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The monocoque form of airplane construction has introduced a number of new problems to the stress calculator and the designer. The problems for the stress calculator fall into two groups: the determination of the stress condition (shell statics) and the determination of the failing strength (shell strength). The present report summarizes the most important theoretical and experimental results on this subject.
This report treats the stress distribution in shell-shaped airplane components (fuselage, wings) as an equilibrium problem; it includes both cylindrical and non-cylindrical shells. In particular, it treats the stress distribution at the point of stress application and at cut-out points.
A mixed method of approximation based on Reissner's variational principle is developed for the linear analysis of interlaminar stresses in laminated composites, with special interest in laminates that contain terminated internal plies (dropped-ply laminates). Two models are derived, one for problems of generalized plane deformation and the other for the axisymmetric response of shells of revolution. A layerwise approach is taken in which the stress field is assumed with an explicit dependence on the thickness coordinate in each layer. The dependence of the stress field on the thickness coordinate is determined such that the three-dimensional equilibrium equations are satisfied by the approximation. The solution domain is reduced to one dimension by integration through the thickness. Continuity of tractions and displacements between layers is imposed. The governing two-point boundary value problem is composed of a system of both differential and algebraic equations (DAE's) and their associated boundary conditions. Careful evaluation of the system of DAE's was required to arrive at a form that allowed application of a one-step finite difference approximation. A two-stage Gauss implicit Runge-Kutta finite difference scheme was used for the solution because of its relatively high degree of accuracy. Patch tests of the two models revealed problems with solution accuracy for the axisymmetric model of a cylindrical shell loaded by internal pressure. Parametric studies of dropped-ply laminate characteristics and their influence on the interlaminar stresses were performed using the generalized plane deformation model. Eccentricity of the middle surface of the laminate through the ply drop-off was found to have a minimal effect on the interlaminar stresses under longitudinal compression, transverse tension, and in-plane shear. A second study found the stiffness change across the ply termination to have a much greater influence on the interlaminar stresses.
Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can be entirely avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom and the significant time savings achieved is demonstrated through an example.
We present high resolution HIRAS 60 and 100 micron images of AGB stars surrounded by fossil dust shells. Resolving the extended emission of the circumstellar dust allows a determination of the mass loss history of the star. We show that the geometry of the 60 micron emission surrounding HR 3126 agrees well with that of the optical reflection nebula. The emission around the carbon star U Hya is resolved into a central point source and a ring of dust, and the mass loss rate in the detached shell is 70 times higher than the current mass loss rate.
Analytic three-dimensional thermoelasticity solutions are presented for static problems of simply supported sandwich panels and cylindrical shells subjected to mechanical and thermal loads. The panels and shells have laminated composite face sheets of arbitrary thickness separated by a core. Each of the individual layers of the face sheets and the core is modeled as a three-dimensional continuum. Analytic first-order sensitivity coefficients are evaluated to assess the sensitivity of the responses to variations in material parameters of the face sheets and the core, as well as to variations in the curvatures and thicknesses of the sandwich and face sheets. Also, the strain energy associated with various stress components in the face sheets and core are calculated and compared. The information obtained in the present study can aid the development and assessment of two-dimensional models for sandwich structures and illuminate the role of particular material parameters in an equivalent model for the core.
A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric response of viscoplastic shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. Spatial discretization is performed using finite elements, with discontinuous stress resultants across element interfaces. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) with an implicit constitutive update. The sensitivity coefficients are evaluated using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading, and a circular plate subjected to impulsive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to thickness, mass density, Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients are presented, along with spatial distributions of these quantities at selected times.
The supernova remnant 0540-69.3 in the Large Magellanic Cloud has been observed with the Roentgen Satellite (ROSAT) HRI detector. The outer shell was resolved from the bright central region and its X-ray morphology and luminosity determined. One-quarter of the soft X-rays originate in this shell. This result and a simple blast-wave model imply that the energy release in the supernova was about 2 x 10(exp 51) ergs.
With new hydrodynamic techniques, the relatively fast evolutionary stages of a star prior to core collapse may be explicitly computed in two spatial dimensions, with a treatment of the microphysics (e.g., nuclear reactions, equation of state, neutrino cooling) which is comparable to typical one-dimensional simulations. The nature of shell oxygen burning in a massive star, prior to core collapse, is used as a first example; it is of particular interest because it is (1) the region in which Ni-56 will be produced by the supernova shock, (2) the region of the 'mass cut', which will separate the collapsed core from the ejected mantle, (3) the site of much of the explosive nucleosynthesis, and (4) a suggested source of symmetry breaking to drive mixing instabilities which were observed in SN 1987A. The nature of the shell burning affects the size of the core which will collapse. The method is illustrated on this test case, and the character of the convection is examined.
We have used a 20-channel bolometer array on NASA's Kuiper Airborne Observatory to obtain photometry and size information for several main sequence stars surrounded by dust shells. The observations were made at 50 and/or 100 micrometers on flights based in Christchurch, New Zealand, in 1992, 1993. The stars include the 'Vega-like' star, Beta Pic, as well as two stars, HD 135344 and HD 139614, suggested by subsequent studies to belong possibly to the same class. The results of our observations are best interpreted as upper limits to the far-infrared sizes of the dust clouds around these stars. In addition to the basic size and flux measurements, we have fit simple, optically thin models to the Beta Pic data to explore the range of shell parameters consistent with our limits and with previous observations.
