A new formulation, based on the semi-analytical finite element method, is proposed for elastic shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential. Dynamic pressure acting on the walls is derived from Bernoulli's equation. Imposing the requirement that the normal components of velocity of the solid and fluid be equal, introduces fluid-structure coupling. The proposed technique has been validated using results available in the literature. This study shows that instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency and this phenomenon is also independent of the type of structural boundary conditions imposed. © 2002 Elsevier Science Ltd. All rights reserved.

Chandramouli Padmanabhan

Department of Mechanical Engineering

Natrajan Ganesan

Boundary conditions

finite element method

Flow of fluids

Natural frequencies

FLUID FLOW INSTABILITY

Shells (structures)

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IIT Madras

A semi-analytical coupled finite element formulation for shells conveying fluids

Computers and Structures

Cylindrical shell filled with hot liquid is analyzed for buckling and vibration behavior using semi-analytical finite element method. A parametric study is conducted on a 316L stainless-steel cylinder filled with hot liquid. The temperature distribution in shell domain is obtained by using axisymmetric eight-node ring finite elements, capable of taking axial variation of temperature into account. Three-node ring elements are used for buckling and vibration analysis, formulated using semi-analytical finite element method. Thermal stress resultants and moment resultants in the shell are estimated and static buckling analysis is carried out to find the buckling temperature of the container for different levels of filling of liquid and for two different boundary conditions. Free vibration analysis carried out by considering initial stress effect and added mass effect due to hot liquid. Two different geometries are considered to study the effect of geometry on buckling temperature. © 2004 Elsevier Ltd. All rights reserved.

Journal of Sound and Vibration

Buckling and vibration of circular cylindrical shells containing hot liquid

The flow of hot fluid having a harmonic component superposed on the mean flow velocity is considered flowing through an insulated cylindrical shell. The cylindrical shell will be subjected to thermal load due to the flow of hot fluid. The semi-analytical finite element forms the basis for modelling the structural continuum under the influence of temperature and the flowing fluid. The fluid flowing through the cylindrical shell is incompressible and linear potential flow theory is used to formulate the fluid domain. Bernoulli's principle and impermeability conditions of the fluid are the basis for a coupled fluid-structure interaction analysis. Model reduction technique in conjunction with the fourth order Runge-Kutta method using Gill's coefficient is adopted to compute the state transition matrix which provides the stability information of the periodic system. The results of the theoretical studies are presented related to instability regions due to a pulsatile flow of hot fluid through a cylindrical shell. Hot fluid at various magnitude of constant temperature limited by the critical thermal buckling temperature is considered in the study. The effect of fluid temperature and excitation parameter on the behavior of dynamic instability of the system is examined. © 2003 Elsevier Ltd. All rights reserved.

A study on the dynamic stability of a cylindrical shell conveying a pulsatile flow of hot fluid

Vast literature is available for modeling the coupled fluid structure interaction involving the flow of a pulsatile fluid through pipes/shells under ambient temperature. In contrast it is found that there is no literature on such problems under the influence of temperature. This paper considers the evaluation of dynamic instability regions due to a flow of pulsating hot fluid through an insulated composite cylindrical shell. A coupled fluid structure interaction model in conjunction with uncoupled thermomechanical model is used for analysis. The system's equations of motion containing periodic coefficients are expressed in modal domain considering linear transformation. Fourth order Runge-Kutta method using Gill's coefficient is adopted to compute the state transition matrix which provides the stability information of the periodic system following the Floquet-Liapunov theory. Pulsatile flow of water at various magnitude of steady state temperature is considered and hence the effect of water temperature on the instability regions is analyzed. The influence of lamina fibre angle on the instability regions is also examined. © 2004 Elsevier Ltd. All rights reserved.

Composite Structures

Parametric resonance of a composite cylindrical shell containing pulsatile flow of hot fluid

A coupled fluid structure interaction problem is analyzed using semi-analytical finite element method involving composite cylindrical shells conveying hot fluid for free vibration and buckling behavior. The system under study is assumed to have a steady flow of hot fluid and the temperature variation is axi-symmetric. First order shear deformation theory is used to model the elastic shells of revolution. Geometric stiffness matrix is evaluated to consider the effects of axi-symmetric temperature variation through the shell continuum due to flow of hot fluid. The fluid domain is modeled using the wave equation. Numerical results of the studies on composite cylindrical shells made of HS-Graphite/Epoxy with two different length to radius ratios and clamped-clamped boundary condition conveying hot fluid are presented. The variation of the natural frequency of the coupled system is evaluated with the steady flow of the hot fluid. The influence of the temperature on the mean axial flow velocity through the shell is critically examined. The critical velocity of the hot fluid and cold fluid which leads to shell instability is compared thus establishing the fact that the lowest critical velocity of the hot fluid coincides with the mode corresponding to the lowest critical thermal buckling temperature. Various fibre angles are also considered in the study and its influence is also examined. © 2003 Elsevier Science Ltd. All rights reserved.

Free vibration and buckling analysis of composite cylindrical shells conveying hot fluid

The finite element code is developed based on the displacement field proposed by Wilkins et al. to find out the natural frequencies and loss factors of fluid filled cylindrical shells with a constrained viscoelastic layer in between two facings made of composite material. The fluid effect on the natural frequencies and loss factors are taken care of by the added mass of the fluid on the structure. Effects of the fluid height, ratio of core to facing thickness and facing fibre orientation on the natural frequencies and loss factors of cylindrical shells are presented.

Journal	Computers and Structures
ISSN	00457949
Open Access	No