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In this paper, we expand the previous theory to be applied to a generic drop size distribution with spheroidal raindrops including spherical raindrops. Results will be used to discuss the multiple scattering effects on the backscatter measurements acquired by a W-band nadir-pointing radar.
To understand better the effect of shape and size of lung and chest wall on the distribution of stresses, strains, and surface pressures, we analyzed a theoretical model using the technique of finite elements. First we investigated the effects of changing the chest wall shape during expansion, and second we studied lungs of a variety of inherent shapes and sizes. We found that, in general, the distributions of alveolar size, mechanical stresses, and surface pressures in the lungs were dominated by the weight of the lung and that changing the shape of the lung or chest wall had relatively little effect. Only at high states of expansion where the lung was very stiff did changing the shape of the chest wall cause substantial changes. Altering the inherent shape of the lung generally had little effect but the topographical differences in stresses and surface pressures were approximately proportional to lung height. The results are generally consistent with those found in the dog by Hoppin et al (1969).
The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.
Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.
A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. Interlaminar stress results obtained from the global/local analyses compares well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. Specific processors used during the analyses are described in general terms. The application of this global/local technique is not limited software system, and was developed and described in as general a manner as possible.
The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.
Transmission electron microscope study of the track density gradients and irradiation geometries of track-rich grains and chondrules in sections of Fayetteville and Kapoeta, and in sections of lunar breccias and grains from lunar soil. A substantial fraction (50 to 90%) of the meteoritic track-rich grains and chondrules show evidence of having been irradiated anisotropically in their different faces, as would be expected for irradiation on the surface of a parent body. The observations thus support the hypothesis that the irradiation of these grains and chondrules took place on the regoliths of asteroidal-sized bodies. Measurements of steepest track density gradients indicate that, while there are finite differences between spectra exhibited by individual gas-rich meteorites, the average solar flare spectral shapes have been similar over the last 4 b.y. or so.
A continuing effort to develop a comprehensive capability for thermal-structural analysis and automated design (sizing) is reviewed. A principal role in the activity is played by the finite element program SPAR which contains both an efficient structural and thermal analysis capability. The benefit of having thermal and structural analyses in the same finite element program is illustrated by the application of SPAR to design calculations for the National Transonic Facility - a cryogenic wind tunnel under construction at Langley. Some experience with large-scale thermal structural analysis problems, particularly the space shuttle orbiter, has led to the identification of some analysis needs. Those needs include automated model generation and data output for lumped parameter thermal analysis, faster solution methods for nonlinear transient heat transfer, automated interpolation of temperature data from a thermal finite element model to a dissimilar structural finite model, and automated techniques to identify the times at which the critical combinations of transient heating and loads occur on a structure.
In singular perturbation problems, control of zone size variation can affect the effort required to obtain accurate, numerical solutions of finite difference equations. The mesh is generated by the solution of potential equations. Numerical results for a singular perturbation problem in two dimensions are presented. The mesh was used in calculations of resistive magnetohydrodynamic flow in two dimensions.
The latest version of the NASCAP/LEO digital computer code used to simulate the PIX 2 experiment is discussed. NASCAP is a finite-element code and previous versions were restricted to a single fixed mesh size. As a consequence the resolution was dictated by the largest physical dimension to be modeled. The latest version of NASCAP/LEO can subdivide selected regions. This permitted the modeling of the overall Delta launch vehicle in the primary computational grid at a coarse resolution, with subdivided regions at finer resolution being used to pick up the details of the experiment module configuration. Langmuir probe data from the flight were used to estimate the space plasma density and temperature and the Delta ground potential relative to the space plasma. This information is needed for input to NASCAP. Because of the uncertainty or variability in the values of these parameters, it was necessary to explore a range around the nominal value in order to determine the variation in current collection. The flight data from PIX 2 were also compared with the results of the NASCAP simulation.
Defined and justified here are the conceptual design and operation of a critical set of experiments expected to yield information on suppressants and on suppressant delivery systems under realistic spacecraft-fire conditions (smoldering). Specific experiment parameters are provided on the solid fuel (carbon), oxidants (habitable spacecraft atmospheres), fuel/oxidant supply, mixing mode, and rate (quiescent and finite; ventilated and replenishable), ignition mode, event, and reignition tendency, fire-zone size, fire conditions, lifetime, and consequences (toxicity), suppressants (CO2, H2O, N2) and suppressant delivery systems, and diagnostics. Candidate suppressants were identified after an analysis of how reduced gravity alters combustion, and how these alterations may influence the modes, mechanisms, and capacities of terrestrial agents to suppress unwanted combustion, or fire. Preferred spacecraft suppression concepts included the local, near-quiescent application of a gas, vapor, or mist that has thermophysical fire-suppression activity and is chemically inert under terrestrial (normal gravity) combustion conditions. The scale, number, and duration (about 1 hour) of the proposed low-gravity experiments were estimated using data not only on the limitations imposed by spacecraft-carrier (Shuttle or Space Station Freedom) accommodations, but also data on the details and experience of standardized smolder-suppression experiments at normal gravity. Deliberately incorporated into the conceptual design was sufficient interchangeability for the prototype experimental package to fly either on Shuttle now or Freedom later. This flexibility is provided by the design concept of up to 25 modular fuel canisters within a containment vessel, which permits both integration into existing low-gravity in-space combustion experiments and simultaneous testing of separate experiments to conserve utilities and time.
