Conical Shell Structures Research Articles

Experimental identification of the vibration modes of liquid‐filled conical tanks and validation of a numerical model

AbstractTruncated conical‐shaped shells are widely used as containment vessels in elevated water tanks. In the aftermath of earthquakes, water tanks play a vital role in supplying the water needed for extinguishing fires that usually occur during these catastrophic events. As such, special attention has to be given when designing water tanks in order to assure safety and functionality of these structures during a seismic event. To the best of the authors' knowledge, this paper reports the first experimental program conducted to evaluate the dynamic characteristics of liquid‐filled flexible conical shell structures. A small‐scale aluminium conical shell model was mounted to a shaking table and subjected to a set of dynamic excitations. In the first phase of the experimental program, acceleration measurements were used to identify the first two modes of vibration. In the second experimental phase, the cos(θ)‐modes were identified through base shear and overturning moment measurements. The study was also conducted analytically using a numerical model that was previously developed by El Damatty et al. The model accounts for the effect of the added mass resulting from the developed hydrodynamic pressure through a proper fluid–structure interaction formulation. Tests conducted in the two experimental phases were simulated using this numerical model. In general, the experimental and analytical predictions of the dynamic characteristics of the tested model were in very good agreement. This provides a validation of the previously developed numerical model. The analytical model was then implemented to assess the generalized added mass of the contained fluid. Copyright © 2003 John Wiley & Sons, Ltd.

Analysis of laminated conical shell structures using higher order models

In this paper is presented a numerical method for the structural analysis of laminated conical shell panels using a quadrilateral isoparametric finite element based on the higher order shear deformation theory. The displacement expressions used for the longitudinal and circumferential components of the displacement field are given by power series of the transversal coordinate and the condition of zero stresses in the top and bottom surfaces of the shell is imposed. The shape functions used for the transversal displacement are C 1 conforming and the finite element is a conical/cylindrical panel with 8 nodes and 40 degrees of freedom. The model presented performs static analysis with arbitrary boundary conditions and loads, as well eigenvalue problems (free vibration and buckling). Illustrative examples are presented and discussed.

Application of Linear Programming to the Limit Analysis of Conical-Shaped Steel Water Tanks

In the past two decades, accidental failure of conical-shaped steel water tanks under hydrostatic pressure has been reported. For safety analysis, the limit analysis of such structures is formulated as a linear programming problem. Comparing with experimental and numerical results available in the literature, the accuracy of the linear programming approach is found to be high, with respect to the limit loads and failure modes of the conical shell structures. In the process of formulation, the equilibrium conditions of the problem, not the constitutive equations, are directly involved. Thus, overestimation of the stiffness for thin plates or shells resulting from inadequate constitutive equations—a phenomenon often encountered in the nonlinear finite-element analysis for thin-walled panels or shells—does not exist. Based on the internal forces at collapse, some important mechanical aspects as related to the failure mechanism and failure modes, as well as some structural characteristics, are also discussed.

Scanning tunneling microscopy of carbon nanotubes and nanocones

Tubular and conical carbon shell structures can be synthesized in the vapor phase. Very hot carbon vapor, after being deposited onto highly oriented pyrolytic graphite (HOPG), forms a variety of nanostructures, in particular single-shell tubes, multishell tubes, bundles of tubes, and cones. The structures were analyzed by scanning tunneling microscopy (STM) in UHV. Atomic resolution images show directly the surface atomic structures of the tubes and their helicities. A growth pathway is proposed for fullerenes, tubes, and cones.

Dynamic Buckling of Conical Shells with Imperfections

A study has been made to determine the dynamic stability of a truncated thin circular conical shell with various geometrical imperfections and under a wide variety of dynamic loading conditions. The method of solutions utilizes a Galerkin procedure. By assuming the deformation modes, the final nonlinear differential equations of motion are derived by minimizing the total energy of the system with respect to each of the undetermined modal amplitudes. A Runge-Kutta integration scheme is then used to solve these nonlinear differential equations numerically. From the characteristics of the shell response, a criterion for the buckling load is established. It is found that the tendency of dynamic buckling of a conical shell structure decreases with increase of the opening angle of the cone. Conical shells are also found to be less sensitive to initial geometric imperfections than the cylinder.

Interactive design of large end rings on stiffened conical shells using composites

Design study methods and results are presented of a composite reinforced base ring for the conical aeroshell structure of the planetary lander vehicle for Project Viking, an unmanned mission to Mars. The aeroshell is a ring and stringer-stiffened conical shell structure having a half angle of 70° with a large base ring mounted at the outer edge of the cone and a large pay-load ring in the interior with many smaller rings spaced along the inside shell surface. The purpose of the structure is to develop the aerodynamic drag required to decelerate the lander in the Mars atmosphere to facilitate a soft landing. The shell, therefore, must be designed to resist external pressure loads during Martian entry. Unlike conventional shell structures, the Viking aeroshell has no connecting supports at its large diameter edge and, therefore, it must resist the external pressure as an unsupported inertially loaded shell. Very little design information is available on large shell structures under these loading conditions. The structural weight of the aeroshell must be reduced to the minimum possible level while still retaining structural integrity. A currently proposed design for this structure is all metal, and the base ring accounts for 41 per cent of the total aeroshell structural weight. One possible method of reducing the weight of the proposed design is to selectively apply filamentary composites to reinforce a redesigned base ring. The filamentary reinforced base ring must be designed to take into account all possible modes of failure under the maximum design load conditions. The possible modes of failure are local or general buckling of the shell, ring buckling, and exceedence of the maximum permissible stress levels. The design of a shell structure of this complexity requires the use of the latest technology available in a large general purpose shell buckling program. A large general purpose non-linear shell buckling program developed by Lockheed (BOSOR 2) was used. Since the amount of computational effort is considerable for such a study, the turnaround time for using such a program as an aid in the design process was reduced by adapting the program to an interactive real time graphical system using the facilities of the Langley Research Center CDC computer complex. This paper describes the shell structure model and the stability results of a large Langley Research Center Viking aeroshell model, the BOSOR 2 computer program and its adaptation to an interactive system, and the design strategy used to re-design the base ring and the weight savings achieveable by composite reinforcements.

Structural dynamics aspects of the Gemini program.

The Gemini Program has proceeded well into its flight phase. This advanced state of development permits a review of the adequacy of the structural dynamics analyses and tests performed. The areas covered include: 1) environmental prediction techniques based on flight data combined with wind-tunnel oscillatory pressure data, trajectory information, and ground test data; 2) the tests of individual components, modules, and ultimately the entire spacecraft to these environments; 3) the response of ring-stiffened conical shell structure to a nonuniform aerodynamic forcing function, based on ground vibration tests and wind-tunnel data with pressure correlation; 4) docking system development by analysis and |-scale model testing utilizing a zero spring rate support for six-degree-of-freedom motion; 5) stability of moored vehicles under thrust; 6) pyrotechnic shock transmitted through structure for separation devices; and 7) flutter. Where applicable, the analyses are compared with ground test results and available flight data.