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At least 109 records · Page 6

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NASA NTRS1977

Stress analysis and stress-intensity factors for finite geometry solids containing rectangular surface cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses, and the stress-intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress-intensity factors are also obtained for a through-thickness, center-cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress-intensity factors for commonly encountered surface crack geometries in finite solids

Gyekenyesi, J. P.↗

NASA NTRS1978

An efficient, direct finite difference method for computing sound propagation in arbitrarily shaped two-dimensional and axisymmetric ducts without flow

An efficient, direct finite difference method is presented for computing sound propagation in non-stepped two-dimensional and axisymmetric ducts of arbitrarily varying cross section without mean flow. The method is not restricted by axial variation of acoustic impedance of the duct wall linings. The non-uniform two-dimensional or axisymmetric duct is conformally mapped numerically into a rectangular or cylindrical computational domain using a new procedure based on a method of fast direct solution of the Cauchy-Riemann equations. The resulting Helmholtz equation in the computational domain is separable. The solution to the governing equation and boundary conditions is expressed as a linear combination of fundamental solutions. The fundamental solutions are computed only once for each duct shape by means of the fast direct cyclic reduction method for the discrete solution of separable elliptic equations. Numerical results for several examples are presented to show the applicability and efficiency of the method.

Chakravarthy, S.↗

NASA NTRS1978

Mixed boundary-value problems in mechanics

Definitions in the case of multiple series equations and multiple integral equations are examined. In considering the solution of a given mixed boundary value problem perhaps the simplest technique is the direct application of the method of complex potentials provided the problem admits such potentials and the domain and the boundary conditions are suitable for such an application. The direct application of complex potentials is described with the aid of examples, taking into account a problem in potential theory, the case of periodic cuts, and an elasticity problem for a nonhomogeneous plane. The reduction to singular integral equations is discussed along with the numerical solution of singular integral equations of the first kind, integral equations with generalized Cauchy kernels, and singular integral equations of the second kind.

Erdogan, F.↗

NASA NTRS1978

Numerical solution of a class of integral equations arising in two-dimensional aerodynamics

We consider the numerical solution of a class of integral equations arising in the determination of the compressible flow about a thin airfoil in a ventilated wind tunnel. The integral equations are of the first kind with kernels having a Cauchy singularity. Using appropriately chosen Hilbert spaces, it is shown that the kernel gives rise to a mapping which is the sum of a unitary operator and a compact operator. This allows the problem to be studied in terms of an equivalent integral equation of the second kind. A convergent numerical algorithm for its solution is derived by using Galerkin's method. It is shown that this algorithm is numerically equivalent to Bland's collocation method, which is then used as the method of computation. Extensive numerical calculations are presented establishing the validity of the theory.

Fromme, J.↗

NASA NTRS1977

Lunar farside tectonics and volcanism

The reported study is primarily concerned with the identification and mapping of structural and volcanic features on the lunar farside. The study represents a continuation and extension of a similar investigation made of the nearside of the moon by Scott et al. (1975). Mapping reveals that tectonic structures on the moon's farside are comparatively scarce and such less prominently developed than those on the nearside. Rilles and mare-type ridges that form major linear and basin concentric systems on the nearside are nearly absent on the farside as are large normal faults like Rupes Recta and Rupes Cauchy. The azimuth orientations of five types of geologic structures were measured, including lineaments, crater chains, terra ridges, faults and linear rilles, and straight segments of crater rims. Mare basalts are concentrated in low regions, especially in a large southern basin which is also the site of relatively numerous volcanic constructs as well as geochemical and magnetic anomalies.

Scott, D. H.↗

NASA NTRS1979

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Skollermo, G.↗

NASA NTRS1979

Two dimensional aerodynamic interference effects on oscillating airfoils with flaps in ventilated subsonic wind tunnels

The numerical computation of unsteady airloads acting upon thin airfoils with multiple leading and trailing-edge controls in two-dimensional ventilated subsonic wind tunnels is studied. The foundation of the computational method is strengthened with a new and more powerful mathematical existence and convergence theory for solving Cauchy singular integral equations of the first kind, and the method of convergence acceleration by extrapolation to the limit is introduced to analyze airfoils with flaps. New results are presented for steady and unsteady flow, including the effect of acoustic resonance between ventilated wind-tunnel walls and airfoils with oscillating flaps. The computer program TWODI is available for general use and a complete set of instructions is provided.

Fromme, J.↗

NASA NTRS1979

Integral equations for flows in wind tunnels

This paper surveys recent work on the use of integral equations for the calculation of wind tunnel interference. Due to the large number of possible physical situations, the discussion is limited to two-dimensional subsonic and transonic flows. In the subsonic case, the governing boundary value problems are shown to reduce to a class of Cauchy singular equations generalizing the classical airfoil equation. The theory and numerical solution are developed in some detail. For transonic flows nonlinear singular equations result, and a brief discussion of the work of Kraft and Kraft and Lo on their numerical solution is given. Some typical numerical results are presented and directions for future research are indicated.

