A semi-analytical evaluation of displacement dependent pressure on buckling of functionally graded material shells of revolution

[+] Author and Article Information
Majid Khayat

Department of Civil Engineering, Shahid Chamran University of Ahvaz

Davood Poorveis

Department of Civil Engineering, Shahid Chamran University of Ahvaz

Shapour Moradi

Department of Mechanical Engineering, Shahid Chamran University of Ahvaz

1Corresponding author.

ASME doi:10.1115/1.4037042 History: Received May 30, 2016; Revised June 02, 2017


Linearized buckling analysis of functionally graded shells of revolution subjected to displacement dependent pressure which remain normal to the shell middle surface throughout the deformation process is described in this work. Material properties are assumed to be temperature dependent, and varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and metal. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness shear flexibility with Sanders-type of kinematic nonlinearity. Displacements and rotations in the shell middle surface are approximated by combining polynomial functions in the meridional direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix which accounts for variation of load direction derived for each strip and after assembling global load stiffness matrix of the shell which may be un-symmetric is formed. The un-symmetric parts which are due to load non-uniformity and unconstrained boundaries have been separated. The results indicate that considering pressure stiffness causes buckling pressure reduction. A detailed numerical study is carried out to bring out the effects of power-law index of functional graded material and geometry of the shell on the effect of follower action of lateral pressure on buckling load diminishes.

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