Showing papers on "Spherical shell published in 1972"

A Large Deformation Elastic-Viscoplastic Analysis of a Thick-Walled Spherical Shell

Abstract: : A large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading The theory does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading The theory is based on relating the essential parameters to state variables; the particular constitutive relations are motivated by the equations of dislocation dynamics A numerical scheme for calculating deformations is developed and applied to a thick walled spherical shell under internal pressure Various numerical examples are presented (Author)

On the Postbuckling Behavior of Imperfection-Sensitive Structures in the Plastic Range

Abstract: Axisymmetric plastic deformation of imperfection sensitive spherical shell after elastic buckling, considering load carrying capacity

Quantum Electromagnetic Zero‐Point Energy of a Conducting Spherical Shell

Abstract: The quantum zero‐point energy of a conducting spherical shell was first calculated by Boyer [Phys. Rev. 174, 1764 (1968)]. Because of the importance of this calculation and also of Boyer's uncertainty about the analytical dependence of the energy on the cutoff function, we have checked the calculation independently. We determine an analytic continuation of the energy function using the Mellin transform, and thereby show how an exact value of the self‐energy can be obtained from the divergent series. We also compute an approximate value of the self‐energy by extrapolating a direct numerical evaluation of the cutoff integrals. These calculations confirm Bover's result.

Axisymmetric inertial oscillations of a fluid in a rotating spherical shell

Abstract: Introduction . This paper is concerned with an interpretation of some experiments on certain axisymmetric inertial oscillations of a rotating fluid in a thick spherical shell. These oscillations are the counterparts to the ones reported by Aldridge and Toomre† (1969) for a full sphere of rotating fluid. A description of the arrangements for both experiments is presented in A & T; some of the measured eigen-frequencies for spherical shells of rotating fluid given by Aldridge (1967) are presented here for comparison with values calculated from a variational principle.

Axisymmetric Postbuckling and Nonsymmetric Buckling of a Spherical Shell Compressed Between Rigid Plates

Abstract: Presents an analysis of the stresses and deflections produced during axisymmetric postbuckling and determines the deformation states at which the shell may buckle into a nonsymmetric shape. The analysis accounts for finite deflections and rotations, but assumes that the material remains linearly elastic throughout the deformation. An experiment shows that both the primary axisymmetric bifurcation point and the secondary nonsymmetric bifurcation point are stable for a shell with R/h approximately equal to 40.

Bifurcation Buckling as an Approximation of the Collapse Load for General Shells

Abstract: A computer program, STAGS, for nonlinear analysis of shells of general shape has been extended to include a branch for bifurcation buckling analysis. In the case of general shells, failure usually occurs by means of collapse at a limit point rather than through bifurcation. Therefore, the paper contains also a discussion of the practical applicability of the bifurcation buckling theory. Several example cases are presented in which results from a bifurcation buckling analysis are compared to results from a rigorous nonlinear analysis. It is emphasized by these examples that the classical buckling analysis may give results of little or no value if the shell geometry deteriorates appreciably (Brazier effect) or stresses are redistributed (statical indeterminance) in the subcritical load range. On the other hand, there are cases in which the less costly bifurcation analysis can be substituted for the rigorous collapse analysis. OMPLICATED shell structures for which the weight economy is of utmost importance, such as present space shuttle configurations, have resulted in an increase in the interest in two-dimension al shell analysis. Simultaneously remarkable improvements in numerical methods an4 in computer technology have greatly enhanced our capability to handle such problems. Hence, computer programs for the buckling analysis of shells of general shape qr loading are being offered to a public which to a large extent may be unaware of the limitations of the theory on which these programs are based. A computer program for buckling analysis of shells of general shape or loading based on the classical bifurcation theory must be used with some caution. A bifurcation point indicates a load level at and above which some new deformation mode is possible. Therefore, the bifurca- tion analysis is a rigorous solution of the problem only if the failure mode is orthogonal to the prebuckling deformation pattern. This, of course, is unlikely to be the case if the shape of the shell or its loading is of a general nature, and for such shells buckling or collapse will in most cases occur through the passing of a limit point (a maximum in a load displacement curve). However, the "classical" buckling theory (bifurcation from linear membrane solution) sometimes gives good approximations to the buckling load even for cases which are outside its scope. For an axially loaded cylinder with the edges restrained from radial displacements, the rigorous nonlinear analysis shows that the displacements approach infinity as the axial stress approaches the critical value The STAGS computer program has been under development for about three years. The program performs a nonlinear analysis of shells by use of a two-dimensional finite difference grid and an energy principle. Displacement and stress histories are computed corresponding to a given history of applied load, displacement or temperature. The theoretical background for STAGS is presented in Ref. 1 and its scope is discussed in more detail in Ref. 2. It applies to any shell for which a reference surface and a suitable set of gridlines (following shell boundaries) can be defined. The shell wall thickness can vary and material properties can vary with the surface coordinates and through the thickness. Cutouts in the shell wall and discrete stiffening can be included.

