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Research Papers: Design and Analysis

Strength and Buckling Problems of Dished Heads of Pressure Vessels—Contemporary Look

[+] Author and Article Information
Krzysztof Magnucki

Institute of Rail Vehicles TABOR,
Warszawska 181,
Poznan 61-055, Poland
e-mail: krzysztof.magnucki@tabor.com.pl

Jerzy Lewinski

Institute of Rail Vehicles TABOR,
Warszawska 181,
Poznan 61-055, Poland
e-mail: jerzy.lewinski@tabor.com.pl

Rafal Cichy

Institute of Rail Vehicles TABOR,
Warszawska 181,
Poznan 61-055, Poland
e-mail: rafal.cichy@tabor.com.pl

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received October 25, 2017; final manuscript received March 28, 2018; published online May 10, 2018. Assoc. Editor: Kiminobu Hojo.

J. Pressure Vessel Technol 140(4), 041201 (May 10, 2018) (14 pages) Paper No: PVT-17-1212; doi: 10.1115/1.4039844 History: Received October 25, 2017; Revised March 28, 2018

The paper is a review work devoted to dished heads of various meridian shapes. Geometry of the shells of revolution, the membrane state, and the edge effect occurring in the shells are described. Exemplary analytical and numerical finite element method (FEM) studies of torispherical, ellipsoidal, Cassini-ovaloidal, and untypical special dished heads are presented. The results of the above-mentioned two methods are compared. Moreover, numerical research of elastic buckling of the above-mentioned selected heads under external pressure is carried out. Literature related to each of the considered head types is quoted and discussed, with special attention paid to the works developed in the 21st century. In concluding remarks, the stress concentration and buckling of these structures are commented, with consideration of the head meridian shapes.

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Figures

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Fig. 1

Axial section of the middle surface of the shell of revolution

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Fig. 2

Scheme of the membrane forces of the shell under symmetrical load

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Fig. 3

Scheme of forces, bending moments, and displacements on the shell edges

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Fig. 4

(a) Axial section of the half torispherical head and (b) the graph of the principal radius of the meridian R1(θ)

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Fig. 5

The Huber–Mises stresses in the vessel with torispherical head: (a) general view—Huber–Mises stresses and (b) the Huber–Mises stresses diagram

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Fig. 6

(a) Axial section of the half ellipsoidal head and (b) the graph of the principal radius of the meridian R1(θ)

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Fig. 7

Scheme of the transverse force Q0, the bending moment M0, and the meridional force N0 in the joint of the ellipsoidal head with the cylindrical shell

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Fig. 8

The Huber–Mises stresses in the vessel with ellipsoidal head of relative depth δ = 0.5—analytical solution

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Fig. 9

The Huber–Mises stresses in the vessel with ellipsoidal head of relative depth δ = 0.6—analytical solution

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Fig. 10

The Huber–Mises stresses in the vessel with ellipsoidal head of relative depth δ = 0.5—FEM calculation: (a) general view—Huber–Mises stresses and (b) the Huber–Mises stresses diagram

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Fig. 11

The Huber–Mises stresses in the vessel with ellipsoidal head of relative depth δ = 0.6—FEM calculation: (a) general view—Huber–Mises stresses and (b) the Huber–Mises stresses diagram

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Fig. 12

The Huber–Mises stresses in the vessel with hemispherical head—analytical solution

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Fig. 13

The Huber–Mises stresses in the vessel with hemispherical head—FEM calculation: (a) general view—Huber–Mises stresses and (b) the Huber–Mises stresses diagram

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Fig. 14

(a) Axial section of the half Cassini ovaloidal head and (b) the graph of the principal radius of the meridian R1(ξ)

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Fig. 15

The Huber–Mises stresses in the vessel with Cassini ovaloidal head—analytical solution

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Fig. 16

The Huber–Mises stresses in the vessel with Cassini ovaloidal head—FEM calculation: (a) general view—Huber–Mises stresses and (b) the Huber–Mises stresses diagram

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Fig. 17

(a) Axial section of the half special dished head and (b) the graph of the principal radiuses of the meridian R1(x) and the parallel R2(x)

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Fig. 18

The Huber–Mises stresses in the vessel with special dished head

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Fig. 19

The Huber–Mises stresses in the vessel with special head—FEM calculation: (a) general view—Huber–Mises stresses and (b) the Huber–Mises stresses diagram

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Fig. 20

Buckling shape of the torispherical head—the critical pressure pCR,FEM(torisph)=0.412 MPa

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Fig. 21

Buckling shape of the ellipsoidal head of relative depth δ = 0.5—the critical pressure pCR,FEM(ellip, 0.5)=1.041 MPa

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Fig. 22

Buckling shape of the ellipsoidal head of relative depth δ = 0.6—the critical pressure pCR,FEM(ellip, 0.6)=1.491 MPa

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Fig. 23

Buckling shape of the hemispherical head—the critical pressure pCR,FEM(hemisph)=3.940 MPa

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Fig. 24

Buckling shape of the Cassini ovaloidal head—the critical pressure pCR,FEM(Cass)=0.474 MPa

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Fig. 25

Buckling shape of the special head—the critical pressure pCR,FEM(spec)=0.769 MPa

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Fig. 26

First buckling modes of ellipsoidal head subjected to axial force acting on the nozzle: (a) compression and (b) tension

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