Nonaxisymmetric solution bifurcation and the stability of shells of revolution with a singular perturbation

1986 ◽  
Vol 26 (6) ◽  
pp. 899-907 ◽  
Author(s):  
V. V. Larchenko
Keyword(s):  
Singular Perturbation ◽  
Shells Of Revolution ◽  
The Stability ◽  
Solution Bifurcation

Two perturbation results for nondegenerate solutions of some semilinear Dirichlet problems

1989 ◽  
Vol 111 (1-2) ◽  
pp. 1-11 ◽  
Author(s):  
Mario Michele Coclite
Keyword(s):  
Differential Operator ◽  
Singular Perturbation ◽  
Nonlinear Term ◽  
Dirichlet Problems ◽  
The Stability

SynopsisThe stability of nondegenerate solutions of some semilinear Dirichlet problems is studied. Two specific situations are considered: firstly, a singular perturbation of the differential operator; secondly, a perturbation of the nonlinear term using a term which also depends on the gradient of the solution.

Asymptotic Solutions for Orthotropic Nonhomogeneous Shells of Revolution

1974 ◽  
Vol 41 (3) ◽  
pp. 753-758 ◽  
Author(s):  
O. A. Fettahlioglu ◽  
C. R. Steele
Keyword(s):  
Shells Of Revolution ◽  
Shell Wall ◽  
Layered Shell ◽  
Asymptotic Results ◽  
Closed Form Solutions ◽  
Support Points ◽  
Temperature Distributions ◽  
Bending Stresses ◽  
Stress And Deformation ◽  
The Stability

Approximate closed-form solutions are obtained for the static stress and deformation as well as the stability of an orthotropic layered shell of revolution with properties which vary along the meridian and through the wall thickness. The shell is subjected to axisymmetrical load and temperature distributions. The nonlinear “prestress” or “pressurization” effect is taken into consideration. It is of interest that due to the nonhomogeneity of the shell wall significant bending stresses can occur far from support points. The asymptotic results agree with numerical values obtained from two computer programs using direct numerical methods, even for shells that are relatively shallow.

scholarly journals Prediction of the Boundary States for Thin-Walled Axisymmetric Shells Under Internal Pressure and Tension Loads

2020 ◽  
Vol 70 (1) ◽  
pp. 57-68
Author(s):  
Kozbur Halyna ◽  
Shkodzinsky Oleh ◽  
Kozbur Ihor ◽  
Gashchyn Nadiia
Keyword(s):  
Plastic Deformation ◽  
Maximum Load ◽  
Stability Loss ◽  
Shells Of Revolution ◽  
Plastic Deformation Process ◽  
Boundary States ◽  
True Stresses ◽  
Stress States ◽  
Stress Ratios ◽  
The Stability

AbstractA method for calculating the ultimate true stresses arising in the walls of shells of revolution in the area of uniform plastic deformation is developed in the research. In order to derive the stability loss for the plastic deformation process the criterion of maximum load is taken as the basis, simple differential equations were solved. It has been shown analytically that the level of the boundary true stresses is much lower when the values of the principal stress ratios approach to 2 or 1/2 compared to the adjacent stress states.

Stability Analysis of Ring-Stiffened Shells of Revolution

1982 ◽  
Vol 26 (02) ◽  
pp. 125-134
Author(s):  
J. Subbia ◽  
R. Natarajan
Keyword(s):  
Stability Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Instability Mode ◽  
Shells Of Revolution ◽  
External Hydrostatic Pressure ◽  
Buckling Mode ◽  
Stiffened Shells ◽  
Bifurcation Buckling ◽  
The Stability

A finite-element formulation is presented for the stability analysis of ring-stiffened shells of revolution using linear bifurcation buckling theory. Critical pressures and mode shapes in both general instability mode and interframe buckling mode have been obtained using this formulation. Three different boundary conditions have been studied and their effect on the stability characteristics is reported. A sophisticated theoretical model has been evolved to treat the external hydrostatic pressure as a follower force. Critical pressures for cylinders with internal and external stiffening are compared.

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