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At least 19 records

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Pandya, S. A.↗

3D Euler flow solutions using unstructured Cartesian and prismatic grids

A hyperbolic prismatic grid generation technique is combined with a background Cartesian grid for the study of inviscid three-dimensional flows. The mathematics of the hyperbolic prismatic grid generation algorithm are described, and some simple inviscid demonstration cases are presented. By combining the simplicity of the Cartesian background grid with the geometric flexibility and computational efficiencies inherent to prismatic grids, this approach shows promise for improving computational aerodynamic simulations.

Melton, John E.↗

Buckling of prismatic structures under biaxial loading

A one term analysis is presented for the elastic buckling of prismatic structures with either classical simple support or completely clamped boundary conditions on the transverse ends. Results suggest that a one term solution based on an appropriate choice of coordinate functions may lead to satisfactory buckling loads for other prismatic structures with completely clamped and other end conditions.

Ashour, H. A.↗

Global functions in global-local finite-element analysis of localized stresses in prismatic structures

An important consideration in the global local finite-element method (GLFEM) is the availability of global functions for the given problem. The role and mathematical requirements of these global functions in a GLFEM analysis of localized stress states in prismatic structures are discussed. A method is described for determining these global functions. Underlying this method are theorems due to Toupin and Knowles on strain energy decay rates, which are related to a quantitative expression of Saint-Venant's principle. It is mentioned that a mathematically complete set of global functions can be generated, so that any arbitrary interface condition between the finite element and global subregions can be represented. Convergence to the true behavior can be achieved with increasing global functions and finite-element degrees of freedom. Specific attention is devoted to mathematically two-dimensional and three-dimensional prismatic structures. Comments are offered on the GLFEM analysis of NASA flat panel with a discontinuous stiffener. Methods for determining global functions for other effects are also indicated, such as steady-state dynamics and bodies under initial stress.

Dong, Stanley B.↗

An advanced space photovoltaic concentrator array using Fresnel lenses, gallium arsenide cells, and prismatic cell covers

The current status of a space concentrator array which uses refractive optics, gallium arsenide cells, and prismatic cell covers to achieve excellent performance at a very low array mass is documented. The prismatically covered cells have established records for space cell performance (24.2 percent efficient at 100 AM0 suns and 25 C) and terrestrial single-junction cell performance (29.3 percent efficient at 200 AM1.5 suns and 25 C).

O'Neill, Mark J.↗

Simulation of patch and slot antennas using FEM with prismatic elements and investigations of artificial absorber mesh termination schemes

Year 1 progress can be characterized with four major achievements which are crucial toward the development of robust, easy to use antenna analysis code on doubly conformal platforms. (1) A new FEM code was developed using prismatic meshes. This code is based on a new edge based distorted prism and is particularly attractive for growing meshes associated with printed slot and patch antennas on doubly conformal platforms. It is anticipated that this technology will lead to interactive, simple to use codes for a large class of antenna geometries. Moreover, the codes can be expanded to include modeling of the circuit characteristics. An attached report describes the theory and validation of the new prismatic code using reference calculations and measured data collected at the NASA Langley facilities. The agreement between the measured and calculated data is impressive even for the coated patch configuration. (2) A scheme was developed for improved feed modeling in the context of FEM. A new approach based on the voltage continuity condition was devised and successfully tested in modeling coax cables and aperture fed antennas. An important aspect of this new feed modeling approach is the ability to completely separate the feed and antenna mesh regions. In this manner, different elements can be used in each of the regions leading to substantially improved accuracy and meshing simplicity. (3) A most important development this year has been the introduction of the perfectly matched interface (PMI) layer for truncating finite element meshes. So far the robust boundary integral method has been used for truncating the finite element meshes. However, this approach is not suitable for antennas on nonplanar platforms. The PMI layer is a lossy anisotropic absorber with zero reflection at its interface. (4) We were able to interface our antenna code FEMA_CYL (for antennas on cylindrical platforms) with a standard high frequency code. This interface was achieved by first generating equivalent magnetic currents across the antenna aperture using the FEM code. These currents were employed as the sources in the high frequency code.

