Solution of static problems of shells of revolution of medium thickness under axisymmetric loading with the aid of digital computers

O. Yu. Kalekin; E. S. Shishkina

doi:10.1007/bf00885492

Solution of static problems of shells of revolution of medium thickness under axisymmetric loading with the aid of digital computers

Soviet Applied Mechanics ◽

10.1007/bf00885492 ◽

1967 ◽

Vol 3 (5) ◽

pp. 41-44

Author(s):

O. Yu. Kalekin ◽

E. S. Shishkina

Keyword(s):

Shells Of Revolution ◽

Medium Thickness ◽

Axisymmetric Loading ◽

Digital Computers

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A stiffness method for elastic-plastic shells of revolution

Journal of Strain Analysis ◽

10.1243/03093247v014339 ◽

1966 ◽

Vol 1 (4) ◽

pp. 339-350 ◽

Cited By ~ 21

Author(s):

P V Marcal ◽

W R Pilgrim

Keyword(s):

Pressure Vessel ◽

Computer Programme ◽

Shells Of Revolution ◽

Step Method ◽

Axisymmetric Loading ◽

Elastic Plastic ◽

Stiffness Method ◽

Experimental Values

A stiffness method is proposed for the analysis of elastic-plastic shells of revolution with axisymmetric loading. A step-by-step method of integration is used in a computer programme developed to implement the method. Calculations were performed for a toroidal bellows and a torispherical pressure vessel head; the results agree with experimental values.

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A Method for the Calculation of Natural Frequencies of Orthotropic Axisymmetrically Loaded Shells of Revolution

Journal of Vibration and Acoustics ◽

10.1115/1.2930390 ◽

1994 ◽

Vol 116 (1) ◽

pp. 16-25 ◽

Cited By ~ 6

Author(s):

A. Kayran ◽

J. R. Vinson ◽

E. Selcuk Ardic

Keyword(s):

Numerical Integration ◽

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Natural Frequencies ◽

Shell Of Revolution ◽

Initial Stresses ◽

Integration Technique ◽

Shells Of Revolution ◽

Axisymmetric Loading

A methodology is presented for the calculation of the natural frequencies of orthotropic axisymmetrically loaded shells of revolution including the effect of transverse shear deformation. The fundamental system of equations governing the free vibration of the stress-free shells of revolution are modified such that the initial stresses due to the axisymmetric loading are incorporated into the analysis. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method which makes use of the multisegment numerical integration technique. This method is commonly known as frequency trial method. The solution for the initial stresses due to axisymmetric loading is omitted; since the application of the transfer matrix method, making use of multisegment numerical integration technique for both linear and nonlinear equations are available in the literature. The method is verified by applying it to the solution of the natural frequencies of spinning disks, for which exact solutions exist in the literature, and a deep paraboloid for which approximate solutions exist. The governing equations for a shell of revolution are used to approximate circular disks by decreasing the curvature of the shell of revolution to very low values, and good agreement is seen between the results of the present method and the exact solution for spinning disks and the approximate solution for a deep paraboloid.

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