Showing papers on "Spherical shell published in 1970"
64 citations
TL;DR: In this article, an analysis of stresses and deflections produced in a thin, complete spherical shell when it is compressed between two parallel rigid plates is presented, and the deformation state at which the contact region buckles is given.
Abstract: Abstract : The paper presents an analysis of stresses and deflections produced in a thin, complete spherical shell when it is compressed between two parallel rigid plates. The analysis accounts for finite deflections and rotations, but assumes that the material remains linearly elastic throughout the deformation. It is also assumed that the region of the shell which is in contact with the plate remains flat. The deformation state at which the contact region buckles is given. (Author)
61 citations
TL;DR: This paper is concerned with a theoretical model of the head, an attempt to theoretically model what is considered a very complicated situation with the hope of deducing from the analysis the most prominent features of cranioceiebral trauma.
59 citations
TL;DR: Clamped shallow spherical cap elastic buckling and initial postbuckling behavior under uniformly distributed load over circular region centered at apex was studied in this article, where the authors showed that the buckling behavior was similar to ours.
Abstract: Clamped shallow spherical cap elastic buckling and initial postbuckling behavior under uniformly distributed load over circular region centered at apex
53 citations
46 citations
TL;DR: In this paper, a two-phase isotropic homogeneous poroelastic material is taken as a model of the living bone in the sense that the osseous tissue is considered as a linear perfectly elastic solid and the fluid substances filling the cavities as a Newtonian viscous fluid.
Abstract: Two-phase isotropic homogeneous poroelastic material is taken as a model of the living bone in the sense that the osseous tissue is considered as a linear perfectly elastic solid and the fluid substances filling the cavities as a Newtonian viscous fluid. Using the Heinrich-Desoyer formulation of the consolidation theory of Terzaghi-Biot adapted to the spherical bodies and the Laplace transformation, the pressure head function is determined first. The complimentary solution of the equation for the displacement of the solid phase is then adapted from the classical elastic solution in terms of the Legendre polynomials. For simplicity, only the axisymmetric case is considered. The integration constants are determined from the third governing equation as well as from the boundary and initial conditions. Three illustrative examples are investigated in detail, assuming hydrostatic load: (1) a thick-walled shell if the fluid pressure may be disregarded, (2) a solid poroelastic sphere, (3) a thin-walled poroelastic shell. In case 2, the rheological model describing the behavior of the body seems to correspond to the Kelvin-Voigt model proposed for osseous tissues by Zarek and Edwards.
35 citations
01 Aug 1970
TL;DR: Fluid filled elastic spherical shell, calculating free vibration axisymmetric response and fundamental mode as mentioned in this paper, and the fundamental mode of the shell is calculated using the free vibration response.
Abstract: Fluid filled elastic spherical shell, calculating free vibration axisymmetric response and fundamental mode
20 citations
TL;DR: In this article, the interaction of a plane acoustic step wave with an elastic spherical shell is studied, and the mathematical model of the shell incorporates the effects of membrane, bending, rotatory inertia, and shear deformation.
Abstract: The interaction of a plane acoustic step wave with an elastic spherical shell is studied. The mathematical model of the shell incorporates the effects of membrane, bending, rotatory inertia, and shear deformation. A Laplace transform with respect to the time coordinate is used in the analysis, and the transformed solution is obtained in the form of a partial‐wave expansion. By Watson's transformation, this partial‐wave expansion is then converted into a series of integrals, which are evaluated asymptotically. The origins of the reflected and diffracted wave are then identified. Evaluation of the inverse Laplace integral gives the wavefronts and the amplitudes of the shell response and the fluid pressure in the acoustic medium at the wavefronts. A comparison of the results from the membrane and the refined theories of shells is made. Besides, the transient response in a short time after arrival of the incident wave is also computed numerically in the lit region far from the shadow boundary.
18 citations
TL;DR: In this paper, the thermal stability of a simply supported bimetallic shallow spherical shell is investigated and it is shown that the minimum initial height of the shell for which buckling is possible is strongly dependent upon the material properties.
Abstract: The paper considers the thermal stability of a simply supported bimetallic shallow spherical shell. Only rotationally symmetric modes of deflection are considered. It is found that the minimum initial height of the shell for which buckling is possible is strongly dependent upon the material properties of the shell. It is conjectured that if the edges of the shell are clamped, no buckling is possible.
18 citations
TL;DR: In this article, a separable homogeneous solution for the displacements and stresses in a freely vibrating deep spherical shell exhibiting spherical isotropy is derived, including the effects of shear deformation, rotary inertia, and transverse normal strain.
