SEARCH · Search NASA

Results for “boundary value problems”

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.

SourceResearch connectionFrom yearThrough year

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

At least 811 records · Page 45

All sources NASA NTRS DOE OSTI

NASA NTRS1985

Analytical results for post-buckling behaviour of plates in compression and in shear

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Stein, M.↗

NASA NTRS1986

A pseudospectral Legendre method for hyperbolic equations with an improved stability condition

A new pseudospectral method is introduced for solving hyperbolic partial differential equations. This method uses different grid points than previously used pseudospectral methods: in fact the grid points are related to the zeroes of the Legendre polynomials. The main advantage of this method is that the allowable time step is proportional to the inverse of the number of grid points 1/N rather than to 1/n(2) (as in the case of other pseudospectral methods applied to mixed initial boundary value problems). A highly accurate time discretization suitable for these spectral methods is discussed.

Tal-Ezer, Hillel↗

NASA NTRS1986

Stress patterns in an interplate shear zone - An effective anisotropic model and implications for the Transverse Ranges, California

The pervasive Quaternary strike-slip (or wrench) structure that occurs in southern California is analyzed by solving a series of planar, linear elastic boundary value problems of tractional type that assume pure shear forces at infinity. It is concluded that the cross-cutting tectonic fabric of the Transverse Ranges in southern California causes the Ranges to act as a stress concentrator. In addition, it is found that rigid rotation of the Transverse Ranges is mechanically supported by an asymmetric distribution of stress and elastic strain encircling it. It is noted that for Quaternary tectonic orientation, a clockwise sense to this rotation is expected.

Ivins, E. R.↗

NASA NTRS1986

MHD simulation of the 'geoeffectiveness' of interplanetary disturbances

A series of examples is used to evaluate the 'geoeffectiveness' prediction technique that is based on the classical, initial boundary value problem of MHD. For the nonplanar simulation of a corotating stream, it is shown that the technique can compute relevant solar wind parameters at the earth's location. For the nonplanar simulation of a complex series of events, qualitative agreement is found for large-scale structures, but the phasing and amplitudes are not satisfactory. Preliminary work with a fully three-dimensional, time-dependent simulation of a flare-generated interplanetary shock wave shows that the effect of the latitudinal variation produces attenuation of the heliolongitudinal component of the IMF and of the radial velocity.

Dryer, M.↗

NASA NTRS1986

Vortical Flows Research Program of the Fluid Dynamics Research Branch

The research interests of the staff of the Fluid Dynamics Research Branch in the general area of vortex flows are summarized. A major factor in the development of enchanced maneuverability and reduced drag by aerodynamic means is the use of effective vortex control devices. The key to control is the use of emerging computational tools for predicting viscous fluid flow in close coordination with fundamental experiments. In fact, the extremely complex flow fields resulting from numerical solutions to boundary value problems based on the Navier-Stokes equations requires an intimate relationship between computation and experiment. The field of vortex flows is important in so many practical areas that a concerted effort in this area is justified. A brief background of the research activity undertaken is presented, including a proposed classification of the research areas. The classification makes a distinction between issues related to vortex formation and structure, and work on vortex interactions and evolution. Examples of current research results are provided, along with references where available. Based upon the current status of research and planning, speculation on future research directions of the group is also given.

Source record↗

NASA NTRS1988

Modeling and estimation of a low degree geopotential model from terrestrial gravity data

The development of appropriate modeling and adjustment procedures for the estimation of harmonic coefficients of the geopotential, from surface gravity data was studied, in order to provide an optimum way of utilizing the terrestrial gravity information in combination solutions currently developed at NASA/Goddard Space Flight Center, for use in the TOPEX/POSEIDON mission. The mathematical modeling was based on the fundamental boundary condition of the linearized Molodensky boundary value problem. Atmospheric and ellipsoidal corrections were applied to the surface anomalies. Terrestrial gravity solutions were found to be in good agreement with the satellite ones over areas which are well surveyed (gravimetrically), such as North America or Australia. However, systematic differences between the terrestrial only models and GEMT1, over extended regions in Africa, the Soviet Union, and China were found. In Africa, gravity anomaly differences on the order of 20 mgals and undulation differences on the order of 15 meters, over regions extending 2000 km in diameter, occur. Comparisons of the GEMT1 implied undulations with 32 well distributed Doppler derived undulations gave an RMS difference of 2.6 m, while corresponding comparison with undulations implied by the terrestrial solution gave RMS difference on the order of 15 m, which implies that the terrestrial data in that region are substantially in error.

