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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Flutter and Divergence Analysis using the Generalized Aeroelastic Analysis Method

The Generalized Aeroelastic Analysis Method (GAAM) is applied to the analysis of three well-studied checkcases: restrained and unrestrained airfoil models, and a wing model. An eigenvalue iteration procedure is used for converging upon roots of the complex stability matrix. For the airfoil models, exact root loci are given which clearly illustrate the nature of the flutter and divergence instabilities. The singularities involved are enumerated, including an additional pole at the origin for the unrestrained airfoil case and the emergence of an additional pole on the positive real axis at the divergence speed for the restrained airfoil case. Inconsistencies and differences among published aeroelastic root loci and the new, exact results are discussed and resolved. The generalization of a Doublet Lattice Method computer code is described and the code is applied to the calculation of root loci for the wing model for incompressible and for subsonic flow conditions. The error introduced in the reduction of the singular integral equation underlying the unsteady lifting surface theory to a linear algebraic equation is discussed. Acknowledging this inherent error, the solutions of the algebraic equation by GAAM are termed 'exact.' The singularities of the problem are discussed and exponential series approximations used in the evaluation of the kernel function shown to introduce a dense collection of poles and zeroes on the negative real axis. Again, inconsistencies and differences among published aeroelastic root loci and the new 'exact' results are discussed and resolved. In all cases, aeroelastic flutter and divergence speeds and frequencies are in good agreement with published results. The GAAM solution procedure allows complete control over Mach number, velocity, density, and complex frequency. Thus all points on the computed root loci can be matched-point, consistent solutions without recourse to complex mode tracking logic or dataset interpolation, as in the k and p-k solution methods.

Edwards, John W.↗
NASA NTRS1984

The unified acoustic and aerodynamic prediction theory of advanced propellers in the time domain

This paper presents some numerical results for the noise of an advanced supersonic propeller based on a formulation published last year. This formulation was derived to overcome some of the practical numerical difficulties associated with other acoustic formulations. The approach is based on the Ffowcs Williams-Hawkings equation and time domain analysis is used. To illustrate the method of solution, a model problem in three dimensions and based on the Laplace equation is solved. A brief sketch of derivation of the acoustic formula is then given. Another model problem is used to verify validity of the acoustic formulation. A recent singular integral equation for aerodynamic applications derived from the acoustic formula is also presented here.

Farassat, F.↗
NASA NTRS1973

The inclusion problem with a crack crossing the boundary

The problem of an elastic plane containing an elastic inclusion is considered. It is assumed that both the plane and the inclusion contain a radial crack and the two cracks are collinear. The problem is formulated in terms of a system of singular integral equations. In the interesting limiting cases in which the crack tips approach the interface from either one or both sides, the dominant parts of the kernels become generalized Cauchy kernels giving rise to stress singularities of other than minus 1/2 power. For these unusual cases of a crack terminating at or crossing the interface stress intensity factors are defined and some detailed results are given for various crack-inclusion geometries and material combinations.

Erdogan, F.↗
NASA NTRS1983

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Long, L. N.↗
NASA NTRS1974

Fracture and contact problems for an elastic wedge

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Erdogan, F.↗
NASA NTRS1976

Fracture and contact problems for an elastic wedge

The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Erdogan, F.↗
NASA NTRS1997

Frictionless Contact of Multilayered Composite Half Planes Containing Layers With Complex Eigenvalues

A previously developed local-global stiffness matrix methodology for the response of a composite half plane, arbitrarily layered with isotropic, orthotropic or monoclinic plies, to indentation by a rigid parabolic punch is further extended to accommodate the presence of layers with complex eigenvalues (e.g., honeycomb or piezoelectric layers). First, a generalized plane deformation solution for the displacement field in an orthotropic layer or half plane characterized by complex eigenvalues is obtained using Fourier transforms. A local stiffness matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assembled into a global stiffness matrix for the entire multilayered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy-type and regular parts using the asymptotic properties of the local stiffness matrix and a relationship between Fourier and finite Hilbert transform of the contact pressure. The solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials developed by Erdogan and Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as those exhibited by honeycomb, on the load versus contact length response and contact pressure distributions for half planes containing typical composite materials.

