Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Integral transforms”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Theoretical Investigation of Thermo-Mechanical Behavior of Carbon Nanotube-Based Composites Using the Integral Transform Method

This project uses the integral transform technique to model the problem of nanotube behavior as an axially symmetric system of shells. Assuming that the nanotube behavior can be described by the equations of elasticity, we seek a stress function x which satisfies the biharmonic equation: del(exp 4) chi = [partial deriv(r(exp 2)) + partial deriv(r) + partial deriv(z(exp 2))] chi = 0. The method of integral transformations is used to transform the differential equation. The symmetry with respect to the z-axis indicates that we only need to consider the sine transform of the stress function: X(bar)(r,zeta) = integral(from 0 to infinity) chi(r,z)sin(zeta,z) dz.

Pawloski, Janice S.↗
DOE OSTI2024

Transformer with integral inductor

In accordance with one embodiment is a transformer with a core comprising a perimeter portion and central intervening portion. The central intervening portion is separated from the perimeter portion by air gaps, creating an opening on either side of the intervening portion. A primary winding and secondary winding are wound around the central intervening portion of the core. The primary winding is capable of electromagnetic interaction with the secondary winding. A pair of ferrite members arranged outward from a central axis of the central intervening portion of the core and increases a series inductance with the primary winding. In accordance with another aspect of the disclosure, each ferrite member may have an air gap associated with the core to facilitate heat dissipation from the transformer.

Rastogi, Sagar K.↗
NASA NTRS1974

A note on a broken layer in an orthotropic laminate composite

An orthotropic laminate composite containing a completely broken layer is considered. The problem is formulated in terms of integral transforms and then reduced to a singular integral equation which is solved numerically. The strength of stress singularity at the crack tip is determined from a characteristic equation which is obtained by studying the dominant part of the singular integral equation near the end points. The stress intensity factors are given for various material properties.

Arin, K.↗
NASA NTRS1977

A note on a broken layer in an orthotropic laminate composite

An orthotropic laminate composite containing a completely broken layer is considered. The problem is formulated in terms of integral transforms and then reduced to a singular integral equation which is solved numerically. The strength of stress singularity at the crack tip is determined from a characteristic equation which is obtained by studying the dominant part of the singular integral equation near the end points. The stress intensity factors are given for various material properties.

Arin, K.↗
NASA NTRS2003

The Filtered Abel Transform and Its Application in Combustion Diagnostics

Many non-intrusive combustion diagnosis methods generate line-of-sight projections of a flame field. To reconstruct the spatial field of the measured properties, these projections need to be deconvoluted. When the spatial field is axisymmetric, commonly used deconvolution method include the Abel transforms, the onion peeling method and the two-dimensional Fourier transform method and its derivatives such as the filtered back projection methods. This paper proposes a new approach for performing the Abel transform method is developed, which possesses the exactness of the Abel transform and the flexibility of incorporating various filters in the reconstruction process. The Abel transform is an exact method and the simplest among these commonly used methods. It is evinced in this paper that all the exact reconstruction methods for axisymmetric distributions must be equivalent to the Abel transform because of its uniqueness and exactness. Detailed proof is presented to show that the two dimensional Fourier methods when applied to axisymmetric cases is identical to the Abel transform. Discrepancies among various reconstruction method stem from the different approximations made to perform numerical calculations. An equation relating the spectrum of a set of projection date to that of the corresponding spatial distribution is obtained, which shows that the spectrum of the projection is equal to the Abel transform of the spectrum of the corresponding spatial distribution. From the equation, if either the projection or the distribution is bandwidth limited, the other is also bandwidth limited, and both have the same bandwidth. If the two are not bandwidth limited, the Abel transform has a bias against low wave number components in most practical cases. This explains why the Abel transform and all exact deconvolution methods are sensitive to high wave number noises. The filtered Abel transform is based on the fact that the Abel transform of filtered projection data is equal to an integral transform of the original projection data with the kernel function being the Abel transform of the filtering function. The kernel function is independent of the projection data and can be obtained separately when the filtering function is selected. Users can select the best filtering function for a particular set of experimental data. When the kernal function is obtained, it can be used repeatedly to a number of projection data sets (rovs) from the same experiment. When an entire flame image that contains a large number of projection lines needs to be processed, the new approach significantly reduces computational effort in comparison with the conventional approach in which each projection data set is deconvoluted separately. Computer codes have been developed to perform the filter Abel transform for an entire flame field. Measured soot volume fraction data of a jet diffusion flame are processed as an example.

Simons, Stephen N.↗
NASA NTRS1986

Algorithms versus architectures for computational chemistry

The algorithms employed are computationally intensive and, as a result, increased performance (both algorithmic and architectural) is required to improve accuracy and to treat larger molecular systems. Several benchmark quantum chemistry codes are examined on a variety of architectures. While these codes are only a small portion of a typical quantum chemistry library, they illustrate many of the computationally intensive kernels and data manipulation requirements of some applications. Furthermore, understanding the performance of the existing algorithm on present and proposed supercomputers serves as a guide for future programs and algorithm development. The algorithms investigated are: (1) a sparse symmetric matrix vector product; (2) a four index integral transformation; and (3) the calculation of diatomic two electron Slater integrals. The vectorization strategies are examined for these algorithms for both the Cyber 205 and Cray XMP. In addition, multiprocessor implementations of the algorithms are looked at on the Cray XMP and on the MIT static data flow machine proposed by DENNIS.

Partridge, H.↗