• 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.

• Structural Engineering and Mechanics
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• 제66권3호
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• pp.295-303
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• 2018

The semi-analytical method to study the nonlinear dynamic behavior of simply supported spiral stiffened functionally graded (FG) cylindrical shells subjected to an axial compression is presented. The FG shell is surrounded by damping and linear/nonlinear elastic foundation. The proposed linear model is based on the two-parameter elastic foundation (Winkler and Pasternak). A three-parameter elastic foundation with hardening/softening cubic nonlinearity is used for nonlinear model. The material properties of the shell and stiffeners are assumed to be FG. Based on the classical plate theory of shells and von $K{\acute{a}}rm{\acute{a}}n$ nonlinear equations, smeared stiffeners technique and Galerkin method, this paper solves the nonlinear vibration problem. The fourth order Runge-Kutta method is used to find the nonlinear dynamic responses. Results are given to consider effects of spiral stiffeners with various angles, elastic foundation and damping coefficients on the nonlinear dynamic response of spiral stiffened simply supported FG cylindrical shells.

• Structural Engineering and Mechanics
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• 제75권1호
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• pp.87-100
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• 2020

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under 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, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, 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 combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

• Steel and Composite Structures
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• 제32권4호
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• pp.509-519
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• 2019

In this paper, an analytical approach for the free vibration analysis of spiral stiffened functionally graded (SSFG) cylindrical shells is investigated. The SSFG shell is resting on linear and non-linear elastic foundation with damping force. The elastic foundation for the linear model is according to Winkler and Pasternak parameters and for the non-linear model, one cubic term is added. The material constitutive of the stiffeners is continuously changed through the thickness. Using the Galerkin method based on the von $K\acute{a}rm\acute{a}n$ equations and the smeared stiffeners technique, the non-linear vibration problem has been solved. The effects of different geometrical and material parameters on the free vibration response of SSFG cylindrical shells are adopted. The results show that the angles of stiffeners and elastic foundation parameters strongly effect on the natural frequencies of the SSFG cylindrical shell.

• 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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• 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.