Showing papers on "Shell (structure) published in 1985"

A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation

Abstract: This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.

Shell Crossings and the Tolman Model

Abstract: We consider the problem of shell crossings and regular maxima in the Tolman model. The necessary and sufficient conditions which guarantee no shell crossings will arise in Tolman models are derived, and we show explicitly that a Tolman model (in general, with a surface layer) may contain both elliptic and hyperbolic regions without developing any shell crossings and without the hyperbolic regions recollapsing. This finding is contrary to the recent hypothesis of Zel'dovich and Grishchuk. We also show that the properties that distinguish shell crossings from more serious singularities in spherical symmetry are independent of the equation of state.

Geometrically non-linear transient analysis of laminated, doubly curved shells

Abstract: A dynamic, shear deformation theory of a doubly curved shell is used to develop a finite element for geometrically non-linear (in the von Karman sense) transient analysis of laminated composite shells. The element is employed to determine the transient response of spherical and cylindrical shells with various boundary conditions and loading. The effect of shear deformation and geometric non-linearity on the transient response is investigated. The numerical results presented here for transient analysis of laminated composite shells should serve as references for future investigations.

Buckling of Laminated Composite Plates and Shell Panels

Abstract: : This work summarizes the technical literature dealing with buckling and post-buckling behavior of laminated composite plates and shell panels. Emphasis is given to modern materials used in the aerospace industry having fiber-matrix constituents (e.g., glass-epoxy, boron-epoxy, graphite-epoxy, boron-aluminum), but other applications are also considered (e.g., plywood, paperboard). Geometric configurations taken up are either flat (plates) or cylindrically curved (shells), and have rectangular planform. All possible types of loading conditions and edge constraint conditions are considered. Both symmetrically and unsymmetrically laminated configurations are included, with symmetrical laminates represented by orthotropic or anisotropic plate or shell theory. Complicating effects dealt with include: internal holes, shear deformation, sandwich plates with soft cores, local instability, inelastic materials, hygrothermal effects and stiffeners. Approximately 400 references are used. Extension numerical results are presented in graphical and tabular form. Both theoretical and experimental results are summarized. Keywords: Vibrations; Unsymmetric laminates.

Nonlinear Pressure Waves in a Fluid-Filled Elastic Tube

Abstract: The nonlinear pressure wave propagation in a straight thin elastic tube containing an inviscid incompressible fluid is considered using the shell theories which are extended to the second order of magnitude of deformations. The nonlinear effects being taken into account are due to the convective motion of fluid, nonlinear strains and stress-strain relations. Though our problems are considerably simplified by the shell theories, the resultant equations for the displacements of the middle surface are still complicated. Therefore, further considerations are confined to the asymptotic state in which the system of equations can be reduced to the Korteweg-de Vries (K-dV) equation and the relation between the multi-soliton solutions and peaking and steepening phenomena is discussed.

Shell microstructures of Cambrian molluscs replicated by phosphate

Abstract: The original microstructure of the aragonistic and calcite shells of Cambrian molluscs is frequently visible at high magnifications on the surfaces of phosphatic internal moulds. More rarely, the nature of the original microstructure may be determined by examining the internal surfaces of phosphate layers which coated the shells, or by examining the phosphate fillings of the tunnels made by endolithic algae within the shells. Because the original aragonitic microstructures of molluscan shells are almost invariably destroyed by recrystallisation in rocks older than the Carboniferous, the discovery of replicated shell microstructures has provided a new understanding of the evolution of the molluscan shell. Most of the common molluscan microstructures — spherulitic prismatic aragonite, tangentially arranged fibrous aragonite, crossed-lamellar aragonite, nacre and foliated calcite — had probably appeared by at least the beginning of the Middle Cambrian, and most are found in representatives of the Class Monop...

Atomic inner-shell excitation induced by coherent motion of outer-shell electrons.

Abstract: Outer-shell electrons coherently driven by intense radiation can transfer energy in a direct intra-atomic process to inner-shell excitations. Provided that the effective momentum transfer ..delta..q is sufficiently low (..delta..qowig10 MeV/u), is evaluated in a limiting form closely resembling the Bethe result for inelastic electron scattering from atoms.

Optimal laminate configurations of cylindrical shells for axial buckling

Abstract: Optimum laminate configurations for laminated cylindrical shells under axial compression are investigated and obtained under buckling constraints. Complete freedom is given in the selection of the ply angle variation through the thickness. Twelve lamination parameters are introduced to describe laminate properties, and the optimal values of these parameters are obtained numerically. It is shown that there are many different optimal configurations which give the same buckling load. The optimality condition for the laminate configurations is derived semiempirically from the numerical results in terms of the lamination parameters. The maximum buckling load is obtained in terms of material properties. Some examples of optimal laminate configurations are presented. It is shown that one of the optimal laminate configurations can be obtained when an infinite number of infinitely thin layers are arranged so that the shell becomes quasi-isotropic in the shell surface and quasihomogeneous through the thickness.

