Influences of elastic foundations and boundary conditions on the buckling of laminated shell structures subjected to combined loads

2011 ◽  
Vol 93 (8) ◽  
pp. 2126-2134 ◽  
Author(s):  
A.H. Sofiyev
Author(s):  
Shahin Mohammadrezazadeh ◽  
Ali Asghar Jafari

This paper investigates the nonlinear vibration responses of laminated composite conical shells surrounded by elastic foundations under S-S and C-C boundary conditions via an approximate approach. The laminated composite conical shells are modeled based on classical shell theory of Love employing von Karman nonlinear theory. Nonlinear vibration equation of the conical shells is extracted by handling Lagrange method. The linear and nonlinear vibration responses are obtained via an approximate method which combines Lindstedt-Poincare method with modal analysis. The validation of this study is carried out through the comparison of the results of this study with results of published literature. The effects of several parameters including the constants of elastic foundations, boundary conditions, total thickness, length, large edge radius and semi-vertex angle on the values of fundamental linear frequency and curves of amplitude parameter versus nonlinear frequency ratio for laminated composite conical shells with both S-S and C-C boundary conditions are investigated.


Author(s):  
A Naderi ◽  
A R Saidi

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.


1950 ◽  
Vol 163 (1) ◽  
pp. 307-310 ◽  
Author(s):  
A. A. Wells

The equation d4 y/ dx4- f(x)y + g(x) = 0 may be solved by means of the differential analyser, but only straightforwardly when the four boundary conditions are specified at one point. When the equation is associated with beams on elastic foundations, or elastic shells, the boundary conditions are more often specified at two points, and a quicker method of solution is desirable. In the analogue, direct use is made of the beam in the form of an elastic wire, supported at intervals in cradles on which weights may be made to simulate the terms f(x)y and g(x); the wire takes up a transversely deflected form which may be measured, and boundary conditions are imposed where they are required. A specific problem is examined and the results are shown to agree reasonably with the solution by calculation. A disadvantage when d2 y/dx2 is required is the inaccuracy inherent in differentiating by finite differences, but for engineering calculations the simplicity of the method may have its advantages. The solution of a typical pressure-vessel problem, by means of the analogue, is described.


2020 ◽  
Vol 8 (6) ◽  
pp. 4362-4366

Thin shell structures have very high load bearing capacity, hence find wide applications in the field of mechanical engineering, structural engineering, sea shore structures, aerospace industries and nuclear engineering structures. The major failure of thin shell structures is buckling. Oil carrying pipelines, hull structures, oil tankers are few examples in which thin cylindrical shell structures fails by buckling under external pressure loading. In order to avoid the buckling failure, prediction of critical buckling pressure is important in thin shell structures under external pressure. But this critical buckling pressure depends on boundary conditions, imperfections, thickness variation of shells etc. To estimate the effects of these parameters on Critical Buckling Pressure (CBP) require a reliable experimental test rig. Hence in our proposed work, efforts are taken to develop a simple cost-effective reliable test rig to determine the effects of these parameter variations on the critical buckling pressure. For developing the test rig two important components to be designed properly namely, external cover cylinder and online pressure measurement system. The external cover cylinder with lid which contains test cylindrical shell inside should be designed in such a way that it should be leak proof and rigid so as to withstand the internal working pressure with negligible deformations. Hence, a ring and stinger stiffened cylindrical shell is taken as external cylindrical shell. The pressure variation in the test rig should be recorded online so as to predict the critical buckling pressure accurately. Hence, PC interfaced microcontroller-based pressure measurement system is developed in our proposed work. The test cylinder considered for this work is made of mild steel of size diameter 456 mm, length 456 mm and thickness 1 mm. The classical (simply supported) boundary conditions are assumed and simulated on both sides of the test cylinders. The experimental critical buckling pressures are compared with the FE results and both the results have good agreement


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