Abstract: In this paper, a separable homogeneous solution for the displacements and stresses in a freely vibrating deep spherical shell exhibiting spherical isotropy is derived. A six‐mode shell theory is proposed that includes the effects of shear deformation, rotary inertia, and transverse normal strain. The frequency spectra, corresponding to three different materials with varying degrees of anisotropy, are analyzed for two values of thickness‐to‐mean‐radius ratios. Also, open spherical shells under various boundary conditions are investigated and mode shapes are studied.
14 citations
TL;DR: In this article, the authors used the variational theorem for creep to study the initial and subsequent forms of the stress resultants and displacements of thin shallow spherical shells under uniform external pressure.
Abstract: The variational theorem for creep is used to study the creep deflections and collapse times for simply supported thin shallow spherical shells under uniform external pressure. The initial and subsequent forms of the stress resultants and displacements are obtained with the aid of the elastic theory of thin shallow spherical shells. The variational theorem for creep leads to a set of simultaneous ordinary differential equations with prescribed initial conditions. Numerical solutions are generated by means of the Runge-Kutta method. Theoretical predictions for creep deflections and collapse times are compared with experimental data for five test shells at each of three different pressure levels for Type 6/6 Nylon. It was found that the theory predicts creep deflections that are consistently smaller than the experimental values, whereas the theoretical collapse times are consistently larger than the experimental collapse times. The discrepancy between the theoretical predictions for creep deflections and collapses times and the experimental data is believed to be due largely to the deviations which occur between the theoretical and actual stress and displacement mode shapes with the passage of time. Closer agreement should be expected when more time flexibility is built into these mode forms.
TL;DR: In this article, a numerical scheme for calculating large isothermal elastoplastic (non-strain hardening) deformations is presented, which enables one to carry the material through various loading-unloading programs and is designed in a way that permits changing the form of the constitutive laws.
Abstract: A numerical scheme for calculating large isothermal elastoplastic (non-strain hardening) deformations is presented. It is an extension of the scheme used in Ref. [1] to calculate large elastic deformations. Finite differences are used and the deformation is followed in small time steps. For each time cycle a system of non-linear equations is set-up, and solved by the Newton-Raphson method. The scheme enables one to carry the material through various loading-unloading programs, and is designed in a way that permits changing the form of the constitutive laws. The scheme is used to solve the spherically symmetric problem. The inflation and unloading of a thick-walled spherical shell is studied in detail. A comparison with Hill's solution for the infinitesimal case shows the deviations caused by geometrical non-linearity.
DOI•
01 Jan 1970
TL;DR: In this article, the authors present the results of tests on four different types of bricks, two made of PLASTIC and two of REINFORCED Mortars.
Abstract: A PREVIOUS STUDY OF THE BUCKLING OF A CYLINDRICAL SHELL ROOF IS NOTED WHEREIN PLASTIC MODELS DID NOT REPRODUCE WELL THE BUCKLING BEHAVIOR OF REINFORCED MORTAR SHELLS. IT WAS SHOWN FOR THIS CASE THAT THE BUCKLING LOAD OF THE REINFORCED MORTAR SHELLS WAS SIGNIFICANTLY INFLUENCED BY CRACKING DUE TO TRANSVERSE BENDING MOMENTS. AS A CONSEQUENCE THE PLASTIC MODELS, WHICH EXHIBITED ELASTIC BEHAVIOR, COULD NOT SIMULATE THE REINFORCED MORTAR MODELS. IN THIS PAPER THE RESULTS OF TESTS ON FOUR SPHERICAL DOMES, TWO MADE OF PLASTIC AND TWO OF REINFORCED MORTAR ARE PRESENTED. THE STATE OF STRESS PRIOR TO BUCKLING IN THE SPHERICAL SHELL CASE DOES NOT LEAD TO SIGNIFICANT CRACKING AS IN THE CYLINDRICAL SHELL STUDY. AS A CONSEQUENCE THE PLASTIC DOMES, WITHIN THE LIMITS TO WHICH THE TANGENT MODULUS OF ELASTICITY OF THE MORTAR COULD BE DEDUCED, DID QUALITATIVELY AND QUANTITATIVELY SIMULATE THE REINFORCED MORTAR DOMES. /ACI/
TL;DR: Bellman et al. as discussed by the authors showed that the system of equations for the total reflection function considered by them admits two solutions, and the character of the numerical methods employed was such as to select the spurious solution.
31 Jan 1970
TL;DR: In this article, a program designated FLASH was developed to provide a means to study the propagation of monochromatic radiation from a plane parallel source through a spherical shell atmosphere.