Fromme, J. A.↗

NASA NTRS1981

Analysis of the tensile stress-strain behavior of elastomers at constant strain rates. I - Criteria for separability of the time and strain effects

A theoretical analysis of the tensile stress-strain relation of elastomers at constant strain rate is presented which shows that the time and the stress effect are separable if the experimental time scale coincides with a segment of the relaxation modulus that can be described by a single power law. It is also shown that time-strain separability is valid if the strain function is linearly proportional to the Cauchy strain, and that when time-strain separability holds, two strain-dependent quantities can be obtained experimentally. In the case where time and strain effect are not separable, superposition can be achieved only by using temperature and strain-dependent shift factors.

Hong, S. D.↗

NASA NTRS1982

The crack problem for a nonhomogeneous plane

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Delale, F.↗

NASA NTRS1982

On the failure of hyperbolicity in elasticity

The failure of hyperbolicity leading to the instability as an ill-posedness of the Cauchy problem is investigated for elasticity. The criteria for that instability are derived in terms of the potential energy as a function of the strain invariants. The theory is illustrated by examples.

Zak, M.↗

NASA NTRS1982

Considerations in cross-validation type density smoothing with a look at some data

Experience gained in applying nonparametric maximum likelihood techniques of density estimation to judge the comparative quality of various estimators is reported. Two invariate data sets of one hundered samples (one Cauchy, one natural normal) are considered as well as studies in the multivariate case.

Schuster, E. F.↗

NASA NTRS1983

A method for modifying two-dimensional adaptive wind-tunnel walls including analytical and experimental verification

The theoretical development of a simple and consistent method for removing the interference in adaptive-wall wind tunnels is reported. A Cauchy integral formulation of the velocities in an imaginary infinite extension of the real wind-tunnel flow is obtained and evaluated on a closed contour dividing the real and imaginary flow. The contour consists of the upper and lower effective wind-tunnel walls (wall plus boundary-layer displacement thickness) and upstream and downstream boundaries perpendicular to the axial tunnel flow. The resulting integral expressions for the streamwise and normal perturbation velocities on the contour are integrated by assuming a linear variation of the velocities between data-measurement stations along the contour. In an iterative process, the velocity components calculated on the upper and lower boundaries are then used to correct the shape of the wall to remove the interference. Convergence of the technique is shown numerically for the cases of a circular cylinder and a lifting and nonlifting NACA 0012 airfoil in incompressible flow. Experimental convergence at a transonic Mach number is demonstrated by using an NACA 0012 airfoil at zero lift.

Everhart, J. L.↗

NASA NTRS1983

A semi-direct solver for compressible 3-dimensional rotational flow

An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.

Chang, S. C.↗

NASA NTRS1983

A semi-direct solver for compressible three-dimensional rotational flow

Chang, S.-C.↗

NASA NTRS1983

Analysis of coolant entrance boundary shape of porous region to control cooling along exit boundary

A cooled porous region has a plane surface exposed to a specified spatially varying heat flux. The coolant leaves the region through this surface, and it is desired to control the flow distribution to maintain a specified uniform surface temperature. This is accomplished by having the coolant entrance surface shaped to provide in the region the necessary variation of path length and, hence, flow resistance. The surface shape at the coolant entrance is found by solving a Cauchy boundary value problem. An exact solution is obtained that will deal with a wide variety of heating distributions for both two- and three-dimensional shapes.

Siegel, R.↗

NASA NTRS1983

The crack problem for a nonhomogeneous plane

Delale, F.↗

NASA NTRS1983

Explicit Hilbert-space representations of atomic and molecular photoabsorption spectra - Computational studies of Stieltjes-Tchebycheff functions

Computational methods are reported for construction of discrete and continuum Schroedinger states in atoms and molecules employing explicit Hilbert space procedures familiar from bound state studies. As theoretical development, the Schroedinger problem of interest is described, the Cauchy-Lanczos bases and orthonormal polynomials used in constructing L-squared Stieltjes-Tchebycheff (ST) approximations to the discrete and continuum states are defined, and certain properties of these functions are indicated. Advantages and limitations of the ST approach to spectral studies relative to more conventional calculations are discussed, and aspects of the approach in single-channel approximations to larger molecules are described. Procedures are indicated for construction of photoejection anisotropies and for performing coupled-channel calculations employing the ST formalism. Finally, explicit descriptive intercomparisons are made of the nature and diagnostic value of ST functions with more conventional scattering functions.

Hermann, M. R.↗