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At least 397 records · Page 22

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NASA NTRS1986

Effect of debond growth on stress-intensity factors in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

Stress-intensity factors are determined for a cracked infinite sheet adhesively bonded to a stringer, and debonding of the adhesive layer is predicted. The stringer is modeled as a semi-infinite sheet. Adhesive nonlinearity is also included. Both the sheet and stringer are treated as homogeneous, orthotropic materials. A set of integral equations is formulated and solved to obtain the adhesive shear stresses and crack-tip stress-intensity factors. Adhesive debonding is predicted using a rupture criterion based on the combined adhesive stresses. When the crack is not under the stringer, the debond extends along the edge of the stringer. When the crack tip is beneath the stringer, the debond grows to the end of the crack, then along the edge of the stringer. Stress levels required for debond initiation decrease as the crack tip is moved beneath the stringer. With a nonlinear adhesive, the debond initiates at higher applied stress levels than in linear adhesive cases. Compared with the linear adhesive solution, modeling a nonlinear adhesive causes the stress-intensity factor to increase when the bond is assumed to remain intact but causes the stress-intensity factor to decrease when debonding is included.

Bigelow, C. A.↗

NASA NTRS1988

Effect of adhesive debond on stress-intensity factors in bonded composite panels

Stress-intensity factors are calculated for a cracked infinite sheet adhesively bonded to a stringer, and debonding of the adhesive layer is predicted. The stringer is modeled as a semiinfinite sheet. Adhesive nonlinearity is also included. Both the sheet and stringer are treated as homogeneous, orthotropic materials, a set of integral equations is formulated and solved to obtain the adhesive shear stresses and crack-tip stress-intensity factors. Adhesive debonding is predicted using a rupture criterion based on the combined adhesive stresses. A through-the-thickness crack is located in the infinite sheet perpendicular to the edge of the stringer. When the crack is not under the stringer, the debond extends along the edge of the stringer. When the crack tip is beneath the stringer, the debond extends to the crack tip, then along the edge of the stringer. Stress levels required for debond initiation decrease as the crack tip is moved beneath the stringer. With a nonlinear adhesive, the debond initiates at higher applied stress levels than in linear adhesive cases. Compared with the linear adhesive solution, modeling a nonlinear adhesive causes the stress-intensity factor to decrease when debonding is included.

Bigelow, C. A.↗

NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗

NASA NTRS1989

Finite element large-amplitude free and forced vibrations of rectangular thin composite plates

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.

Chiang, C. K.↗

NASA NTRS1985

A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis

A Taylor-Galerkin finite element solution algorithm for transient nonlinear thermal-structural analysis of large, complex structural problems subjected to rapidly applied thermal-structural loads is described. The two-step Taylor-Galerkin algorithm is an application of an algorithm recently developed for problems in compressible fluid dynamics. The element integrals that appear in the algorithm can be evaluated in closed form for two and three dimensional elements.

Thornton, Earl A.↗

NASA NTRS1987

A creep-rupture model of filament-wound spherical pressure vessels

The creep-rupture model is that of a quasi-isotropic filament-wound spherical pressure vessel, subjected to internal pressurization. The matrix material of the composite system is assumed to be linearly viscoelastic. Internal damage resulting from the relaxation of the matrix and the corresponding increase in microcracks is represented by a functional relationship between circumferential strain and transverse modulus. The numerical solution to this nonlinear problem is an iterative technique, whereby the elastic-viscoelastic correspondence principle is employed. In the Laplace domain, the associated elastic solution is obtained and this solution is inverted by the multidata method to yield the time-dependent solution.

Dozier, Jan D.↗

NASA NTRS1953

On transonic flow past a wave-shaped wall

This report is an extension of a previous investigation (described in NACA rep. 1069) concerned with the solution of the nonlinear differential equation for transonic flow past a wavy wall. In the present work several new notions are introduced which permit the solution of the recursion formulas arising from the method of integration in series. In addition, a novel numerical tests of convergence, applied to the power series (in transonic similarity parameter) representing the local Mach number distribution at the boundary, indicates that smooth symmetrical potential flow past the wavy wall is no longer possible once the critical value of the stream Mach number has been exceeded.

Kaplan, Carl↗

NASA NTRS1994

Parasitic instabilities in magnetized, differentially rotating disks

Velikhov, Chandrasekhar, Balbus & Hawley have discovered a MHD instability of differentially rotating fluids that may explain the effective viscosity of accretion disks. If the unperturbed magnetic energy density is much less than the gas pressure, this `magnetorotational' instability (MRI) arises on small scales and is approximately incompressible. If the unperturbed field is suffiently, strong, the MRI is suppressed. We therefore ask whether the MRI mechanism can amplify even very weak initial fields until they reach equipartition with the gas pressure. We show that in the total incompressible limit, the MRI modes are exact solutions of the nonlinear fluid equations, even if the perturbed magnetic field is much larger than the unperturbed field. Also, we present a new exact solution in the opposite limit that the magnetic pressure is much larger than that of the gas. On the other hand, we show that the incompressible MRI modes are themselves subject to parasitic instabilities with instantaneous growth rates proportional to the MRI amplitude. Some of the parasitic instabilities are of the Kelvin-Helmholtz type, while others are less familiar. The eigenfunctions of the latter group suggest that they may promote rapid reconnection of the MRI field. Thus, parasitic modes may stop MRI growth at subequipartition amplitudes if it developes from a sufficiently weak initital field.