Zhang, Wang↗
NASA NTRS1976

Fracture of composite panels

The fracture problem in panels consisting of periodically arranged load carrying and buffer strips of different materials is considered. The main emphasis is placed on the problem of a crack terminating at and crossing the interfaces and on the stress free end problem. The problem is formulated in terms of a system of singular integral equations, and numerical solutions are obtained for certain material combinations. With the study of possible crack propagation and delamination in mind, certain stress intensity factors are defined and calculated. A main result is that when the crack touches or intersects a bimaterial interface, the stress state has no longer the standard square root singularity, and, to study further propagation of the crack, the conventional fracture models need to be modified, or new models need to be developed.

Erdogan, F.↗
NASA NTRS1973

Two bonded half planes with a crack going through the interface

The plane problem of two bonded elastic half planes containing a finite crack perpendicular to and going through the interface is considered. The problem is formulated as a system of singular integral equations with generalized Cauchy kernels. Even though the system has three irregular points, it is shown that the unknown functions are algebraically related at the irregular point on the interface and the integral equations can be solved by a method developed previously. The system of integral equations is shown to yield the same characteristic equation as that for two bonded quarter planes in the general case of the through crack, and the characteristic equation for a crack tip terminating at the interface in the special case. The numerical results given in the paper include the stress intensity factors at the crack tips, the normal and shear components of the stress intensity factors at the singular point on the interface, and the crack surface displacements.

Erdogan, F.↗
NASA NTRS1971

Radiation from a parallel-plate waveguide into a dielectric or plasma layer.

An analytical solution for radiation from a truncated parallel-plate waveguide into a dielectric or plasma slab is obtained by solving the Hilbert problem associated with a certain singular integral equation. The technique has the advantage that the edge condition is easily shown to be satisfied, and numerical results can be obtained with excellent accuracy. Numerical results are presented for a variety of dielectric and plasma slabs, parallel-plate separations, and aperture-to-slab distances.

Kostelnicek, R. J.↗
NASA NTRS1972

Penny-shaped interface crack between an elastic layer and a half space.

The axially symmetric elastostatic problem for a layer bonded to a half space with different material properties is considered. It is assumed that the bi-material interface contains a penny-shaped crack the surfaces of which are subjected to known tractions. The solution of the problem is reduced to that of a system of singular integral equations of the second kind. A numerical example for an aluminum-epoxy material combination is given. The stress intensity factors and the strain energy release rate are calculated and are given as functions of layer thickness-to-crack radius ratio.

Erdogan, F.↗
NASA NTRS1972

A circumferential crack in a cylindrical shell under torsion.

The fully antisymmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.

Erdogan, F.↗
NASA NTRS1972

The inverse scattering problem at fixed angular momentum for nonlocal separable interactions

The problem of inverse scattering at fixed angular momentum is considered. The problem is particularized to the case of nonlocal separable interactions. A brief survey of the inverse problem for nonlocal separable interactions is presented. This problem can be solved exactly by integration. It amounts to solving singular integral equations of the Hilbert-Mushkhelishvili type, which have been studied extensively in the past and appear in many areas of physics, including theory of elasticity and dispersions relations in high energy physics.

Chadan, K.↗
NASA NTRS1973

Bonded half planes containing an arbitrarily oriented crack

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

Erdogan, F.↗
NASA NTRS1973

Interaction between parallel cracks in layered composites

The plane strain problem of a multi-layered composite with parallel cracks is considered. The main objective is to study the interaction between parallel and collinear cracks. The problem is formulated in terms of a set of simultaneous singular integral equations which are solved numerically. The effect of material properties on the interaction between cracks is also demonstrated.

Ratwani, M.↗