Graphite/epoxy composite thin shell structures were simulated to investigate damage and fracture progression due to internal pressure and axial loading. Defective and defect-free structures (thin cylinders) were examined. The three different laminates examined had fiber orientations of (90/0/+/-0)(sub s), where 0 is 45, 60, and 75 deg. CODSTRAN, an integrated computer code that scales up constituent level properties to the structural level and accounts for all possible failure modes, was used to simulate composite degradation under loading. Damage initiation, growth, accumulation, and propagation to fracture were included in the simulation. Burst pressures for defective and defect-free shells were compared to evaluate damage tolerance. The results showed that damage initiation began with matrix failure whereas damage and/or fracture progression occurred as a result of additional matrix failure and fiber fracture. In both thin cylinder cases examined (defective and defect-free), the optimum layup configuration was (90/0/+/-60)(sub s) because it had the best damage tolerance with respect to the burst pressure.
The Composite Armored Vehicle (CAV) is an advanced technology demonstrator of an all-composite ground combat vehicle. The CAV upper hull is made of a tough light-weight S2-glass/epoxy laminate with embedded ceramic tiles that serve as armor. The tiles are bonded to a rubber mat with a carefully selected, highly viscoelastic adhesive. The integration of armor and structure offers an efficient combination of ballistic protection and structural performance. The analysis of this anisotropic construction, with its inherent discontinuous and periodic nature, however, poses several challenges. The present paper describes a shell-based 'element-layering' technique that properly accounts for these effects and for the concentrated transverse shear flexibility in the rubber mat. One of the most important advantages of the element-layering technique over advanced higher-order elements is that it is based on conventional elements. This advantage allows the models to be portable to other structural analysis codes, a prerequisite in a program that involves the computational facilities of several manufacturers and government laboratories. The element-layering technique was implemented into an auto-layering program that automatically transforms a conventional shell model into a multi-layered model. The effects of tile layer homogenization, tile placement patterns, and tile gap size on the analysis results are described.
Silicon carbide (SiC) is known to form in circumstellar shells around carbon stars. SiC can come in two basic types - hexagonal alpha-SiC or cubic beta-SiC. Laboratory studies have shown that both types of SiC exhibit an emission feature in the 11-11.5 micron region, the size and shape of the feature varying with type, size and shape of the SiC grains. Such a feature can be seen in the spectra of carbon stars. Silicon carbide grains have also been found in meteorites. The aim of the current work is to identity the type(s) of SiC found in circumstellar shells and how they might relate to meteoritic SiC samples. We have used the CGS3 spectrometer at the 3.8 m UKIRT to obtain 7.5-13.5 micron spectra of 31 definite or proposed carbon stars. After flux-calibration, each spectrum was fitted using a chi(exp 2)-minimisation routine equipped with the published laboratory optical constants of six different samples of small SiC particles, together with the ability to fit the underlying continuum using a range of grain emissivity laws. It was found that the majority of observed SiC emission features could only be fitted by alpha-SiC grains. The lack of beta-SiC is surprising, as this is the form most commonly found in meteorites. Included in the sample were four sources, all of which have been proposed to be carbon stars, that appear to show the SiC feature in absorption.
We present results from an ongoing effort to classify the infrared spectra produced by circumstellar dust shells. Earlier efforts concentrated on oxygen-rich dust shells from sources associated with the asymptotic giant branch (AGB). Here, we describe the expansion of our classification to include S stars, supergiants, and carbon stars.
A model-based Linear Quadratic Regulator (LQR) method for controlling vibrations in cylindrical shells is presented. Surface-mounted piezo-ceramic patches are employed as actuators which leads to unbounded control input operators. Modified Donnell-Mushtari shell equations incorporating strong or Kelvin-Voigt damping are used to model the system. The model is then abstractly formulated in terms of sesquilinear forms. This provides a framework amenable for proving model well-posedness and convergence of LQR gains using analytic semigroup results combined with LQR theory for unbounded input operators. Finally, numerical examples demonstrating the effectiveness of the method are presented.
The mosaics of pointed Rosat Position Sensitive Proportional Counter (PSPC) observations of the Large Magellanic Cloud (LMC) were used to study the X-ray characteristics of supergiant shells. Diffuse soft X-ray emission above the background was detected in all of the well-defined supergiant shells. The large range of X-ray properties can be explained by differential obscuration, temperature density differences, and localized heating by supernova remnants.
A PDE-based feedback control method for thin cylindrical shells with surface-mounted piezoceramic actuators is presented. Donnell-Mushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The well-posedness of this model and the associated LQR problem with an unbounded input operator are established through analytic semigroup theory. The model is discretized using a Galerkin expansion with basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The effectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples.
An answer is sought to the question of today, in 1997, after so many years of concentrated research effort in designing buckling critical thin walled shells, why one cannot do any better than using the rather conservative Lower Bound Design Philosophy of the sixties. It will be shown that with the establishment of Initial Imperfection Data Banks and the introduction of Probabilistic Design Procedures one has a viable alternative, that when used judiciously, may lead to improved shell design recommendations.