Linearized buckling analysis of functionally graded shells of revolution subjected to displacement-dependent pressure, which remains normal to the shell's middle surface throughout the deformation process, is described in this work. Material properties are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and a metal. The governing equations are derived based on the first-order shear deformation theory, which accounts for through the thickness shear flexibility with Sanders type of kinematic nonlinearity. Displacements and rotations in the shell's middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix, also known as the pressure stiffness matrix, which accounts for the variation of load direction, is derived for each strip and after assembling resulted in the global load stiffness matrix of the shell, which may be unsymmetric. The load stiffness matrix can be divided into two unsymmetric parts (i.e., load nonuniformity and unconstrained boundary effects) and a symmetric part. The main part of this research is to quantify the effects of these unsymmetries on the follower action of lateral pressure. A detailed numerical study is carried out to assess the influence of various parameters such as power law index of functionally graded material (FGM) and shell geometry interaction with load distribution, and shell boundary conditions on the follower buckling pressure reduction factor. The results indicate that, when applied individually, unconstrained boundary effect and longitudinal nonuniformity of lateral pressure have little effect on the follower buckling reduction factor, but when combined with each other and with circumferentially loading nonuniformity, intensify this effect.

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# Semi-Analytical Approach in Buckling Analysis of Functionally Graded Shells of Revolution Subjected to Displacement Dependent Pressure

Majid Khayat

,
Majid Khayat

Department of Civil Engineering,

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: khayatmajid@yahoo.com

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: khayatmajid@yahoo.com

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Davood Poorveis

,
Davood Poorveis

Assistant Professor

Department of Civil Engineering,

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: dpoorveis@scu.ac.ir

Department of Civil Engineering,

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: dpoorveis@scu.ac.ir

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Shapour Moradi

Shapour Moradi

Professor

Department of Mechanical Engineering,

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: moradis@scu.ac.ir

Department of Mechanical Engineering,

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: moradis@scu.ac.ir

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Majid Khayat

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: khayatmajid@yahoo.com

Davood Poorveis

Department of Civil Engineering,

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: dpoorveis@scu.ac.ir

Shapour Moradi

Department of Mechanical Engineering,

Shahid Chamran University of Ahvaz,

Ahvaz 61357, Iran

e-mail: moradis@scu.ac.ir

1

Corresponding author.
Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 30, 2016; final manuscript received June 2, 2017; published online August 30, 2017. Assoc. Editor: Albert E. Segall.

*J. Pressure Vessel Technol*. Dec 2017, 139(6): 061202 (19 pages)

**Published Online:**August 30, 2017

Article history

Received:

May 30, 2016

Revised:

June 2, 2017

Citation

Khayat, M., Poorveis, D., and Moradi, S. (August 30, 2017). "Semi-Analytical Approach in Buckling Analysis of Functionally Graded Shells of Revolution Subjected to Displacement Dependent Pressure." ASME. *J. Pressure Vessel Technol*. December 2017; 139(6): 061202. https://doi.org/10.1115/1.4037042

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