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At least 271 records · Page 15

Theoretical Elastic Stress Distributions Arising from Discontinuities and Edge Loads in Several Shell-Type Structures

The deformation and complete stress distribution are determined for each of the following edge loaded thin shells of revolution: (1) a right circular cylinder, (2) a frustum of a right circular cone, and (3) a portion of a sphere. The locations of the maximum circumferential and meridional stresses on both the inner and outer surfaces are also found. The basic equations for the above were selected from the published literature on the subject and expanded to produce to resultant-stress equations in closed from where practicable to do so. Equations are also developed for the discontinuity shear force and bending moment at each of the following junction: (1) axial change of thickness in a circular cylinder, (2) axial change of thickness in a cone, (3) change of thickness in a portion of a sphere, (4) a cylinder and a cone, (5) a cylinder and a portion of a sphere(6) a cylinder and a flat head, and (7) a cone and a portion of a sphere.

Johns, Robert H.↗

Fracture and Stress Evolution on Europa: New Insights Into Fracture Interpretation and Ice Thickness Estimates Using Fracture Mechanics Analyses

The work completed during the funding period has provided many important insights into fracturing behavior in Europa's ice shell. It has been determined that fracturing through time is likely to have been controlled by the effects of nonsynchronous rotation stresses and that as much as 720 deg of said rotation may have occurred during the visible geologic history. It has been determined that there are at least two distinct styles of strike-slip faulting and that their mutual evolutionary styles are likely to have been different, with one involving a significant dilational component during shear motion. It has been determined that secondary fracturing in perturbed stress fields adjacent to older structures such as faults is a prevalent process on Europa. It has been determined that cycloidal ridges are likely to experience shear stresses along the existing segment portions as they propagate, which affects propagation direction and ultimately induces tailcracking at the segment tip than then initiates a new cycle of cycloid segment growth. Finally, it has been established that mechanical methods (e.g., flexure analysis) can be used to determine the elastic thickness of the ice shell, which, although probably only several km thick, is likely to be spatially variable, being thinner under bands but thicker under ridged plains terrain.

Kattenhorn, Simon↗

Radiative lifetimes of zincblende CdSe/CdS quantum dots

Recent synthetic advances have made available very monodisperse zincblende CdSe/CdS quantum dots having near-unity photoluminescence quantum yields. Because of the absence of nonradiative decay pathways, accurate values of the radiative lifetimes can be obtained from time-resolved PL measurements. Radiative lifetimes can also be obtained from the Einstein relations, using the static absorption spectra and the relative thermal populations in the angular momentum sublevels. We found that one of the inputs into these calculations is the shell thickness, and it is useful to be able to determine shell thickness from spectroscopic measurements. We use an empirically corrected effective mass model to produce a “map” of exciton wavelength as a function of core size and shell thickness. These calculations use an elastic continuum model and the known lattice and elastic constants to include the effect of lattice strain on the band gap energy. The map is in agreement with the known CdSe sizing curve and with the shell thicknesses of zincblende core/shell particles obtained from TEM images. Furthermore, if selenium–sulfur diffusion is included and lattice strain is omitted from the calculation then the resulting map is appropriate for wurtzite CdSe/CdS quantum dots synthesized at high temperatures, and this map is very similar to one previously reported (J. Am. Chem. Soc. 2009, 131, 14299). Radiative lifetimes determined from time-resolved measurements are compared to values obtained from the Einstein relations, and found to be in excellent agreement. For a specific core size (2.64 nm diameter, in the present case), radiative lifetimes are found to decrease with increasing shell thickness. Thus, this is similar to the size dependence of one-component CdSe quantum dots and in contrast to the size dependence in type-II quantum dots.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Intermediate energy proton-deuteron elastic scattering

A fully symmetrized multiple scattering series is considered for the description of proton-deuteron elastic scattering. An off-shell continuation of the experimentally known twobody amplitudes that retains the exchange symmeteries required for the calculation is presented. The one boson exchange terms of the two body amplitudes are evaluated exactly in this off-shell prescription. The first two terms of the multiple scattering series are calculated explicitly whereas multiple scattering effects are obtained as minimum variance estimates from the 146-MeV data of Postma and Wilson. The multiple scattering corrections indeed consist of low order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

Wilson, J. W.↗

Gas-driven water volcanism in the resurfacing of Europa

The creation of pathways for resurfacing of water or volatiles in a model of Europa in which an ocean underlies a thin ice shell is subjected to linear elastic fracture mechanical treatment. The gas-filled portion of the upward-propagating cracks pinches off from the water-filled portion, and may rapidly rise to the surface. The eruption thus generated is at first dominated by gas, but may subsequently include a less extended foam eruption; there may be no direct relationship between this resurfacing phenomenon and the geological features thus far noted on the Europa surface.

