Free Vibration of Functionally Graded Sandwich Shallow Shells on Winkler and Pasternak Foundations with General Boundary Restraints

Wang, Xiancheng; Li, Wei; Yao, Jianjun; Wan, Zhenshuai; Fu, Yu; Sheng, Tang

doi:10.1155/2019/7527148

Cited by 3 publications

(1 citation statement)

References 45 publications

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“…The governing differential equations of the bending problem of simply supported shallow spherical shells on Winkler foundation [9,[11][12][13][14][15][16] can be expressed as follows:…”

Section: Fundamental Equationsmentioning

confidence: 99%

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

Yuan

Yang

et al. 2020

Civ Eng J

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The governing differential equations of the bending problem of simply supported shallow spherical shells on Winkler foundation are simplified to an independent equation of radial deflection. The independent equation of radial deflection is decomposed to two Laplace operators by intermediate variable. The R-function theory is applied to describe a shallow spherical shell on Winkler foundation with concave boundary, and then a quasi-Green's function is established by using the fundamental solution and the normalized boundary equation. The quasi-Green's function satisfies the homogeneous boundary condition of the problem. The Laplace operators of the problem are reduced to two simultaneous Fredholm integral equations of the second kind by the Green's formula. The singularity of the kernel of the integral equation is eliminated by choosing a suitable form of the normalized boundary equation. The integral equations are discretized into the homogeneous linear algebraic equations to proceed numerical computing. The singular term in the discrete equation is eliminated by the integral method. Some numerical examples are given to verify the validity of the proposed method in calculating simple boundary conditions and polygonal boundary conditions. A comparison with the ANSYS finite element (FEM) solution shows a good agreement, and it demonstrates the feasibility and efficiency of the present method.

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“…The governing differential equations of the bending problem of simply supported shallow spherical shells on Winkler foundation [9,[11][12][13][14][15][16] can be expressed as follows:…”

Section: Fundamental Equationsmentioning

confidence: 99%

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

Yuan

Yang

et al. 2020

Civ Eng J

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Free Vibration Characteristics of Sandwich Conical Shells With FGM Face Sheets: A Finite Element Approach

Singha

Das²,

Agarwal

et al. 2019

Volume 1: Compressors, Fans, and Pumps; Turbines; Heat Transfer; Structures and Dynamics

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This paper presents an analytical investigation on the free vibration characteristics of symmetric sandwich conical shell with functionally graded material (FGM) face sheets using finite element method. Sandwich-type structures offer higher stiffness to weight ratio with excellent thermal barrier in high temperature application extending the operational life of the component. The sandwich-type conical structure used in the advanced supersonic and hypersonic space vehicles. The material properties of FGM face sheets are considered to be varied in thickness direction as per simple power law distribution in terms of the volume fractions of the FGM constituents. The core layer is considered as homogeneous and made of an isotropic material (Titanium alloy-Ti–6Al–4V). A finite element method is used to reduce the governing equations of vibration problem. The QR iteration algorithm used to solve the standard eigen value problem for determine the natural frequencies. Convergence studies are performed in respect of mesh sizes to substantiate the accuracy of the proposed method. Computer codes developed to obtain the numerical results for the combined effects of twist angle and rotational speed on the free vibration characteristics of symmetric sandwich conical shell with FGM face sheets. A detailed numerical study is carried out to examine the influence of the sandwich plate type, volume fraction index on the free vibration characteristics. The typical mode shapes are also illustrated for different cases.

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Assessment of a new higher-order shear and normal deformation theory for the static response of functionally graded shallow shells

Shinde,

Sayyad,

Naik

2024

Curved and Layered Structures

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Static response of simply supported functionally graded (FG) shallow shells using a new higher-order shear and normal deformation theory is focused in this article. The effects of transverse strains and stresses on the bending response of FG shell are considered by the present theory. The current theory considers the impacts of transverse normal and shear deformations that meet the requirements for traction-free boundary conditions. The virtual work principle is applied to the mathematical formulation of the present theory. The simply supported doubly curved shallow shell problems under the static transverse load are analyzed using Navier’s solution technique. To verify the existing theory, the current results are, whenever possible, compared with those that have already been published. Additionally, a few benchmark results are presented in this article that will be helpful to researchers in the future.

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Free Vibration of Functionally Graded Sandwich Shallow Shells on Winkler and Pasternak Foundations with General Boundary Restraints

Cited by 3 publications

References 45 publications

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

Free Vibration Characteristics of Sandwich Conical Shells With FGM Face Sheets: A Finite Element Approach

Assessment of a new higher-order shear and normal deformation theory for the static response of functionally graded shallow shells

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