Goodman, Jeremy↗

NASA NTRS1991

Prediction of unsteady aerodynamic loads in cascades using the linearized Euler equations on deforming grids

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. Using the linearized Euler technique, one decomposes the flow into a mean (or steady) flow plus an unsteady, harmonically varying, small disturbance flow. Linear variable coefficient equations describe the small disturbance behavior of the flow, and are solved using a pseudo-time marching Lax-Wendroff scheme. For the blade motion problem, a harmonically deforming computational rid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition. The paper also presents a new, numerically exact, nonreflecting far-field boundary condition based on an eigenanalysis of the discretized equations. Computed flow solutions demonstrate the computational accuracy and efficiency of the present method. The solution of the linearized Euler equations requires one to two orders of magnitude less computer time than solution of the nonlinear Euler equations using traditional time-accurate time-marching techniques. In addition, the deformable grid significantly improves the accuracy of the solution.

Hall, Kenneth C.↗

NASA NTRS1996

Validation Tests of TASS for Application to 3-D Vortex Simulations

Direct analytical solutions can be useful in validating the Core formulation of numerical systems. In this document an exact analytical solution to the nonlinear Navier-Stokes equation is compared to the numerical results from the three-dimensional Terminal Area Simulation System (TASS). This exact solution, of which the derivation is included, is for Beltrami type flow. Direct comparison of TASS to the analytical Beltrami solution is then used in evaluating the accuracy of TASS.

Switzer, George F.↗

NASA NTRS1983

Numerical methods for stiff systems of two-point boundary value problems

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Flaherty, J. E.↗

NASA NTRS1973

Estimation and detection of signals in multiplicative noise

A class of detection-estimation problems on matrix Lie groups is defined in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear in nature, it is possible to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite dimensional optimal solution to a nonlinear estimation problem and can be viewed as consisting of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid body rotational control system.

Willsky, A. S.↗

NASA NTRS1993

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Chiang, C. K.↗

NASA NTRS2006

Development of Design Analysis Methods for C/SiC Composite Structures

The stress-strain behavior at room temperature and at 1100 C (2000 F) was measured for two carbon-fiber-reinforced silicon carbide (C/SiC) composite materials: a two-dimensional plain-weave quasi-isotropic laminate and a three-dimensional angle-interlock woven composite. Micromechanics-based material models were developed for predicting the response properties of these two materials. The micromechanics based material models were calibrated by correlating the predicted material property values with the measured values. Four-point beam bending sub-element specimens were fabricated with these two fiber architectures and four-point bending tests were performed at room temperature and at 1100 C. Displacements and strains were measured at various locations along the beam and recorded as a function of load magnitude. The calibrated material models were used in concert with a nonlinear finite element solution to simulate the structural response of these two materials in the four-point beam bending tests. The structural response predicted by the nonlinear analysis method compares favorably with the measured response for both materials and for both test temperatures. Results show that the material models scale up fairly well from coupon to subcomponent level.

Sullivan, Roy M.↗

NASA NTRS1995

High-order essentially non-oscillatory methods for computational aeroacoustics

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. In addition, it is desirable to highly resolve discontinuities that can develop in the solutions of the Euler or Navier-Stokes equations. The class of essentially non-oscillatory (ENO) shock-capturing schemes has been designed to have both of these properties. The dual capacity of ENO schemes for high-order accuracy and non-oscillatory shock-capturing is achieved through the use of adaptive stenciling, which makes these schemes highly nonlinear. These schemes are briefly described and referenced herein. A fourth-order algorithm is then applied to the solution of an acoustic wave in a quasi-one-dimensional converging-diverging nozzle.

Casper, Jay↗

NASA NTRS2013

Powered Descent Guidance with General Thrust-Pointing Constraints

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Carson, John M., III↗

NASA NTRS1990

Unsteady three-dimensional marginal separation, including breakdown

A situation involving a three-dimensional marginal separation is considered, where a (steady) boundary layer flow is on the verge of separating at a point (located along a line of symmetry/centerline). At this point, a triple-deck is included, thereby permitting a small amount of interaction to occur. Unsteadiness is included within this interaction region through some external means. It is shown that the problem reduces to the solution of a nonlinear, unsteady, partial-integro system, which is solved numerically by means of time-marching together with a pseudo-spectral method spatially. A number of solutions to this system are presented which strongly suggest a breakdown of this system may occur, at a finite spatial position, at a finite time. The structure and details of this breakdown are then described.

Duck, Peter W.↗

NASA NTRS1986

Using Hough harmonics to validate and assess nonlinear shallow-water models

The implementation of a technique for locating programming errors in shallow-water codes, establishing the correctness of the code, and assessing the performance of the numerical model under various flow conditions is described. The right-hand side of the differential equations is modified in such a way that the exact solution of the nonlinear initial-value problem is known, so that the truncation errors of the numerical scheme can be studied in detail. The exact solution is prescribed to be any linear combination of Hough harmonics which propagate in time according to their natural frequencies.

Dee, Dick P.↗