Gong, J.↗

Use of prismatic films to control light distribution

Piping light for illumination purposes is a concept which has been around for a long time. In fact, it was the subject of an 1881 United States patent which proposed the use of mirrors inside a tube to reflect light from wall to wall down the tube. The use of conventional mirrors for this purpose, however, has not worked because mirrors do not reflect well enough. On the other hand, optical fibers composed of certain glasses or plastics are known to transport light much more efficiently. The light that enters is reflected back and forth within the walls of the fiber until it reaches the other end. This is possible by means of a principle known as 'total internal reflection'. No light escapes through the walls and very little is absorbed in the bulk of the fiber. However, while optical fibers are very efficient in transporting light, they are impractical for transporting large quantities of light. Lorne Whitehead, as a student at the University of British Columbia, recognized that prismatic materials could be used to create a 'prism light guide', a hollow structure that can efficiently transport large quantities of light. This invention is a pipe whose transparent walls are formed on the outside into precise prismatic facets. The facets are efficient total internal reflection mirrors which prevent light travelling down the guide from escaping. Very little light is absorbed by the pipe because light travels primarily in the air space within the hollow guide. And, because the guide is hollow, weight and cost factors are much more favorable than would be the case with very large solid fibers. Recent advances in precision micromachining, polymer processing, and certain other manufacturing technologies have made the development of OLF (Optical Lighting Film) possible. The process is referred to as 'microreplication' and has been found to have broad applicability in a number of diverse product areas.

Kneipp, K. G.↗

A Finite-Element Approach for Modeling Inviscid and Viscous Compressible Flows using Prismatic Grids

The Galerkin finite-element method is used to solve the Euler and Navier-Stokes equations on prismatic meshes. It is shown that the prismatic grid is advantageous for correctly and efficiently capturing the boundary layers in high Reynolds number flows. It can be captured accurately because of the ability to cluster grid points normal to the body. The efficiency derives from the implicit treatment of the normal direction. To treat the normal direction implicitly, a semi-implicit Runge-Kutta time stepping scheme is developed. The semi-implicit algorithm is validated on simple geometries for inviscid and viscous flows and its convergence history is compared to that of the explicit Runge-Kutta scheme. The semi-implicit scheme is shown to be a factor of 3 to 4 faster in terms of CPU time to convergence.

Pandya, S. A.↗

Computation of Thin-Walled Prismatic Shells

We consider a prismatic shell consisting of a finite number of narrow rectangular plates and having in the cross-section a finite number of closed contours (fig. 1(a)). We shall assume that the rectangular plates composing the shell are rigidly joined so that there is no motion of any kind of one plate relative to the others meeting at a given connecting line. The position of a point on the middle prismatic surface is considered to be defined by the coordinate z, the distance to a certain initial cross-section z = O, end the coordinate s determining its position on the contour of the cross-section.

Vlasov, V. Z.↗

Buckling and vibration of any prismatic assembly of shear and compression loaded anisotropic plates with an arbitrary supporting structure

The computer program designated 'VIPASA', which accurately treats buckling and vibration in prismatic plate assemblies with a response that varies sinusoidally in the longitudinal direction, has been found to be limited by the production of an in-plane shear loading of component plates that produces skewed mode shapes. These do not conform to desired support conditions. This problem is presently overcome through a coupling of the VIPASA stiffness matrices for different wavelength responses by means of the Lagrangian Multipliers method. The theory extends to supports at arbitrary locations, and even to the support provided by any elastic structure. The generality and capabilities of VIPASA have been retained in the computer program designated 'VICON', which permits constraints and a supporting structure consisting of any number of transverse beam columns.

Anderson, M. S.↗

Quantification of Saint-Venant's Principle for a General Prismatic Member

A semi-analytic finite element method for finding the decay rates of edge effects in anisotropic layered plates was extended to the treatment of prismatic members of an arbitrary cross section composed of any number of anisotropic elements. The displacement fields corresponding to the decay rates with positive real part were determined for a homogenous graphite/epoxy plate two units thick. The behavior of a rectangular beam is also considered.

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