Pavlis, Nikolaos K.↗

NASA NTRS1988

Numerical methods for incompressible viscous flows with engineering applications

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

Rose, M. E.↗

NASA NTRS1987

On the solution of integral equations with strongly singular kernels

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

Kaya, A. C.↗

NASA NTRS1988

Minimum time attitude slewing maneuvers of a rigid spacecraft

The minimum time attitude slewing motion of a rigid spacecraft with its controls provided by torques and forces, which have their upper and lower limits prescribed, is considered. The two-point boundary-value problem is derived by applying the Pontriagin's Maximum Principle to the system and solved by using a quasi-linearization algorithm. The nominal solutions to the problem as well as the starting values of the total slewing time and the unknown initial costates for this algorithm are generated by using Euler's eigenaxis rotation theorem. It is pointed out that one of the four initial costates associated with the quaternions can be arbitrarily selected without affecting the optimal controls and, thus, simplifying the computation. The minimum slewing time is determined by shortening the total slewing time until at least one of the controls becomes a bang-bang type. Several numerical tests for the rigidized SCOLE model are presented to show the applications of the methods.

Li, Feiyue↗

NASA NTRS1987

The role of damage-softened material behavior in the fracture of composites and adhesives

The failure mechanism of polymer composites and adhesives with high strain in the zone near and ahead of the crack tip is investigated analytically, summarizing the findings of Ungsuwarungsri (1986). A double-cantilever-beam specimen with the nonlinear material confined to a thin strip between two wedge-loaded elastic beams is modeled as a beam on a nonlinear foundation; the two-point boundary-value problem for stationary and propagating cracks is solved numerically; and an FEM approach is applied to study the behavior of the nonlinear strip in detail. Typical results are presented in extensive graphs, and the accuracy and efficiency of the present method are shown to be superior to those of the Berry (1963) procedure.

Ungsuwarungsri, T.↗

NASA NTRS1987

A parallelized elliptic solver for reacting flows

A modified Newton algorithm for the solution of nonlinear elliptic boundary value problems via finite discretization methods is presented. A serial implementation of this algorithm which has recently been applied successfully to the computation of an axisymmetric over-ventilated subsonic laminar methane-air jet diffusion flame is described. Parallel implementation issues and a complexity theory are presented. Included as well are actual performance data for model systems obtained on the Intel Hypercube and a discussion of its implications for modeling realistic systems.

Keyes, David E.↗

NASA NTRS1988

The dynamics and control of the in-orbit SCOLE configuration

The study of the dynamics of the Spacecraft Control Laboratory Experiment (SCOLE) is extended to emphasize the synthesis of control laws for both the linearized system as well as the large amplitude slewing maneuvers required to rapidly reorient the antenna line of sight. For control of the system through small amplitude displacements from the nominal equilibrium position LQR techniques are used to develop the control laws. Pontryagin's maximum principle is applied to minimize the time required for the slewing of a general rigid spacecraft system. The minimum slewing time is calculated based on a quasi-linearization algorithm for the resulting two point boundary value problem. The effect of delay in the control input on the stability of a continuously acting controller (designed without considering the delay) is studied analytically for a second order plant. System instability can result even for delays which are only a small fraction of the natural period of motion.

