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Mathematical model for predicting dynamic response of thin elastic shells of revolution during water impact
A simple toy model is used to study the spatial distribution of rich clusters in a generic type of explosion scenario. The model, parameterized by the distribution of shell radii and the filling factor, places spherical shells at random and identifies each 'knot' as a cluster. The resulting cluster correlation function is close to a power law extending to the diameter of the largest spheres. Richer clusters form at the intersections of bigger shells and so have stronger correlations. Typical shell radii and filling factors are required to produce the observed number density of clusters. Models with a power-law radius distribution also reproduce the richness distribution of clusters in the Abell catalog. Supercluster multiplicity functions, void probabilities, number counts, topology statistics, and velocity correlations confirm the presence of strong superclustering and quantify the non-Gaussian nature of the model.
With the computer program by Hofmeister, Kippenhahn, Weigert (1964, from now on referred to as ''I") the evolution of a population I star of 7.0 solar masses has been followed. The results presented here are based on a sequence of 119 models, the first of which represents the homogeneous main sequence state and has a convective core containing 26% of the mass. The following models describe the phase of depletion of hydrogen in the core, which is shrinking in mass until the convection around the centre disappears. After this the gradual development of a hydrogen burning shell source is shown. The models show the evolution into the red giant region, while the helium core is contracting until helium burning starts at the centre and a new convective core is built up. The luminousity is increased about 1 magnitude compared with the main sequence state. At the same time the outer convective region grows in mass and covers at the maximum 71% of the total mass of the star. During the evolution to the red giant state, the evolutionary track crosses the region of the cepheids. Some aspects of the corresponding models are discussed.
This study quantitatively tests the proposed model of induced nucleation of carbonaceous grains in carbon-rich red giant stars. Induced nucleation is the process of grain growth initiated by the presence of reactive surfaces provided by seed particles. The numerical study was performed using a deailed chemical kinetic model of carbon deposition, grain coagulation, and homogeneous nucleation of polycyclic aromatic hydrocarbons (PAHs). The model uses a method of moments to keep track of developing grain population in the forming dust shell. We test the efficiency of grain formation for large ranges of dust shell parameters typical for carbon stars. Our model is capable of producing a range of optically thick and thin dust shells in carbon stars. Results are in accord with (IRAS) spectral classes of carbon stars. The resulting composite grains produced are consistent with those recently found in ancient meteorites. This model also provides a realistic explanation for high abundances of (PAHs) in the interstellar medium and some planetary nebulae.
Based on geologic observations provided by Magellan's first cycle of data collection and recent models of mantle convection in spherical shells and crustal deformation, the major topographic and geologic features of Venus are incorporated into a model of global mantle dynamics. Consideration is given to volcanic rises, such as Beta Regio and Atla Regio, plateau-shaped highlands dominated by complex ridged terrain (e.g., Ovda Regio and Alpha Regio), and circular lowland regions, such as Atalanta Planitia. Each of these features is related to either mantle plumes (hotspots) or mantle downwellings (coldspots).
It is well known that real shell structures can have significantly lower buckling loads and even different mode shapes than the theoretical predictions for perfect structures. Much of this difference can be attributed to geometric and loading imperfections, and geometrically nonlinear effects. The realistic buckling response can be investigated using geometrically nonlinear finite element analyses and including radial imperfections. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of cylindrical shell structures under uniaxial compressive load. The approach for modeling several sandwich composite cylinders with two-dimensional general-purpose shell elements and the influence of the element type selection and element size on the buckling load is discussed. The influence of geometric imperfections of various magnitudes on buckling behavior of a sandwich composite cylinder was also investigated.
It is well known that manufactured shell structures can have significantly lower buckling loads and different mode shapes than the theoretical predictions for perfect structures. Much of this difference can be attributed to geometric and loading imperfections, and geometrically nonlinear effects. The buckling response of cylindrical structures can be investigated using geometrically nonlinear finite element analyses and including radial imperfections. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of cylindrical shell structures under uniaxial compressive load. The approach for modeling several sandwich composite cylinders with two-dimensional general-purpose shell elements and the influence of the element type selection and element size on the buckling load is discussed. The influence of geometric imperfections of various magnitudes on buckling behavior of a sandwich composite cylinder was also investigated.
It is well known that manufactured shell structures can have significantly lower buckling loads and different mode shapes than the theoretical predictions for perfect structures. Much of this difference can be attributed to geometric and loading imperfections, and geometrically nonlinear effects. The buckling response of cylindrical structures can be investigated using geometrically nonlinear finite element analyses and including radial imperfections. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of cylindrical shell structures under uniaxial compressive load. The approach for modeling several sandwich composite cylinders with two-dimensional general-purpose shell elements and the influence of the element type selection and element size on the buckling load is discussed. The influence of geometric imperfections of various magnitudes on buckling behavior of a sandwich composite cylinder was also investigated.
