0
Research Papers: Design and Analysis

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

[+] Author and Article Information
Majid Khayat

Department of Civil Engineering,
Shahid Chamran University of Ahvaz,
Ahvaz 61357, Iran
e-mail: khayatmajid@yahoo.com

Davood Poorveis

Assistant Professor
Department of Civil Engineering,
Shahid Chamran University of Ahvaz,
Ahvaz 61357, Iran
e-mail: dpoorveis@scu.ac.ir

Shapour Moradi

Professor
Department of Mechanical Engineering,
Shahid Chamran University of Ahvaz,
Ahvaz 61357, Iran
e-mail: moradis@scu.ac.ir

1Corresponding 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 139(6), 061202 (Aug 30, 2017) (19 pages) Paper No: PVT-16-1089; 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 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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 2

Geometry of shell of revolution

Grahic Jump Location
Fig. 3

An FGM shell of revolution

Grahic Jump Location
Fig. 4

Variation of volume fraction Vm through the thickness for various values of the power-law index, N

Grahic Jump Location
Fig. 5

Force and moment resultants

Grahic Jump Location
Fig. 7

Global and local coordinate systems for a shell of revolution

Grahic Jump Location
Fig. 8

Deformation of an elemental area

Grahic Jump Location
Fig. 9

Hemispherical shell under uniform lateral pressure

Grahic Jump Location
Fig. 10

Influence of base boundary conditions of FG hemispherical shell on the follower buckling reduction factor, μ, (R/h = 25)

Grahic Jump Location
Fig. 11

Influence of base boundary conditions of FG hemispherical shell on the follower buckling reduction factor, μ, (R/h = 50)

Grahic Jump Location
Fig. 12

Influence of base boundary conditions of FG hemispherical shell on the follower buckling reduction factor, μ (R/h = 100)

Grahic Jump Location
Fig. 13

Geometry of conical shell

Grahic Jump Location
Fig. 14

Flutter and divergence dominant instability criteria regions for case “DB”

Grahic Jump Location
Fig. 15

Flutter and divergence dominant instability criteria regions for case “DL”

Grahic Jump Location
Fig. 16

Flutter and divergence dominant instability criteria regions for case “DC”

Grahic Jump Location
Fig. 17

Flutter and divergence dominant instability criteria regions for case “DLB”

Grahic Jump Location
Fig. 18

Flutter and divergence dominant instability criteria regions for case “DCB”

Grahic Jump Location
Fig. 19

Flutter and divergence dominant instability criteria regions for case “DCL”

Grahic Jump Location
Fig. 20

Flutter and divergence dominant instability criteria regions for case “DCLB”

Grahic Jump Location
Fig. 21

Influence of domain, free boundary, and load nonuniformity of external virtual work integrals on the follower buckling reduction factor: (a) (γ  = 0 deg and h = 5 mm), (b) (γ  = 15 deg and h = 5 mm), (c) (γ  = 30 deg and h = 5 mm), and (d) (γ  = 45 deg and h = 5 mm)

Grahic Jump Location
Fig. 22

Influence of domain, free boundary, and load nonuniformity of external virtual work integrals on the follower buckling reduction factor: (a) (γ  = 0 deg and h = 7.5 mm), (b) (γ  = 15 deg and h = 7.5 mm), (c) (γ  = 30 deg and h = 7.5 mm), and (d) (γ  = 45 deg and h = 7.5 mm)

Grahic Jump Location
Fig. 23

Influence of domain, free boundary, and load nonuniformity of external virtual work integrals on the follower buckling reduction factor: (a) (γ  = 0 deg and h = 10 mm), (b) (γ = 15 deg and h = 10 mm), (c) (γ  = 30 deg and h = 10 mm), and (d) (γ  = 45 deg and h = 10 mm)

Grahic Jump Location
Fig. 24

Catenary shell geometry: (a) meridian section and (b) circumferential section

Grahic Jump Location
Fig. 25

Cycloid shell geometry: (a) meridian section and (b) circumferential section

Grahic Jump Location
Fig. 26

Parabolic shell geometry: (a) meridian section and (b) circumferential section

Grahic Jump Location
Fig. 27

Elliptic shell geometry: (a) meridian section and (b) circumferential section

Grahic Jump Location
Fig. 28

Lateral buckling pressure of various FG shells of revolution for h = 1.25 mm

Grahic Jump Location
Fig. 29

Lateral buckling pressure of various FG shells of revolution for h = 2.5 mm

Grahic Jump Location
Fig. 30

Lateral buckling pressure of various FG shells of revolution for h = 5 mm

Grahic Jump Location
Fig. 31

Variation of follower buckling reduction factor, μ  for different shells of revolution (h = 1.25 mm)

Grahic Jump Location
Fig. 32

Variation of follower buckling reduction factor, μ for different shells of revolution (h = 2.5 mm)

Grahic Jump Location
Fig. 33

Variation of follower buckling reduction factor, μ for different shells of revolution (h = 5 mm)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In