Bainum, Peter M.↗

NASA NTRS1988

Optimal post-experiment estimation of poorly modeled dynamic systems

Recently, a novel strategy for post-experiment state estimation of discretely-measured dynamic systems has been developed. The method accounts for errors in the system dynamic model equations in a more general and rigorous manner than do filter-smoother algorithms. The dynamic model error terms do not require the usual process noise assumptions of zero-mean, symmetrically distributed random disturbances. Instead, the model error terms require no prior assumptions other than piecewise continuity. The resulting state estimates are more accurate than filters for applications in which the dynamic model error clearly violates the typical process noise assumptions, and the available measurements are sparse and/or noisy. Estimates of the dynamic model error, in addition to the states, are obtained as part of the solution of a two-point boundary value problem, and may be exploited for numerous reasons. In this paper, the basic technique is explained, and several example applications are given. Included among the examples are both state estimation and exploitation of the model error estimates.

Mook, D. Joseph↗

NASA NTRS1988

The dynamics and control of large flexible space structures, part 11

A mathematical model is developed to predict the dynamics of the proposed Spacecraft Control Laboratory Experiment during the stationkeeping phase. The Shuttle and reflector are assumed to be rigid, while the mass connecting the Shuttle to the reflector is assumed to be flexible with elastic deformations small as compared with its length. It is seen that in the presence of gravity-gradient torques, the system assumes a new equilibrium position primarily due to the offset in the mass attachment point to the reflector from the reflector's mass center. Control is assumed to be provided through the Shuttle's three torquers and throught six actuators located by painrs at two points on the mass and at the reflector mass center. Numerical results confirm the robustness of an LQR derived control strategy during stationkeeping with maximum control efforts significantly below saturation levels. The linear regulator theory is also used to derive control laws for the linearized model of the rigidized SCOLE configuration where the mast flexibility is not included. It is seen that this same type of control strategy can be applied for the rapid single axis slewing of the SCOLE through amplitudes as large as 20 degrees. These results provide a definite trade-off between the slightly larger slewing times with the considerable reduction in over-all control effort as compared with the results of the two point boundary value problem application of Pontryagin's Maximum Principle.

Bainum, Peter M.↗

NASA NTRS1988

Boundary force method analyses of notched plates with cracks

The boundary-force method developed by Tan (1985) and Tan et al. (1986) is extended to two-dimensional mixed boundary-value problems in fracture mechanics. The formulation is explained in detail, and results are presented in tables and graphs for sample problems involving an edge crack emanating from a semielliptical and a semicircular notch and an edge crack emanating from a V notch. The accuracy of the approach is demonstrated by comparisons with collocation solutions for an edge-clamped center-cracked tension specimen.

Newman, J. C., Jr.↗

NASA NTRS1988

Methods for analysis of cracks in three-dimensional solids

Various methods used for determining stress-intensity factors for cracked three-dimensional bodies are reviewed. The review is limited to the determination of mode-I stress-intensity factors. Some exact solutions for cracks in infinite solids are presented, and various approximate methods that have been used for the solution of the boundary-value problem of finite solids with cracks are addressed. The techniques used to extract the stress-intensity factors from these solutions are considered, and various methods used to calculate the stress-intensity factors for through-the-thickness cracks, semielliptical surface cracks, and quarter-elliptical corner cracks at holes are compared for the case of remote tensile loading.

Raju, I. S.↗

NASA NTRS1989

Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

NASA NTRS1989

Use of the quasilinearization algorithm for the simulation of LSS slewing

The use of the Maximum Principle for the large angle slewing of large space structures (LSS) usually results in the so-called two-point boundary-value problem, in which many requirements (e.g., minimum time, small amplitude, and limited control power, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical algorithm. There are many candidate algorithms available for this problem (e.g., quasilinearization, gradient, etc.). Here researchers discuss only the quasilinearization method which has been used for several cases of large angle slewing of LSS. The basic idea of this algorithm is to make a series of successive approximations of the solution from a particular solvable case (linear or nonlinear) to a more general practical case. For the rigid spacecraft slewing problem with no constraints on the controls, the solution procedure can be found in the literature. This procedure needs to be modified if a minimum time for the slewing problem is desired with control limits given. Recently, an indirect method for finding the minimum time was developed to meet all these requirements. For the general mixed (including both rigid and flexible parts) problem, an additional constraint of small vibrational amplitude on the flexible parts is imposed.

Li, Feiyue↗