Through‐the‐thickness stress predictions for laminated plates of advanced composite materials

Abstract: A finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures. Plate element behaviour is specified by prescribing independently the neutral surface displacements and rotations, thus relaxing the Kirchhoff hypothesis. Numerical efficiency is achieved due to the simplicity of the element formulation, i.e. the approach yields a displacement dependent multi-layer model. In-plane layer stresses are determined via the constitutive equations, while the transverse shear and short-transverse normal stresses are determined via the equilibrium equations. Accurate transverse stress variations are obtained by appropriately selecting the displacement field for the element. A selective reduced integration technique is utilized in computing element stiffness matrices. Static and spectral (eigenvalue) tests are performed to demonstrate the element modelling capability.

A classification of thin shell theories

Abstract: This paper gives a modern mathematical analysis of the relationships between several, different linear shell theories. It also discusses the asymptotic role played by membrane theory. It presents theorems on the existence and uniqueness of solutions of membrane equations depending on the concavity of the surface.

A flat triangular shell element with improved membrane interpolation

Abstract: An 18 degrees-of-freedom flat triangular shell element is formulated using the DKT bending element and a new membrane stress formulation. The membrane stress formulation is based on a degenerate linear strain triangle utilizing in-plane rotations at each node. This new formulation is very simple and satisfies the plane stress patch test. Based on the numerical results from a rigorous set of test problems, the new formulation is shown to be an improvement over earlier attempts to improve the membrane stress in the shell element.

Spherical acoustic resonator: Effects of shell motion

Abstract: The exact theory of classical elasticity is used to calculate the response of an isotropic spherical shell to an acoustic mode of the fluid enclosed by the shell. The results are used to calculate the shifts of the acoustic resonance frequencies from the values which correspond to perfectly rigid shell walls. Acoustic modes with pressure proportional to Ynm (θ, φ) excite shell vibrations with the radial displacement also proportional to Ynm. The shell response depends upon the mode index n, the ratio of the shell diameters, Poisson’s ratio for the shell material, and a dimensionless frequency parameter. Numerical results for a useful range of acoustic frequencies are presented for radial (n=0) modes and for nonradial modes with mode indices n between 1 and 3. Numerical calculations of the shell resonance frequencies are presented for a wide range of shell thicknesses.

Splice sleeve for reinforcing bars with cylindrical shell

Abstract: A splice sleeve for receiving and connecting adjoining ends of a pair of reinforcing bars or rods in which the sleeve includes a rigid shell having a cylindrical external surface and an internal surface with ridges constructed to provide a wedging action and compression of grouting introduced into the shell In one embodiment, the shell includes an internal surface which tapers inwardly toward the ends of the shell In another embodiment, the shell has a cylindrical internal surface with ridges which increase in height from the centermost ridges to the outer ridges In a further embodiment, the shell has a cylindrical external and internal surface for approximately one-half of its length with the other half of its length being smoothly tapered and provided with external longitudinal flanges and both end portions of the shell have internal ridges with the ridges in the cylindrical portion progressively increasing in radial extent from the inner ridge to the outer ridge and the ridges in the tapering portion of the shell being of constant radial extent In a still further embodiment, the shell is substantially cylindrical throughout it length with only one tip end portion of the shell being sharply tapered inwardly with the wall thickness of the shell being constant and the ridges being constructed to provide a wedging and compression action at each end of the sleeve

Axisymmetrical vibrations of tanks-numerical

Abstract: With few exceptions, current seismic design codes for ground‐based cylindrical tanks neglect the effect of vertical ground acceleration. Such motion can be transmitted, in a flexible tank, into radial pulsations of the tank wall resulting in additional stresses. A numerical study of the axisymmetrical dynamic characteristics of partly‐filled tanks is carried out. Natural frequencies and mode shapes are evaluated by means of a discretization scheme in which the shell is modeled by finite elements and the liquid region is treated analytically. The distribution of the hydrodynamic pressure along the inner surface of the shell as well as the distribution of shell stresses are displayed. For practical applications, a simplified formula is developed to calculate the fundamental natural frequency of full tanks.

High refractive index haloalkyl-functional shell-core polymers and their use in light scattering immunoassays

Abstract: Novel particle reagent for light scattering immunoassays are provided. The particle reagents are high refractive index shell-core polymers, having at least a partial surface coverage by a monomolecular layer of anionic surfactant, covalently bonded to compounds of biological interest. The novel particle reagents are particularly suited to protein immobilization by covalent bonding to the shell and are especially useful for light scattering immunoassays.

