Shell Of Arbitrary Cross Section Research Articles

Geometrically nonlinear numerical procedure for Saint-Venant's problem for a symmetrical elastic shell with a closed contour and circular axis

An original numerical procedure of treating Saint-Venant's problem for toroidal-like shells under pressure and bending moment is suggested. Its peculiarity consists in that the loading and displacement parameters are separated into two groups: the first one describes the ring-like transverse deformation of the shell cross section, while the second the beam-like axial deformation of the latter. One of them is considered separately in the sequential iteration procedure while the other is reckoned to be known. After each step of calculation, the parameters considered to be known are made more exact. A lot of the well-known problems widely presented in the literature are considered. Among them are: (1) Karman's problem, which explains the ovalization of the cross section and the enlarged flexibility of a pipe bend as compared to a straight pipe under bending; (2) the so-called pressure reduction effect when the internal pressure prevents ovalization, which is a demonstration of the influence of the geometrical nonlinearity even at small displacements; (3) Brazier's effect, which deals with nonlinearly enlarged ovalization of an initially straight elastic pipe with an increase in the bending moment. The main advantage of the method is that it allows analyzing a toroidal shell of arbitrary cross section with a variable wall thickness. As an example, a toroidal shell with two long symmetrical axial cracks is considered, where cracks are modeled as the jumps of the contour angular displacement whose values are related to the crack depth.

Minimum Energy Characterizations for the Solution of Saint-Venant's Problem in the Theory of Shells

The linear theory of Cosserat surfaces is employed to study Saint-Venant's problem for cylindrical shells of arbitrary cross-section. We prove minimum energy characterizations for the solution of the relaxed Saint-Venant's problem previously obtained. Then, we determine the global measures of strain appropriate to extension, bending, torsion and flexure for certain classes of solutions to the relaxed problem.

Analysis of Stresses and Displacements in Orthotropic Noncircular Cylindrical Shells Under Centrifugal Loads

This paper addresses the class of stress–strain problems for thin orthotropic cylindrical shells of arbitrary cross section under centrifugal loads. Separating out the variables for a simply supported shell yields a system of ordinary differential equations for which the boundary-value problem is solved by a stable numerical method. Study is made of the distribution of displacements in shells of elliptical cross section versus the ratio of ellipse exes and the eccentricity of the axis of revolution relative to the geometrical axis of symmetry

Geometrical theory of acoustic scattering by thin elastic shells

Based on ray concepts, a geometrical theory is developed for the analysis and synthesis of the pressure and velocity fields of source-excited smooth thin elastic shells with fluid loading. At mid frequencies, these fields are contributed mainly by shell guided leaky membrane waves and specular reflection, provided either the source or observer is away from the shell surface. The theory involves the ray divergence coefficients characterizing the evolution of ray tubes in the fluid or ray strips on the shell, as well as the excitation, radiation, and reflection coefficients, which depend on both the physical and the geometrical properties of the shell. The former may be found by geometrical considerations, while the latter are determined by comparison with the analytic solutions of appropriate canonical problems and subsequent generalization to the perturbed shell configurations. Utilizing circular cylindrical and spherical shells as the canonical examples, this paper demonstrates the construction of the scattered fields from cylindrical shells of arbitrary cross section and from shells of revolution. It extends the concepts of Keller and Karal’s geometrical theory for surface waves [J. B. Keller and F. C. Karal, Jr., J. Appl. Phys. 31, 1039–1046 (1960)].

Geometrical theory of acoustic scattering by thin elastic shells

The sound field scattered by a smooth thin elastic shell immersed in fluid arises largely from specular reflection and acoustic–membrane coupling, unless both source and observer are located near or on the shell. These two contributions have been found to be well described by ray fields for canonical shells in the mid-frequency regime, and hence may be generalized by the principle of localization to accommodate more general geometries. By examining the excitation, propagation, and radiation processes of the supersonic membrane waves on the shell, this paper defines the excitation and radiation coefficients associated with these shell-guided leaky waves as well as the divergence coefficients of the ray tubes characterizing the variation of the wave amplitudes. It extends the concepts of Keller and Karal’s geometrical theory for surface waves [J. B. Keller and F. C. Karal, Jr., J. Appl. Phys. 31, 1039–1046 (1960)]. The explicit evaluation of these coefficients, and therefore the leaky fields, is demonstrated for two classes of shells—cylindrical shells of arbitrary cross section and shells of revolution—based on the knowledge of cylindrical and spherical shell prototypes and differential geometry. The reflected waves are more straightforward and the related coefficients are readily determined. [Work supported by ONR.]

Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section

The plane wave backscattering from a perfectly conducting three-dimensional shell of arbitrary cross section has peen studied. A uniform physical optics (PO) solution, valid across the reflection limits, is derived. The solution, derived from an asymptotic evaluation of the PO integral, includes end-point contributions that account for the diffracted field on edges. It can be improved by the fringe fields derived from an analytical integration of the equivalent edge currents of the physical theory of diffraction (PTD). It is computationally efficient for electrically large shells and compares very well with the finite-element method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

TM Transmission Through Dielectric-Filled Slots in a Conducting Cylindrical Shell of Arbitrary Cross Section

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory. >

Thin shell theories and acoustic wave scattering by infinitely long cylindrical shells of arbitrary cross section

The scattering of acoustic waves by an infinitely long cylindrical shell immersed in a fluid is analyzed. A new approach has been proposed using thin shell theory incorporating the impedance of the shell in the T-matrix formulation. Numerical results are presented for the farfield backscattering amplitude as a function of frequency. Calculations were made for infinitely long circular and elliptic cylindrical shells immersed in water for various shell thicknesses for waves incident at an arbitrary angle in the plane normal to the axis of the cylinder. The impedance resulting from the use of various shell theory approximations for circular cylindrical shells is presented. Love–Timoshenko and Flügge–Byrne–Lurye theories for circular cylindrical shells have been compared with the full elasticity solution using the separation of variables approach. Comments have been made regarding the range of applicability of various shell theories.

Acoustic wave scattering by elastic cylindrical shells in water

Frequency dependence of acoustic wave scattering by an infinite cylindrical shell of arbitrary cross section is analyzed using the T-matrix approach. Explicit expression for the T matrix of a two-layered cylinder is presented. Numerical results are obtained for plane wave incidence normal to the axis of the shell but arbitrary with respect to the noncircular cross section for a range of frequencies. Backscattering cross sections for various angles of incidence are presented for aluminum, steel, and plastic compliant tubes. The results obtained for circular and elliptical cross sections are compared with other available theoretical and experimental results.

Thin shell theories and acoustic wave scattering by infinitely long cylindrical shells of arbitrary cross section

The scattering of acoustic waves by an infinitely long cylindrical shell immersed in a fluid is analyzed. A new approach has been proposed using thin shell theory; incorporating the impedance of the shell in the T‐matrix formulation. Numerical results are presented for the farfield back scattering amplitude as a function of frequency. Calculations were made for infinitely long circular and elliptic cylindrical shells immersed in water for various shell thicknesses, for waves incident at an arbitrary angle in the plane normal to the axis of the cylinder. The impedance resulting from the use of various shell theory approximations for circular cylindrical shells is presented. Love‐Timoshenko and Flugge‐Byrne‐Lurye theories for circular cylindrical shells have been compared with the full elasticity solution using the separation of variables approach. Comments have been made regarding the range of applicability of various shell theories.

Acoustic wave scattering by elastic cylindrical shells in water

Frequency dependence of acoustic wave scattering by an infinite cylindrical shell of arbitrary cross section is analyzed using the T-matrix approach. Numerical results are obtained for plane wave incidence normal to the axis of the shell but arbitrary with respect to the noncircular cross section for a range of frequencies. Results obtained for shells of circular and elliptical cross sections are compared with experimental results.

Low-Frequency Shielding Properties of Conducting Cylindrical Shells of Arbitrary Cross Section

The shielding properties of general, two dimensional, finitely conducting shells with vanishingly thin walls are analyzed by the integral-equation method. For the circular cylinder case, a field plot throughout the shield interior reveals that, at the 'no shielding' frequencies found by Schieber, fields are attenuated greatly, except near the center. The influence of slots in the shell walls is also assessed for both circular and rectangular cylinders. Due to focusing effects, the field at the shield center is even stronger than the incident field at certain resonant frequencies for the slotted cylindrical shells.

The Transient Motion of a Cylindrical Shell of Arbitrary Cross Section in an Acoustic Medium

A solution has been constructed for the transient motion of a viscoelastic cylindrical shell of the arbitrary cross section, surrounded by a fluid medium. The fluid region external to the shell is mapped into the interior of a rectangle. The transformed fluid equation together with the shell equations are expressed in finite-difference form and the time variable suppressed through the application of the Laplace transform. Shell displacements and acoustic pressures are found over the fluid field and at the fluid solid interface.

Variational principles related to the equilibrium shape of a plasma in an axisymmetric torus

Considers the equilibrium shape of a plasma confined in an axisymmetric torus with a perfectly conducting shell of arbitrary cross-section and with (or without) control field coils. This problem leads to a non-classical, free boundary value problem for the flux function psi . A variational, non-linear eigenvalue problem is proposed whose solution defines the function psi in the whole cavity, giving at the same time the boundary of the plasma and the values of psi inside the plasma and in the vacuum. This approach is useful for the analytical study of the problem and also for its numerical solution.