Nondimensional Parameters and Equations for Buckling of Anisotropic Shallow Shells

1994 ◽  
Vol 61 (3) ◽  
pp. 664-669 ◽  
Author(s):  
M. P. Nemeth
Keyword(s):  
Laminated Shells ◽  
Shallow Shells ◽  
Fundamental Parameters ◽  
Combined Loads ◽  
Vlasov Equations ◽  
Shell Buckling ◽  
Bifurcation Buckling ◽  
Z Parameter ◽  
Shear Buckling ◽  
Doubly Curved

A procedure for deriving nondimensional parameters and equations for bifurcation buckling of anisotropic shallow shells subjected to combined loads is presented. First, the Donnell-Mushtari-Vlasov equations governing buckling of symmetrically laminated doubly curved thin elastic shallow shells are presented. Then, the rationale used to perform the nondimensionalization of the buckling equations is presented, and fundamental parameters are identified that represent measures of the shell orthotropy and anisotropy. In addition, nondimensional curvature parameters are identified that are analogues of the well-known Batdorf Z parameter for isotropic shells, and analogues of Dunnell’s and Batdorf s shell buckling equations are presented. Selected results are presented for shear buckling of balanced symmetric laminated shells that illustrate the usefulness of the nondimensional parameters.

scholarly journals Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hui Shi ◽  
Teijun Yang ◽  
Shiliang Jiang ◽  
W. L. Li ◽  
Zhigang Liu
Keyword(s):  
Boundary Conditions ◽  
Current Method ◽  
Vibration Characteristics ◽  
Shallow Shells ◽  
Various Boundary Conditions ◽  
Curvature Effects ◽  
Fourier Series Method ◽  
Vibration Problems ◽  
Elastic Restraints ◽  
Doubly Curved

Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

scholarly journals Non-linear analysis of laminated composite doubly curved shallow shells

2006 ◽  
Vol 28 (1) ◽  
pp. 43-55
Author(s):  
Dao Huy Bich
Keyword(s):  
Laminated Composite ◽  
Governing Equations ◽  
Shallow Shells ◽  
Approximate Analytical Solutions ◽  
Linear Buckling ◽  
Non Linear ◽  
Vibration Problems ◽  
Doubly Curved ◽  
Analytical Expressions ◽  
Load Deflection Curve

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell.

Clamped torispherical shells under external pressure — some new results

1988 ◽  
Vol 23 (1) ◽  
pp. 9-24 ◽  
Author(s):  
J Blachut ◽  
G D Galletly
Keyword(s):  
Failure Mode ◽  
External Pressure ◽  
Spherical Cap ◽  
Geometric Imperfections ◽  
Collapse Pressure ◽  
Modes Of Failure ◽  
Shell Buckling ◽  
Bifurcation Buckling ◽  
Initial Geometric Imperfections ◽  
The One

Perfect clamped torispherical shells subjected to external pressure are analysed in the paper using the BOSOR 5 shell buckling program. Various values of the knuckle radius-to-diameter ratio ( r/D) and the spherical cap radius-to-thickness ratio ( Rs/ t) were studied, as well as four values of σyp, the yield point of the material. Buckling/collapse pressures, modes of failure and the development of plastic zones in the shell wall were determined. A simple diagram is presented which enables the failure mode in these shells to be predicted. The collapse pressures, pc, were also plotted against the parameter Λs (√( pyp/ pcr)). When the controlling failure mode was axisymmetric yielding in the knuckle, the collapse pressure curves depended on the value of σyp, which is unusual. However, when the controlling failure mode was bifurcation buckling (at the crown/knuckle junction), the collapse pressure curves for the various values of σyp all merged, i.e., they were independent of σyp. This latter situation is the one which normally occurs with the buckling of cylindrical and hemispherical shells. A limited investigation was also made into the effects of axisymmetric initial geometric imperfections on the strength of externally-pressurised torispherical shells. When the failure mode was axisymmetric yielding in the knuckle, initial imperfections of moderate size did not affect the collapse pressures. In the cases where bifurcation buckling at the crown/knuckle junction occurred, small initial geometric imperfections at the apex did not affect the buckling pressure, but axisymmetric imperfections at the buckle location did influence it. With the other failure mode (i.e., axisymmetric yielding collapse at the crown of the shell), initial geometric imperfections caused a reduction in the torisphere's strength.

Free Vibration of Curvilinearly Stiffened Shallow Shells

2013 ◽  
Author(s):  
Peng Shi ◽  
Rakesh K. Kapania
Keyword(s):  
Free Vibration ◽  
Ritz Method ◽  
Beam Theory ◽  
Fe Method ◽  
Shallow Shells ◽  
First Order ◽  
Stiffened Shells ◽  
Method Base ◽  
Doubly Curved ◽  
Good Agreement

The free vibration of curvilinearly stiffened doubly curved shallow shells is investigated by the Ritz method. Base on the first order shear deformation shell theory and Timoshenko’s 3-D curved beam theory, the strain and kinetic energies of the stiffened shells are introduced. Numerical results with different geometrical shells and boundary conditions, and different stiffener locations and curvatures are analyzed to verify the feasibility of the presented Ritz method for solving the problems. The results show good agreement with those using the FE method.

Vibration of doubly-curved shallow shells

1996 ◽  
Vol 114 (1-4) ◽  
pp. 95-119 ◽  
Author(s):  
K. M. Liew ◽  
C. W. Lim
Keyword(s):  
Shallow Shells ◽  
Doubly Curved
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