Crawford, Glen D.↗

Non-Newtonian Convection and Compositional Buoyancy: Advances in Modeling Convection and Dome Formation on Europa

Numerical modeling of non-Newtonian convection in ice shows that convection controlled by grain boundary sliding rheology may occur in Europa. This modeling confirms that thermal convection alone cannot produce significant dome elevations. Domes may instead be produced by diapirs initiated by thermal convection that in turn induces compositional segregation. Exclusion of impurities from warm upwellings would allow sufficient buoyancy for icy plumes to account for the observed approximately 100 m topography of domes, provided the ice shell has a small effective elastic thickness (approximately 0.2 to 0.5 km) and contains low eutectic-point impurities at the few percent level.

Pappalardo, R. T.↗

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Noor, A. K.↗

On the motion of a flexible shallow spherical shell in orbit

A mathematical model for the motion of a large, flexible shallow spherical shell in a circular orbit is presented. For small elastic displacements and attitude angles the linearized equations for the roll and yaw (out-of-plane) motions completely separate from the pitch (in-plane) and elastic motions. However, the pitch and only the axisymmetric elastic modes are seen to be coupled in the linear range. With the shell's symmetry axis following the local vertical, the structure undergoes a static deformation under the influence of gravity and inertia. Further, the pitch and roll motions are unstable due to the unfavorable moment of inertia distribution. A rigid lightweight dumbbell with heavy tip masses and connected to the shell at its apex by a spring loaded double gimbal joint is proposed to gravitationally stabilize the structure. It is noted that the dumbbell motion can excite only those elastic modes having one nodal diameter. A sensitivity study of the system response characteristics to the key system parameters is carried out.

Kumar, V. K.↗

A micromechanics-based progressive failure model for laminated composite structures

A micromechanics-based mechanistic model for progressive failure analysis of laminated composite shell structures is developed. A finite-element program for laminated shell analysis is coupled with a micromechanical elasticity solution for predicting failure and effective composite properties. The laminate model is based on a third-order shell theory which allows for both transverse normal and shearing deformations. Results are presented for the progressive failure of a (0/90(4)s graphite/epoxy laminate under uniaxial tension. The effect of fiber volume fraction in the 90-deg plies on laminate behavior was studied, and it was found that decreasing the fiber-volume fraction in the off-axis plies did not affect the laminate stiffness or the ultimate failure load, but significantly increased the load at which initial failure occurred.

Averill, R. C.↗

Parameter identification of material constants in a composite shell structure

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Martinez, David R.↗

The dynamic sphere test problem

In this manuscript we define the dynamic sphere problem as a spherical shell composed of a homogeneous, linearly elastic material. The material exhibits either isotropic or transverse isotropic symmetry. When the problem is formulated in material coordinates, the balance of mass equation is satisfied automatically. Also, the material is assumed to be kept at constant temperature, so the only relevant equation is the equation of motion. The shell has inner radius r i and outer radius r o . Initially, the shell is at rest. We assume that the interior of the shell is a void and we apply a time-varying radial stress on the outer surface.

97 MATHEMATICS AND COMPUTING↗

ELASTIC STABILITY CONSIDERATIONS IN AIRCRAFT STRUCTURAL DESIGN

General instability in shell type structures is a relatively infrequent phenomenon. By general instability is meant that a complete section of a structure becomes elastically unstable, as compared with local crippling or buckling. The first step in design is to rough size the structure and determine its compatibility with air vehicle configuration and system instillations. After this step has been completed, it is possible to survey the layouts to determine whether general instability is likely to occur. The general parameters of length, diameter, frame spacing, element stiffness, etc., are than investigated to determine if a general failing stress exists which is less than any local column, beam column, or panel failing stress. In this way, a well-balanced design is determined and general stability failing modes eliminated.

ELASTIC STABILITY↗

An X-ray and Neutron Scattering Study of the Formation of Core-Shell Type Polyoxometalates

A typical type of core-shell polyoxometalates can be obtained through the Keggin-type polyoxometalatetemplated growth of a layer of spherical shell structure of {Mo72Fe30}. Small angle X-ray scattering is used to study the structural features and stability of the core-shell structures in aqueous solutions. Timeresolved small angle X-ray scattering is applied to monitor the synthetic reactions and a three-stage formation mechanism is proposed to describe the synthesis of the core-shell polyoxometalates based on the monitoring results. New protocols have been developed by fitting the X-ray data with customed physical models, which provide more convincing, objective, and completed data interpretation. Quasielastic and inelastic neutron scattering are used to probe the dynamics of water molecules in the core-shell structures and two different types of water molecules, the confined and structured water, are observed. These water molecules play an important role in bridging core and shell structures and stabilizing the cluster structures.

Yin, Panchao↗