Abstract: : A program designated FLASH has been developed to provide a means to study the propagation of monochromatic radiation from a plane parallel source through a spherical shell atmosphere. A simple illustration of the backward Monte Carlo method utilized in the development of the FLASH program is discussed in order to show the advantage of the method. A brief description of the methods employed in the FLASH program is given to illustrate the application of the backward Monte Carlo treatment of light propagation through a spherical shell atmosphere. Several comparisons of FLASH generated data with data from other calculational methods are shown.
TL;DR: Using Wronskians and recurrence relations of the spherical Bessel functions, it is shown that the inverse matrix M − 1 can be simplified enough to insure an improvement in economy and accuracy in machine computations as discussed by the authors.
Abstract: In their formulation of wave problems in a spherically layered medium, Phinney and Alexander have arrived at a layer-matrix M which forms the fundamental building block of their solution. In actual application of the theory, the inversion of M is needed for each assumed spherical shell. Since numerical inversion of the matrix M may introduce undesired accumulation of errors, an analytical inverse matrix M −1 is obtained. Using Wronskians and recurrence relations of the spherical Bessel functions, it is shown that the inverse matrix M −1 can be simplified enough to insure an improvement in economy and accuracy in machine computations. Some useful properties of the inverse matrix M −1 are discussed which reduce the amount of machine time even further.
TL;DR: In this article, it was shown that the Gegenbauer transform of order 3 2 defined in terms of the Gengenbauber polynomials C n (3 2 ) (x) is appropriate to reduce the partial differential equation of torsional motion of a complete spherical shell to an elementary ordinary differential equation in time.
Patent•
15 Dec 1970
TL;DR: In this article, a cushion composed of short compressible struts with elastomer properties, the spaces between them being filled with a flexibly elastic compound is filled with interstitial filler.
Abstract: The base is located around the vertical centre line of the container with the container resting on it Between the two is a cushion composed of short compressible struts with elastomer properties, the spaces between them being filled with a flexibly elastic compound Both the supports and the mass are stuck to the container and to the base The upper surface of the base proper is concave and matched to the container in such a way that supports of the same length, together with their interstitial filler, form a segment of a spherical shell
TL;DR: In this paper, an incremental variational method is presented for the determination of the inelastic load-deformation relationship, as well as the buckling or collapse load for a shell of revolution which is made of a work hardening material and subjected to axisymmetric loadings.
Abstract: : An incremental variational method is presented for the determination of the inelastic load-deformation relationship, as well as the buckling or collapse load for a shell of revolution which is made of a work hardening material and subjected to axisymmetric loadings. A variational principle involving the Kirchhoff stress tensor, the Green strain tensor, and their rates is employed. The isothermal stress-strain relationship based on a modified J2 incremental theory of plasticity is used. A seven sheet sandwich shell idealization and the finite difference method of variational calculus are utilized in a numerical procedure in order to determine discrete velocities and a subsequent deformation process. The buckling loads of a number of elastic and inelastic cylindrical and truncated conical shells as well as inelastic spherical shell caps are determined. The results of the present analysis, obtained numerically by a Univac 1107 digital computer, compare favorably with available experimental data. (Author)
TL;DR: In this article, nonlinear spinning shallow spherical shell equations solved for equilibrium stress and displacement distributions are solved for inertia loading, and the authors discuss inertia loading and equilibrium stress distribution in spherical shells.
Abstract: Nonlinear spinning shallow spherical shell equations solved for equilibrium stress and displacement distributions, discussing inertia loading
TL;DR: In this paper, the postbuckling behavior of a spherical shell with a constrained rigid boundary has been studied by using the deep shell theory and the shallow shell theory, and the numerical examples indicate that the difference between the results obtained by using Deep Shell Theory and shallow shell Theory is small.
Abstract: The postbuckling behavior of a spherical shell with a constrained rigid boundary has been studied by using the deep shell theory and the shallow shell theory. In the use of the shallow shell theory, the solution for the detached portion of the shell can be expressed in such a form which is independent of the physical and the geometrical properties. It has also been found that for a perfect shell and a shell with a certain type of initial imperfections, there is no bifurcation buckling at a finite stress level. The numerical examples indicate that the difference between the results obtained by using the deep shell theory and that by using the shallow shell theory is small
01 Jan 1970
TL;DR: In this article, the authors considered spherical and cylindrical vessels, subjected to the simultaneous action of constant internal pressure, constant external temperature, and constant internal temperature with a superimposed cyclic temperature fluctuation.
Abstract: Spherical and cylindrical vessels are considered, subjected to the simultaneous action of constant internal pressure, constant external temperature, and constant internal temperature with a superimposed cyclic temperature fluctuation. The vessel material is nonlinearly thermoviscoelastic with temperature dependent creep modulus. The influence of thermal frequency is studied for various cases of interest. A multimembrane analog of the real shell is shown to be useful in examining these effects.