Numerical solution of nonlinear equations for spinning shallow spherical shells

AIAA Journal ◽  
1970 ◽  
Vol 8 (1) ◽  
pp. 185-187 ◽  
Author(s):  
ROY J. BECKEMEYER ◽  
T. S. DAVID ◽  
WALTER EVERSMAN
Keyword(s):  
Numerical Solution ◽  
Nonlinear Equations ◽  
Spherical Shells

A Numerical Solution of the Nonlinear Equations for Axisymmetric Bending of Shallow Spherical Shells

1961 ◽  
Vol 28 (4) ◽  
pp. 557-562 ◽  
Author(s):  
G. A. Thurston
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Nonlinear Equations ◽  
External Pressure ◽  
Spherical Shells ◽  
Axisymmetric Bending

A numerical solution is obtained for the nonlinear equations for clamped, shallow spherical shells under external pressure. Results are presented in the postbuckling range which have not been computed previously. The upper and lower buckling pressures are compared with the experimental data of Kaplan and Fung.

Numerical Solution of Nonlinear Equations

1979 ◽  
Vol 5 (1) ◽  
pp. 64-85 ◽  
Author(s):  
Jorge J. Moré ◽  
Michel Y. Cosnard
Keyword(s):  
Numerical Solution ◽  
Nonlinear Equations

scholarly journals Plastic deformations in the ring spherical shells

2018 ◽  
Vol 251 ◽  
pp. 04060
Author(s):  
Avgustina Astakhova
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Thin Shells ◽  
Stress Dependence ◽  
Strain Intensity ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Development Area

In the present work the results of the study of plastic deformations distribution in the thickness in ring spherical shells are presented. Resolving differential equations system is based on the Hirchhoff-Lave hypothesis, linear thin shells theory and small elastic-plastic deformations theory. The studying of the development area of plastic deformations in shells thickness are performed with using the results of the elastic solutions method. The basic relations of elastic solutions method that allow to determine the distribution areas of plastic deformations in shells thickness and along the generatrix are presented. The diagram of intense stress dependence from the strain intensity with linear hardening is received. The numerical solution is performed by orthogonal run method. Long and short spherical shells under the operation of three evenly distributed ring loads are observed. The shells have a tough jamming along the contour at the bottom and at the top. Dependency between tension intensity and deformations intensity is accepted for the case of a material linear hardening. Area of plastic deformations in shells thickness for three kinds of ring spherical shells are shown. The results for the loads differed by the value in twice are presented.

Frequency Response of Fluid Lines With Nonlinear Boundary Conditions

1971 ◽  
Vol 93 (3) ◽  
pp. 365-372 ◽  
Author(s):  
R. D. Strunk
Keyword(s):  
Boundary Conditions ◽  
Perturbation Method ◽  
Numerical Solution ◽  
Frequency Response ◽  
Nonlinear Equations ◽  
Nonlinear Boundary ◽  
Harmonic Distortion ◽  
Nonlinear Boundary Conditions ◽  
Qualitative Information ◽  
Method Of Solution

The harmonic distortion generated when a fluid line is terminated by a nonlinear orifice characteristic is analyzed by using a perturbation method of solution. The perturbation method is shown to be representative of the true phenomenon and to give very good quantitative as well as qualitative information by comparing the results to a numerical solution of the nonlinear equations. The results presented describe the distortion phenomenon as a function of several dimensionless ratios.

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