristics on the comparison index. For the elliptical cylindrical shells with length-to-radius ratio greater than 16 and major-to-minor axis ratio greater than 0.6, the comparison index reaches to more than 20 percent which is significant. Moreover, the maximum difference is about 30 percent in some cases. The results obtained from the parametric study indicate that the buckling load of long elliptical cylindrical shell under non-follower load is not reliable.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.767-782
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• 2022

In this paper, the nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells exposed to the thermal environment and a uniformly distributed harmonic loading using a semi-analytical method is investigated. The cylindrical shell is surrounded by a nonlinear viscoelastic foundation consisting of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The distribution of temperature and material constitutive of the stiffeners are continuously changed through the thickness direction. The cylindrical shell has three layers consisting of metal, FGM, and ceramic. The interior layer of the cylindrical shell is rich in metal, while the exterior layer is rich in ceramic, and the FG material is located between two layers. The nonlinear vibration problem utilizing the smeared stiffeners technique, the von Kármán equations, and the Galerkin method has been solved. The multiple scales method is utilized to examine the nonlinear vibration behavior of SSMFG cylindrical shells. The considered resonant case is 1:3:9 internal resonance and subharmonic resonance of order 1/3. The influences of different material and geometrical parameters on the vibration behavior of SSMFG cylindrical shells are examined. The results show that the angles of stiffeners, temperature, and elastic foundation parameters have a strong effect on the vibration behaviors of the SSMFG cylindrical shells.

• Structural Engineering and Mechanics
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• 제27권3호
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• pp.365-391
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• 2007

The vibration and stability analysis is investigated for composite cylindrical shells that composed of ceramic, FGM, and metal layers subjected to various loads. Material properties of FG layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations are obtained. Applying Galerkin's method analytic solutions are obtained for the critical parameters. The detailed parametric studies are carried out to study the influences of thickness variations of the FG layer, radius-to-thickness ratio, lengths-to-radius ratio, material composition and material profile index on the critical parameters of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.

• 한국소음진동공학회논문집
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• 제19권11호
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• pp.1119-1125
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• 2009

The coupled fluid-structure interaction problem is analyzed using the theoretical method to investigate the coupled vibration characteristics of functionally graded material(FGM) cylindrical shells conveying an incompressible, inviscid fluid. Material properties are assumed to vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The steady flow of fluid is described by the classical potential flow theory. The motion of shell represented by the first order shear deformation theory(FSDT) to account for rotary inertia and transverse shear strains. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. Numerical examples are presented and compared with exiting results.

• Steel and Composite Structures
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• 제28권6호
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• pp.735-748
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• 2018

In this study, the semi-analytical finite strip method is adopted to examine the free vibration of cylindrical shells made up of functionally graded material. The properties of functionally graded shells are assumed to be temperature-dependent and vary continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of ceramic and metal. The material properties of the shells and stiffeners are assumed to be continuously graded in the thickness direction. Theoretical formulations based on the smeared stiffeners technique and the classical shell theory with first-order shear deformation theory which accounts for through thickness shear flexibility are employed. The finite strip method is applied to five different shell theories, namely, Donnell, Reissner, Sanders, Novozhilov, and Teng. The approximate procedure is compared favorably with three-dimensional finite elements. Finally, a detailed numerical study is carried out to bring out the effects of power-law index of the functional graded material, stiffeners, and geometry of the shells on the difference between various shell theories. Finally, the importance of choosing the shell theory in simulating the functionally graded cylindrical shells is addressed.

• Steel and Composite Structures
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• 제37권1호
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• pp.51-73
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• 2020

The present paper investigates the simultaneous resonance behavior of spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with internal and external functionally graded stiffeners under the two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The cylindrical shell has three layers consist of ceramic, FGM, and metal. The exterior layer of the cylindrical shell is rich ceramic while the interior layer is rich metal and the functionally graded material layer is located between these layers. With regard to classical shells theory, von-Kármán equation, and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The simultaneous resonance is obtained using the multiple scales method. Finally, the influences of different material and geometrical parameters on the system resonances are investigated comprehensively.

• Structural Engineering and Mechanics
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• 제61권2호
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• pp.231-244
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• 2017

The aim of this study is to develop a semi-analytical method to investigate fluid-structure coupling of concentric double shells with different lengths and elastic behaviours. Co-axial shells constitute a cylindrical circular container and a baffle submerged inside the stored fluid. The container shell is made of functionally graded materials with mechanical properties changing through its thickness continuously. The baffle made of steel is fixed along its top edge and submerged inside fluid such that its lower edge freely moves. The developed approach is verified using a commercial finite element computer code. Although the model is presented for a specific case in the present work, it can be generalized to investigate coupling of shell-plate structures via fluid. It is shown that the coupling between concentric shells occurs only when they vibrate in a same circumferential mode number, n. It is also revealed that the normalized vibration amplitude of the inner shell is about the same as that of the outer shell, for narrower radial gaps. Moreover, the natural frequencies of the fluid-coupled system gradually decrease and converge to the certain values as the gradient index increases.