Transient solutions of a longitudinally impacted conical shell
Thin conical shell under longitudinal impact, deriving theory for transverse and rotary inertias and transverse shear deformation effects
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Thin conical shell under longitudinal impact, deriving theory for transverse and rotary inertias and transverse shear deformation effects
Bibliography on conical shell instability
Conical shells are commonly used as structural components for launch vehicles. The axial compression experienced during launch is one of the sizing load cases, because it can lead to loss of stability. As Because experimentally testing these large full-scale structures is cumbersome and expensive, it is studied how reduced-scale shells can be designed such that their buckling behavior is representative of the full-scale scale shell behavior. An analytical, sequential scaling procedure methodology is developed based on the nondimensional governing equations for composite conical shells with a symmetric, balanced layup and negligible flexural anisotropy. The buckling behavior of the shells of different size is compared using linear and nonlinear finite element analyses, and good comparisons . Accurate results are obtained for the considered shells in terms of buckling load, displacement, and mode. The inclusion of a geometric imperfections affects reduces the prediction accuracy, but it does not to the extent that the methodology is no longer valid cause the methodology to fail.
The buckling of a truncated elastic conical shell subjected to an axial compression is a classical problem in shell structures. The paper reinvestigates the buckling of an axially compressed truncated conical shell with rigid bulkheads. Two improvements are achieved. First, the condition that the total horizontal displacement must vanish due to rigid bulkhead and axisymmetry is treated as a constraint. This constraint is incorporated into the system through the use of the Lagrange multiplier; then the variational method is used to derive a complete set of boundary conditions for conical shells. Second, the stability is evaluated in the deformed state using the asymptotic solutions of the pair of Donnell-type equations for axisymmetric configuration. The results indicate that the buckling strength of conical shells depends mainly on the condition of the smaller end. In addition to the vertex angle, the distance ratio plays, at least, an equally important role.
Donnell type stability equations for thin circular orthotropic conical shells are presented and solved for external pressure, axial compression and combined loading. The solution is likewise applied to stiffened conical shells. Correlation with equivalent cylindrical shells yields a simple approximate stability analysis for orthotropic or ring-stiffened conical shells under hydrostatic pressure. The general instability of stiffened conical shells under hydrostatic pressure is also analysed by a more accurate approach. Preliminary experimental results for buckling of ring-stiffened conical shells under hydrostatic pressure are presented and discussed.
Equations for thin elastic conical shells and digital program for analysis of stress and deformation on fixed edge segmental conical shells - solution by finite difference technique
The use of the NASTRAN conical shell element in static, eigenvalue, and direct transient analyses is demonstrated. The results of a NASTRAN static solution of an externally pressurized ring-stiffened cylinder agree well with a theoretical discontinuity analysis. Good agreement is also obtained between the NASTRAN direct transient response of a uniform cylinder to a dynamic end load and one-dimensional solutions obtained using a method of characteristics stress wave code and a standing wave solution. Finally, a NASTRAN eigenvalue analysis is performed on a hydroballistic model idealized with conical shell elements.
Constant thickness elastic conical shells subject to lateral loads, deriving asymptotic solution
Stress and stability of thin-walled conical shells for axisymmetric loads
Stability of reinforced cylindrical and conical shells under various types and combinations of loads
Dynamic response of thin elastic conical shells subject to blast loading - membrane theory
Asymptotic solution for conical shells of linearly varying thickness
Buckling of conical shells under axial compression and effects of axially symmetric defects
Resonant frequencies in thin circular conical shells
It is shown that the initial and the buckled shapes of a certain element of a conical shell can be considered as similar to those of an element of a cylindrical shell of which the radius and length are conservatively determined. It is concluded that therefore the buckling pressure of the conical shell is equal to that of the comparable cylindrical shell. A simple method for finding the buckling pressure if it varies along a generatrix is also given.
A theoretical investigation has been made of the flutter, vibration, and buckling of truncated conical shells with generalized elastic edge restraint. The shell analysis is of the classical Donnell type, in-plane inertias and structural damping are neglected, and the aerodynamic loading is represented by the inviscid two-dimensional quasi-steady approximation. An approximate solution is obtained by the generalized Galerkin method. The accuracy and limitations of the analysis are illustrated by comparing numerical results for buckling an vibration with results of other investigations for various boundary conditions, applied loads, and shell geometries and stiffness. Sufficient numerical results are presented to permit the determination of the flutter condition for simply supported isotropic conical shells for a wide range of cone angle, length-radius ration, and radius-thickness ratio. Results are also presented to indicate some effects of variations in edge restraint, applied loads, and ring or stringer stiffening.
We consider in this report the determination of the upper limit of critical loads in the case of simultaneous action of a compressive force, uniformly distributed over plane cross sections, and of isotropic external normal pressure on cylindrical or conical shells of circular cross section. As a starting point we use the differential equations for neutral equilibrium of conical shells which have been used for the solution of the problem of stability of conical shells under torsion and under axial compression; upon solution of the problem it is possible to satisfy all boundary conditions, in contrast to the report where no attention is paid to the fulfillment of the boundary conditions, and to the report where only part of the boundary conditions are satisfied by solution of the problem according to Galerkin's method. Approximate formulas are used for the determination of the critical external normal pressure with simultaneous action of longituninal compression. Let us note that the formulas suggested in reference 5 are not well founded and may lead, in a number of cases, to a substantial mistake in the magnitude of the critical load.
Dynamic axisymmetric buckling of shallow conical shells subjected to impulsive loads