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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.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Damage growth in composite laminates with interleaves

The influence of placing interleaves between fiber reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as two dimensional, isotropic, linearly elastic media made of a damaged layer bonded between two half planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface and may extend up to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. The interleaves are modeled as distributed shear and tension springs. Fourier integral transform techniques are used to develop solutions in terms of singular integral equations. An asymptotic analysis of the integral equations based on Muskhelishvili's techniques reveals logarithmically singular axial stresses in the half plane at the crack tips for the broken layer. For the H shaped crack, similar singularities are found to exist in the axial stresses at the interface crack tips in the layer and the half plane. The solution of the equations is found numerically for the stresses and displacements by using the Hadamard's concept of direct differentiation of Cauchy integrals as well as Gaussian integration techniques.

Goree, James G.↗
NASA NTRS1987

Viscous damping of Alfven normal modes in non-uniform plasmas

The Alfven normal mode in a nonuniform, viscous plasma is investigated. Because the ideal hydromagnetic equation is singular in a nonuniform magnetic field, viscosity is included in order to regularize the equation, analogous to the removal of the singular point by resistivity (Mok and Einaudi, 1985). The eigenvalue equation is then solved numerically for a particular magnetic configuration. The real part of the frequency of this viscous normal mode is found to be similar to the one in the resistive case, while the damping is shown to be comparable, and sometimes to exceed, the resistive effect under certain conditions in which the Lundquist number is sufficiently large. The damping rate is evaluated for various plasma conditions corresponding to different parts of the solar atmosphere. The effects of viscosity are found to dominate resistivity in the quiet sun corona and solar wind.

Mok, Y.↗
NASA NTRS1977

Stress-intensity factors for a wedge-loaded edge crack in a semi-infinite strip

The problem of a semi infinite strip containing an edge crack is considered. It is assumed that the strip is loaded by a frictionless rigid wedge pressed into the crack. The resulting crack contact problem is formulated in terms of a system of singular integral equations. The behavior of the solution near the singular points is studied in detail. A series of numerical examples are given and the results are compared with those obtained by the method of boundary collocation and by the simple beam theory.

Erodogan, F.↗
NASA NTRS1978

Wedge loading of a semi-infinite strip with an edge crack

The problem of a semi-infinite strip containing an edge crack is considered. It is assumed that the strip is loaded by a frictionless rigid wedge pressed into the crack. The resulting crack-contact problem is formulated in terms of a system of singular integral equations. The behavior of the solution near the singular points is studied in detail. A series of numerical examples is given and the results are compared with those obtained by the method of boundary collocation and by the simple beam theory.

Erdogan, F.↗
NASA NTRS1977

Derivation of an integral equation for transonic flows

It is noted that the nonlinear partial differential equation for the perturbation velocity potential and boundary conditions describing steady inviscid compressible transonic flow past a thin two-dimensional airfoil can be transformed into a singular integrodifferential equation and that differentiation of the latter yields an integral equation. Two forms of this integral equation currently exist: one for the singularity that is enclosed in an infinitely long strip of vanishing thickness and the other for the singularity that is enclosed in a vanishing circle. In the present article, a more general integral equation is derived by enclosing the singularity in a vanishing rectangular cavity of arbitrary aspect ratio. The two existing forms of this equation are deduced as special cases distinguished by the respective values for the aspect ratio (infinity for the first form and unity for the second).

Ogana, W.↗
DOE OSTI2024

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2005

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

Ambur, Damodar R.↗
NASA NTRS1976

Nonlinear motion analysis of flexible satellites

The article reviews research on pointing accuracies of flexible satellites with regard to derived equations of motion of individual elements and composite bodies. The solution of these equations may be achieved through the formulation of a set of singularly perturbed equations by eliminating the generalized position vector. These equations are generally solved by a method of asymptotic expansions if certain convergence criteria are satisfied. The analysis may be applied to dual-spin flexible satellites.

Huang, T. C.↗
DOE OSTI2020

Characterization and integration of the singular test integrals in the method-of-moments implementation of the electric-field integral equation

In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green’s function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. In this work, we demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.

42 ENGINEERING↗
NASA NTRS1987

On the solution of integral equations with a generalized Cauchy kernel

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Kaya, A. C.↗
NASA NTRS1974

Contact and crack problems for an elastic wedge

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Erdogan, F.↗
NASA NTRS1973

The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary

Development of a complete theory of the two-dimensional Dirichlet problem for an open boundary. It is shown that the solution of the Dirichlet problem for an open boundary requires the solution of a Fredholm integral equation of the first kind. Although a Fredholm integral equation of the first kind usually has no solution if the kernel is continuous, owing to the logarithmic singularity of the kernel, the equation in this case is converted to a singular integral equation with a Cauchy kernel. It is proven that the homogeneous adjoint equation of the singular integral equation has no nonzero solution. By virtue of this result, and with the aid of an existence theorem known in the theory of singular integral equations, the existence of solutions of the singular integral equation, and then of the unique solution of the Fredholm integral equation of the first kind is proved.

Hayashi, Y.↗
NASA NTRS2001

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Constantinescu, George S.↗
NASA NTRS1996

Singularity Preserving Numerical Methods for Boundary Integral Equations

In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

Kaneko, Hideaki↗