Behavior Of Shallow Spherical Shells Research Articles

Thermally Induced Vibrations of Functionally Graded Shallow Spherical Shells Under Cooling Shock

Based on the first-order shear deformation theory (FSDT), the large-amplitude vibration behavior of shallow spherical shells made of functionally graded materials (FGMs) due to the rapid decrease of temperature (cooling shock) is investigated. FGM is assumed to be a mixture of stainless steel and low-carbon steel whose properties are considered temperature dependent and are estimated based on the power-law model. According to FSDT and von Kármán assumptions, the governing equations of motion in conjunction with corresponding boundary conditions are obtained using Hamilton’s principle. The temperature distribution is also achieved by means of the 1D Fourier transient heat conduction equation, considering two time-dependent thermal loading scenarios. The considered thermal boundary conditions allow that a temperature difference is created with a time delay for the structure under cooling shock. Also, the results of recent experiments are employed to estimate the temperature-dependent properties of structures. In the solution approach, the generalized differential quadrature method and the Newmark-beta integration scheme are utilized. Selected numerical results are presented to study the effects of thermal load rapidity time, geometry, magnitude of thermal load, and material gradient index on the thermally induced vibrations of spherical shells. Stresses generated in the shell due to the thermally induced vibrations are also investigated.

Nonlinear static behaviour of shallow spherical shell on a Kerr foundation

A large deflection analysis of a shallow spherical shell on a Kerr foundation is carried out for a uniformly distributed load and for different edge conditions, using the Sinharay and Banerjee approach. Detailed parametric studies involving variations in geometric, material and foundation properties are made; load-deflection curves for shells on a Kerr foundation are compared with those for shells on an equivalent Pasternak foundation. This study shows that the deflection reduces if the curvature, the Poisson's ratio or the foundation parameters of the shear and lower spring layer are increased. Shells with immovable edges are found to be more prone and vulnerable to changes in various parameters than those with movable edges.

Static and dynamic behaviour of shallow spherical shells on winkler foundation

Large deflection static analysis of shallow spherical shells on Winkler foundation is made, using Berger's and Modified Berger's methods. Small amplitude free vibration analysis of shallow spherical shells on Winkler foundation is carried out various methods. While Modified Berger's method gives better results for static analysis, the original Berger's approach is found to give good results for dynamic analysis

Non-linear dynamic analysis of shallow spherical shells on elastic foundations

The present study investigates the effect of Winkler-Pasternak elastic foundation parameters on the nonlinear dynamic response of shallow spherical shells. The values of foundation parameters ( K ̄ and G ̄ ) have been determined for the minimaximum central response of the shallow shells for both the clamped as well as simply supported immovable edge conditions. Donnell type partial differential equations governing the moderately large amplitude behaviour of shallow spherical shells resting on Winkler-Pasternak elastic foundations under step pressure loading, have been analysed. The space and time-wise integrations of governing equations have been carried out using Chebyshev series and Houbolt techniques, respectively. It is also shown that the present analysis can be extended to study the dynamic buckling of shallow shells resting on elastic foundations.

Non-linear static and dynamic response of spherical shells

In the present investigation an analytical technique using Chebyshev series expansion has been presented and used to study the non-linear transient behavior of shallow spherical shells with and without damping. The two coupled non-linear differential equation governing the shallow shell behavior are initially linearised using Taylor's series expansion. Results have been presented for three types of transient loadings, namely, step function, N-shaped pulse and sine wave pulse. It is shown that accurate results can be obtained using a five terms Chebyshev series expansion which is unlikely in the conventional methods.

On the nonlinear dynamic behavior of shallow spherical shells.

On the nonlinear dynamic behavior of shallow spherical shells.

Experimental investigation of the nonlinear behaviour of shallow spherical shells☆

This paper presents a brief review of some recent contributions in the field of instability of shallow spherical shells. The causes of the apparent inconclusive nature of earlier experimental investigations are examined. This is followed by a report of work carried out in such a manner as to eliminate, as far as possible, some of the factors responsible for experimental error. The results of an experimental investigation of the non-linear stress and deformation characteristics of shallow shell behaviour are presented. Good experimental agreement with theory is shown to be dependent on the preparation of uniform stress free specimens of accurate geometry and on the requirement that the shell be supported in a manner consistent with the assumptions of relevant theory.

Experimental investigation of the nonlinear behaviour of shallow spherical shells

This paper presents a brief review of some recent contributions in the field of instability of shallow spherical shells. The causes of the apparent inconclusive nature of earlier experimental investigations are examined. This is followed by a report of work carried out in such a manner as to eliminate, as far as possible, some of the factors responsible for experimental error. The results of an experimental investigation of the non-linear stress and deformation characteristics of shallow shell behaviour are presented. Good experimental agreement with theory is shown to be dependent on the preparation of uniform stress free specimens of accurate geometry and on the requirement that the shell be supported in a manner consistent with the assumptions of relevant theory.