The objective of the study was to develop a more accurate model for the prediction of the compressive behavior of filament-wound composite cylindrical shells. Results from a closed-form analytical model and a three-dimensional finite element model show that the extensional and bending stiffness of the laminate is significantly reduced in tow cross-over regions and that bending-extension coupling is increased in comparison with classical lamination theory. The material properties predicted by a micromechanics analysis are included in a global finite element model of a filament-wound circular cylindrical shell which also incorporates variations in the laminate stacking thickness. Results from the global shell analysis are compared with experimental data.
A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modeled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a non-dimensional thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.
A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modelled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frames. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a 1-D thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.
A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modeled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a non-dimensional thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.
Mechanically compatible fasteners for use with thin or weakened bone sections in the human mandible are being developed to help reduce large strain discontinuities across the bone/implant interface. Materials being considered for these fasteners are a polyetherertherketone (PEEK) resin with continuous quartz or carbon fiber for the screw. The screws were designed to have a shear strength equivalent to that of compact/trabecular bone and to be used with a conventional nut, nut plate, or an expandable shank/blind nut made of a ceramic filled polymer. Physical and finite element models of the mandible were developed in order to help select the best material fastener design. The models replicate the softer inner core of trabecular bone and the hard outer shell of compact bone. The inner core of the physical model consisted of an expanding foam and the hard outer shell consisted of ceramic particles in an epoxy matrix. This model has some of the cutting and drilling attributes of bone and may be appropriate as an educational tool for surgeons and medical students. The finite element model was exercised to establish boundary conditions consistent with the stress profiles associated with mandible bite forces and muscle loads. Work is continuing to compare stress/strain profiles of a reconstructed mandible with the results from the finite element model. When optimized, these design and fastening techniques may be applicable, not only to other skeletal structures, but to any composite structure.
NASA sponsored composites research and development programs were set in place to develop the critical engineering technologies in large transport aircraft structures. This NASA-Boeing program focused on the critical issues of damage tolerance and pressure containment generic to the fuselage structure of large pressurized aircraft. Skin-stringer and honeycomb sandwich composite fuselage shell designs were evaluated to resolve these issues. Analyses were developed to model the structural response of the fuselage shell designs, and a development test program evaluated the selected design configurations to appropriate load conditions.
An overview of numerical methods describing the structure and dynamics of the mantle is presented with attention given to novel 3D modeling techniques. The paper reviews 3D spherical and Cartesian models for constant viscosity emphasizing the assumptions regarding style of convection, time dependence, and implications for the mantle. Similarly treated are 3D Cartesian models with temperature-dependent viscosities, and briefly examined are models that are based on compressibility, nonlinear viscosity, or plates. Extensive illustrations are presented detailing: (1) temperature variations from models of 3D thermal convection in spherical shells; (2) thermal anomalies in equatorial cross sections; and (3) temperature variations in a spherical shell heated from within. The discussion relates the numerical results of the models with real mantle-convection events, and the simulations are shown to yield increasingly realistic representations of material behavior.
AS&M Inc. performed finite element analysis, with and without discrete damage, of a composite semi-span test article that represents the Boeing 220-passenger transport aircraft composite semi-span test article. A NASTRAN bulk data file and drawings of the test mount fixtures and semi-span components were utilized to generate the baseline finite element model. In this model, the stringer blades are represented by shell elements, and the stringer flanges are combined with the skin. Numerous modeling modifications and discrete source damage scenarios were applied to the test article model throughout the course of the study. This report details the analysis method and results obtained from the composite semi-span study. Analyses were carried out for three load cases: Braked Roll, LOG Down-Bending and 2.5G Up-Bending. These analyses included linear and nonlinear static response, as well as linear and nonlinear buckling response. Results are presented in the form of stress and strain plots. factors of safety for failed elements, buckling loads and modes, deflection prediction tables and plots, and strainage prediction tables and plots. The collected results are presented within this report for comparison to test results.
The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric surface imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method models. Data collection methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps on how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the pre-processing methods and results from Py_TIGIRS are provided and compared for Composite Test Article (CTA) 8.2B. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future development of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.
The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method (FEM) models. Geometry measurement methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps of how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the preprocessing methods and results from Py_TIGIRS are provided and compared for Composite Test Articles (CTA) 8.2, 8.2B, and 8.3. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future developments of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.