Axisymmetrical Vibrations, of Tanks—Analytical

Abstract: An analytical method for the computation of the axisymmetrical dynamic characteristics of partly-filled cylindrical tanks is presented. The liquid is assumed to be inviscid and incompressible. The tank shell is assumed to be of constant thickness and its material to be linearly elastic. Under these assumptions, two coupled partial differential equations govern the vibrations of the shell. Because the tank is partly-filled with liquid, two different solutions are obtained for the lower (wet) and upper (dry) portions of the shell. A system of linear homogeneous algebraic equations is obtained by satisfying the boundary conditions at the bottom and top of the tank and the compatibility equations at the junction of the wet and dry parts of the shell. The determinant of coefficients of this system leads to the frequency equation. The natural frequencies, mode shapes and stress distributions showed excellent agreement with those obtained from a numerical solution.

Protective helmet and locking means

Abstract: A protective helmet (10) characterized in that it comprises a shell (12) shaped to fit about the head of a wearer, the shell (12) comprising an interior and an exterior, a forward region (14) intended in use to be situated adjacent a forehead of the wearer and a rearward region (22) situated at an opposite end of the shell (12) from the forward region (14), and the shell (12) also comprising a basal perimeter, a resilient liner (50) comprising an inner concave side arranged, in use, adjacent the head of the wearer, and an outer convex side adjacent the interior of the shell (12) one or more securing straps (34) attached to the basal perimeter and a locking means (80) to, in use, lockably secure each strap (34), the resilient liner (50) being formed by a shaping process so that a plurality of discrete chambers (58) is located within the liner (50) or between the resilient liner (50) and the shell (12), the resilient liner (50) and the chambers (58) being intended, in use, to absorb mechanical shock imparted to the shell (12) by providing pneumatic and mechanical resistance thereto.

Nonlinear dynamic analysis with a 48 d.o.f. curved thin shell element

Abstract: The developments of an existing 48 degrees-of-freedom (d.o.f.), curved, quadrilateral, thin shell element, for materially and geometrically nonlinear static analysis of shell structures, are extended for the study of dynamic responses of nonlinear shells. The variable-order polynomial representations of the shell surface and the non-axisymmetric definition of the shell boundaries allow the study of the dynamic behaviour of a class of shell structures more general than those treated by using flat plate elements and elements with assumptions of axisymmetry. The equations of motion are based on a Lagrangian frame of reference. A combination of step-by-step and iterative procedures is used for the solution of nonlinear equations. The incremental equations of motion are linearized for computation purposes, and an algorithm for numerical integration based on Newmark's generalized operator for dynamic analysis, using optional iteration, is adopted. The flow theory of plasticity is used in the inelastic range, and perfectly plastic or isotropic strain hardening materials are considered. The spread of plastic zones in the thickness direction is treated by using a layered model. Numerical examples presented include the dynamic analyses of a square plate, a circular annulus, a cylindrical panel and a spherical cap. Comparisons with existing solutions demonstrate the validity and accuracy of the present developments.

Instability of Thin Walled Bars

Abstract: Instability of thin walled bars of variable, open cross sections is analyzed. A thin walled bar is treated as a special case of the membrane shell with the internal constraints (Vlasov’s and Wagner’s assumptions). The geometry of the bar is described by means of coordinates of the discrete points located on the midsurface of the bar. Principal coordinate system is assumed for the cross section. Large deformations of the cross section are analyzed in total Lagrangian formulation. Prebuckling strains are assumed to be small and the Green-Lagrange linearized tensor is used in strain analysis. The general, nonlinear formula for the strain tensor element ge\N\d2\d2 is obtained for the thin walled bars of variable, open cross sections. Special cases derived from this formula are in agreement with already known solutions. Numerical results are obtained by the use of the finite element approach. Stiffness and geometric matrices are constructed for a thin walled, variable element. Typical shape functions are used and a bifurcation point of stability is determined with the help of the eigenproblem solution.

An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 2: Applications

Abstract: In an accompanying paper an extended shakedown theory was described for structures subjected to constant mechanical loads and cyclically varying thermal loads, a circumstance of interest in Fast Reactor design. In this paper the upper bound theorem is used to construct interactive diagrams for a sequence of sample problems. These examples imply that for many shell problems, where the temperature variations occur along the surface, ratchetting occurs in two distinct ways. For low thermal loading the structure deforms in the same mechanism that occurs at plastic collapse when only the mechanical loads are applied. For high levels of thermal loading the mechanism changes to a local concentration of strain. This behavior differs significantly from that of the Bree problem. In one example this mechanism involves through-thickness shear deformation of a plate; as a consequence the use of thin shell theory which ignores shear deformation in numerical solutions of problems of this type is likely to result in nonconservative estimates of inelastic deformations.

Large amplitude free vibrations of shallow spherical shell and cylindrical shell — A new approach

Abstract: In this paper, large amplitude free vibrations of thin elastic shallow spherical and cylindrical shells have been investigated following a new approach. Numerical results for movable as well as immovable edge conditions have been presented graphically and compared with other known results.