A procedure is developed analytically to design and produce an optimized stiffened panel with a centrally located hole. The PASCO panel-buckling analysis and sizing code is employed with the Engineering Analysis Language (EAL) code for finite-element analysis to optimize the design variables. Important design considerations are stiffener height and ply thicknesses in the skin and the stiffener laminates. The EAL code calculates the maximum strains around the hole boundary, and the resulting constraints are combined with the buckling constraint developed by the PASCO code. Cooptimization of the two codes is effected until convergence on the optimal solution is achieved. Results of the analytical procedure are experimentally verified by applying a compressive end-load to graphite-fiber laminated plates with center holes. The experimental results support the analytical procedure, and it is found that for the same weight, the soft-skin designs tested are found to have the best tolerance characteristics and resistance to failure.
Fracture mechanics analysis and test data for a toughened composite material that has a resin-rich interlaminar layer (RIL) were used to investigate in situ strength. Exposure to a range of environmental conditions was considered. A parametric analysis study was performed to judge the effects of laminate and material variables. A finite thickness effect, indicating an interaction between ply group thickness and effective flaw size, was found dominant. The magnitude of the effect was directly related to RIL stiffness. In situ strength was found to decrease with decreasing RIL stiffness. This work indicates the need to use a fracture mechanics model of actual lamina microstructure and heterogeneous properties to predict in situ strength in materials with RIL.
We study the potential performance of multigrid algorithms running on massively parallel computers with the intent of discovering whether presently envisioned machines will provide an efficient platform for such algorithms. We consider the domain parallel version of the standard V cycle algorithm on model problems, discretized using finite difference techniques in two and three dimensions on block structured grids of size 10(exp 6) and 10(exp 9), respectively. Our models of parallel computation were developed to reflect the computing characteristics of the current generation of massively parallel multicomputers. These models are based on an interconnection network of 256 to 16,384 message passing, 'workstation size' processors executing in an SPMD mode. The first model accomplishes interprocessor communications through a multistage permutation network. The communication cost is a logarithmic function which is similar to the costs in a variety of different topologies. The second model allows single stage communication costs only. Both models were designed with information provided by machine developers and utilize implementation derived parameters. With the medium grain parallelism of the current generation and the high fixed cost of an interprocessor communication, our analysis suggests an efficient implementation requires the machine to support the efficient transmission of long messages, (up to 1000 words) or the high initiation cost of a communication must be significantly reduced through an alternative optimization technique. Furthermore, with variable length message capability, our analysis suggests the low diameter multistage networks provide little or no advantage over a simple single stage communications network.
An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite element structural analysis and computational fluid dynamics aerodynamic analysis in a distributed, heterogeneous computing environment that includes high performance parallel computing. A software system has been designed and implemented to integrate a set of existing discipline analysis codes, some of them computationally intensive, into a distributed computational environment for the design of a highspeed civil transport configuration. The paper describes the engineering aspects of formulating the optimization by integrating these analysis codes and associated interface codes into the system. The discipline codes are integrated by using the Java programming language and a Common Object Request Broker Architecture (CORBA) compliant software product. A companion paper presents currently available results.
The understanding of single-scattering properties of complex ice crystals has significance in atmospheric radiative transfer and remote-sensing applications. In this work, light scattering by irregularly shaped Gaussian ice crystals is studied with the finite-difference time-domain (FDTD) technique. For given sample particle shapes and size parameters in the resonance region, the scattering phase matrices and asymmetry factors are calculated. It is found that the deformation of the particle surface can significantly smooth the scattering phase functions and slightly reduce the asymmetry factors. The polarization properties of irregular ice crystals are also significantly different from those of spherical cloud particles. These FDTD results could provide a reference for approximate light-scattering models developed for irregular particle shapes and can have potential applications in developing a much simpler practical light scattering model for ice clouds angular-distribution models and for remote sensing of ice clouds and aerosols using polarized light. (copyright) 2003 Elsevier Science Ltd. All rights reserved.
A multi-scale simulation concept taking into account impact of gravity on liquid phase sintering is described. The gravity influence can be included at both the micro- and macro-scales. At the micro-scale, the diffusion mass-transport is directionally modified in the framework of kinetic Monte-Carlo simulations to include the impact of gravity. The micro-scale simulations can provide the values of the constitutive parameters for macroscopic sintering simulations. At the macro-scale, we are attempting to embed a continuum model of sintering into a finite-element framework that includes the gravity forces and substrate friction. If successful, the finite elements analysis will enable predictions relevant to space-based processing, including size and shape and property predictions. Model experiments are underway to support the models via extraction of viscosity moduli versus composition, particle size, heating rate, temperature and time.
The structural weight reduction of a pressurized Hybrid Wing-Body (HWB) fuselage is a serious challenge. Hence, research and development are presently being continued at NASA under the Environmentally Responsible Aviation (ERA) and Subsonic Fixed Wing (SFW) projects in collaboration with the Boeing Company, Huntington Beach and Air Force Research Laboratory (AFRL). In this paper, a structural analysis of the HWB fuselage and bulkhead panels is presented, with the objectives of design improvement and structural weight reduction. First, orthotropic plate theories for sizing, and equivalent plate analysis with appropriate simplification are considered. Then parametric finite-element analysis of a fuselage section and bulkhead are conducted using advanced stitched composite structural concepts, which are presently being developed at Boeing for pressurized HWB flight vehicles. With this advanced stiffened-shell design, structural weights are computed and compared to the thick sandwich, vaulted-ribbed-shell, and multi-bubble stiffened-shell structural concepts that had been studied previously. The analytical and numerical results are discussed to assess the overall weight/strength advantages.