An approximate theoretical study of the dynamic plastic behavior of shells

Abstract: An approximate theoretical procedure is presented which may be used to estimate the dynamic plastic response of arbitrarily shaped shells. The influence of finite-deflections is retained in the analysis, but material elasticity, strain hardening and strain rate sensitivity are disregarded. The two particular cases of a complete spherical shell which is subjected to a spherically symmetric pressure pulse and a fully clamped cylindrical shell loaded impulsively are considered in some detail. It is observed that the predictions for these two cases agree favourably with the results of more exact rigid-plastic theories.

Electromagnetic Fields and Massive Bodies

Abstract: We consider an example of the effects of massive bodies on static electromagnetic fields in general relativity which yields considerable insight into the fadeaway of multipole moments in nonspherical perturbations of gravitational collapse. We calculate the electromagnetic field of an electrostatic or magnetostatic multipole of fixed strength placed at the center of a massive, nonrotating, spherical shell. If we consider a sequence of static solutions in which the massive shell approaches its own Schwarzschild radius, we find that except in the monopole ($l=0$) case the value of the multipole moment measured by a distant observer goes to zero. Thus, for an arbitrary (but finite) stationary charge and current distribution inside the shell, in the limit as the shell approaches its Schwarzschild radius the only property of the distribution which can be measured by an external observer is the total electric charge.

A New Theory of Spherical Shells with Cracks.

Abstract: : An improved theory of shallow spherical shells which includes the effect of transverse shear deformation is derived The resulting tenth order system of equations are uncoupled and all five boundary conditions along an edge of the shell can be satisfied The method of integral transforms is used to formulate and solve the symmetric problem for a spherical shell containing a finite meridional crack The stress field in the neighborhood of the crack tip is obtained In contrast to the classical shallow shell theory, the angular variation of the stress resultants coincide with that of the stretching, and the Reissner theory of bending of thin plates so that a combined stress-intensity factor can be defined (Author)

Universal solutions for fiber-reinforced compressible isotropic elastic materials

Abstract: Universal solutions for fiber-reinforced compressible isotropic elastic materials under large elastic deformations are obtained, by using inverse methods. The following deformations are investigated: bending, stretching and shearing of a rectangular block; straightening, stretching and shearing of a sector of a circular tube; inflation, eversion, extension, torsion, bending and shearing of a sector of a circular tube; inflation and eversion of a spherical shell. The significance of the reinforcement and the deformed configuration of the fibers is duscussed.

Self-inflatable life preserver apparatus

Abstract: A self-inflatable life preserver including an inflatable annular tube which is stored in a deflated condition within a generally spherical shell suitable for throwing by hand over considerable distances. A pressurized fluid container is positioned within the inflatable tube and is actuated by a trigger mechanism biased toward a first position allowing the pressurized fluid to fill the annular tube; the trigger mechanism being normally held in a second position by a liquid deterioratable strap wrapped about the exterior of the tube. The spherical shell is provided with a number of holes for allowing a liquid (e.g. water) to pass into the shell upon the occurrence of which the strap deteriorates allowing the valve actuator to move to its first position inflating the deflated tube causing the spherical shell to split apart and separate from the inflated preserver.

A Note on the Finite Elastic Inflation of a Thin Spherical Shell

Abstract: The finite elastic inflation of a thin spherical shell is considered for compressible isotropic materials. A numerical method is used which allows the inflation problem to be done for any strain en...

Scattering from an Elastic Spherical Shell

Abstract: : A mathematical model was developed to predict the scattering of a plane acoustic wave from an elastic spherical shell with different fluid media inside and out. The model was developed from the more convenient standpoint of elastic theory rather than from the acoustic point of view. Resulting equations were solved in terms of known functions. Matrix methods were used throughout. A numerical method is presented that takes advantage of some peculiarities of the resulting matrix and is appropriate to computer implementation. Some results of a computer program for the spherical shell are given. A few limiting cases of the exact solutions are compared with previously reported results.

On the reflection of light from an inhomogeneous shell

Abstract: The main contribution to the reflected field from a radially inhomogeneous spherical shell is determined. It is shown that it is much smaller in amplitude than the field reflected by a perfectly conducting sphere coated with the same type of radially inhomogeneous dielectric.

Symmetric Buckling of Inelastic Spherical Shells

Abstract: A numerical method for determining the buckling loads and stresses for elastic-plastic spherical shells subjected to uniform external pressure is presented. No restriction is placed on shallowness in the analysis. The incremental theory of plasticity and the von Mises yield criterion are used in formulating the problem. The governing differential equations are formulated in terms of displacements and are solved with the aid of finite differences, an incremental-iterative technique, and a high speed digital computer. Buckling loads are taken as the first maximum of a load-average deflection curve. Numerical results are presented for a clamped spherical shell. Buckling loads are compared to the elastic complete sphere value and the limit analysis load. The relationship of the radius-thickness ratio to buckling stress is presented.

TransientEM screening in two concentric spherical shell model

Abstract: Different results have been obtained by Negi and Wait in connection with the effect of overburden in electromagnetic exploration by assuming different definitions of screening factor. Both definitions are based on frequency domain considerations. We shall describe the screening characteristics for a transient field with a two-concentric shell model with screening factor=(magnetic field of target and screen-magnetic field of screen alone)/(field of target alone). It is found that the screening factor does become more than one in some situations which means that the EM response of target is more in some cases when the screen is present than when it is absent.

Experimental Investigation on the Collapse Strength of Spherical Shells

Abstract: In order to obtain the collapse strength data on the spherical shells suitable to the pressure capsule of DSSV, collapsing tests were conducted using spherical shell models by means of MHI 1, 200 kg/cm2 hydrostatic tank. These models were made from several kinds of materials including ultra-high yield strength steels such as 18% Ni maraging steel, 10% Ni dual-strengthened steels etc., and machined into near-perfect spherical shape or spheres with initial imperfection of various, thicknesses.From these experiments the following conclusions are obtained : (1) Collapse pressure of relatively thick shells (ha/R10≥0.03) agrees to the theoretical inelastic buckling pressure by Gerard et al.(2) The effect of initial imperfections are evaluated by local radius in case of relatively thick shells. But for thinner shells, this method is not sufficient and nonlinear elasto-plastic analysis will be required.(3) Present results will not always agree with Krenzke's data, especially in thinner shells with flat spot.(4) Fracture appearance of collapsed shells are closely related to the fracture toughness of materials.

The Transient Electromagnetic Response of a Spherical Shell of Arbitrary Thickness

Abstract: Starting with the plane-wave solution for scattering from a two-layer sphere, the quasistatic response of a thin conducting shell is recovered analytically. Responses are also computed for shells of arbitrary thickness, and the range of validity of the thin-shell approximation is determined. These results are extended to the time domain by a numerical inverse Fourier transform which yields the response to a step-function incident field (magnetic or electric). It is found that under the thin-shell approximation, the transient response has a simple single-exponential form. This is modified to some extent when the arbitrary thickness of the shell is allowed for.

The deformation behavior of polyethylene spherulite

Abstract: The deformation behavior of polyethylene spherulite composed of spherical shells (extinction bands) was studied by polarized microscope. The spherulitic films were drawn with various ratios at 20°C and 100°C, and the elongation ratios of each shell were evaluated.The results obtained are as follows;(1) The elongation ratio of the outermost shell, being the same as that of spherulite, is less than that of the sample. This indicates that the relative motion occurs between spherulites. The deviation from affine deformation is less for the hot drawn film than for the cold drawn film.(2) The thickness of each elemental shell is almost uniform for the homogeneously deformed two-dimensional spherulite. Consequently the elongation ratios of outer shells are less than that of inner shells.(3) Similarly a spherical shell in three-dimensional spherulite deform to an ellipsoidal shell, though the thickness of an elemental shell is not uniform. The crystal lamellae constituting these deformed shells must be disrupted to fullfil the geometric requirement.(4) Deformation modes within a three-dimensional spherulite, which are generally deviated from affine deformation, depend on elongation ratios and deformation temperatures.