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NASA NTRS1979

Elastohydrodynamic film thickness measurements of artificially produced nonsmooth surfaces

Optical interferometry is used to measure the elastohydrodynamic (EHD) film thickness associated with artificially produced nonsmooth surfaces. The nonsmooth surfaces are produced by modifying the surfaces of highly-polished balls with irregularities in the form of multiple grooves and dents. By closely spacing these irregularities it is possible not only to produce depressions on the surface of the balls but also to generate pseudo asperities. The average roughness wavelength of this artificially-produced, nonsmooth, surface approximates the average fundamental roughness wavelength found on surfaces of some mechanical elements operating under concentrated contact. By comparing the measured film thickness profiles to the stylus traces of the irregularities, it was possible to observe the local deformations associated with micro-EHD pressure generation. In both pure rolling and pure sliding conditions the artificially-produced asperities are deformed and complete separation exists between them and the mating surface. Such findings demonstrate the importance of local surface topography and resulting micro-EHD effects on the film thickness between rough surfaces in concentrated contact. Sliding data are presented which demonstrate a severe constriction, caused by the irregularities, at the exit of the Hertzian region.

Cusano, C.↗

NASA NTRS1979

Elastohydrodynamic film thickness measurements of artificially-produced nonsmooth surfaces

Optical interferometry is used to measure the elastohydrodynamic (EHD) film thickness associated with artificially produced, nonsmooth surfaces. The nonsmooth surfaces are produced by modifying the surfaces of highly-polished balls with irregularities in the form of multiple grooves and dents. By closely spacing these irregularities, it is possible not only to produce depressions on the surface of the balls but also to generate pseudo asperities. The average roughness wavelength of this artificially-produced, nonsmooth surface approximates the average fundamental roughness wavelength found on surfaces of some mechanical elements operating under concentrated contact. By comparing the measured film thickness profiles to the stylus traces of the irregularities, it is possible to observe the local deformations associated with micro-EHD pressure generation. In both pure rolling and pure sliding conditions, the artificially-produced 'asperities' are deformed and complete separation exists between them and the mating surface. Such findings demonstrate the importance of local surface topography and resulting micro-EHD effects on the film thickness between rough surfaces in concentrated contact. In addition, sliding data are presented which demonstrate a severe constriction, caused by the irregularities, at the exit of the Hertzian region.

Cusano, C.↗

NASA NTRS1993

Nonsmooth trajectory optimization - An approach using continuous simulated annealing

An account is given of the properties of a continuous simulated annealing algorithm that can function as a global optimization tool for nonsmooth dynamic systems, as shown in the case of a trajectory-optimization program implementation. The approach is shown to successfully solve the problem of nonsmooth trajectory optimization for a high performance rigid-body aircraft. The results obtained demonstrate the superiority of the simulated annealing algorithm over widely used algorithms.

Lu, Ping↗

NASA NTRS1992

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Ta'asan, Shlomo↗

NASA NTRS1994

A spectral boundary integral equation method for the 2-D Helmholtz equation

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

Hu, Fang Q.↗

NASA NTRS1972

On backscatter from spatially varying surfaces

The theory of radar backscatter from rough (spatially varying) surfaces is discussed. An integral equation developed to describe the radar backscatter from a perfectly conducting surface is applied to nonsmooth surfaces. The results are compared with those obtained by Beckmann as well as those obtained by Wright. Differences between the three solutions are discussed.

Grody, N. C.↗

NASA NTRS1971

Production of polydisperse sprays.

A device which produces a spray with a controllable drop size distribution is described. This system is especially well suited for generating nonsmooth (e.g., bimodal) distributions, although smooth distributions can also be produced. Droplets of uniform size result from the rapid growth of an oscillatory disturbance in a free liquid jet. Simultaneous generation of droplets of various diameters by this method produces the polydisperse spray. The range of drop diameters is approximately 300-3000 microns.

Pierce, T. H.↗

NASA NTRS1983

A new consistent spatial differencing scheme for the transonic full-potential equation

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes.

Flores, J.↗

NASA NTRS1988

Non-oscillatory spectral Fourier methods for shock wave calculations

A non-oscillatory spectral Fourier method is presented for the solution of hyperbolic partial differential equations. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that no oscillations develop in the solution. Also, the accuracy of the spectral solution of the inviscid Burgers equation is shown to be higher than a fixed order.

Cai, Wei↗

NASA NTRS1988

Optimization-based design of control systems for flexible structures

The purpose of this presentation is to show that it is possible to use nonsmooth optimization algorithms to design both closed-loop finite dimensional compensators and open-loop optimal controls for flexible structures modeled by partial differential equations. An important feature of our approach is that it does not require modal decomposition and hence is immune to instabilities caused by spillover effects. Furthermore, it can be used to design control systems for structures that are modeled by mixed systems of coupled ordinary and partial differential equations.

Polak, E.↗

NASA NTRS1989

Essentially nonoscillatory spectral Fourier methods for shock wave calculations

An essentially nonoscillatory spectral Fourier method for the solution of hyperbolic partial differential equations is presented. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that essentially no oscillations develop in the solution.

Cai, Wei↗

NASA NTRS1991

Supercomputer optimizations for stochastic optimal control applications

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

Chung, Siu-Leung↗

NASA NTRS1991

New displacement-based methods for optimal truss topology design

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

Bendsoe, Martin P.↗

NASA NTRS1990

On the use of distributed sensing in control of large flexible spacecraft

Distributed processing technology is being developed to process signals from distributed sensors using distributed computations. Thiw work presents a scheme for calculating the operators required to emulate a conventional Kalman filter and regulator using such a computer. The scheme makes use of conventional Kalman theory as applied to the control of large flexible structures. The required computation of the distributed operators given the conventional Kalman filter and regulator is explained. A straightforward application of this scheme may lead to nonsmooth operators whose convergence is not apparent. This is illustrated by application to the Mini-Mast, a large flexible truss at the Langley Research Center used for research in structural dynamics and control. Techniques for developing smooth operators are presented. These involve spatial filtering as well as adjusting the design constants in the Kalman theory. Results are presented that illustrate the degree of smoothness achieved.

Montgomery, Raymond C.↗

NASA NTRS1992

Active adhesion concepts for in-orbit structural construction

The in-orbit assembly of structural elements is presently addressed by means of a continuum-based theory of active-adhesion contact/impact which assumes the manufacturability of active adhesion elements by piezoelectric (and similarly behaving) materials. Block bonding characteristics can furnish an effective alternative to optimal control-based, impact surge force-mitigation strategies, especially in the numerous nonsmooth control problems that are difficult to synthesize and implement. Attention is given to design concepts employing combined serial/parallel-bonded active adhesion elements composed of cascaded piezoelectric devices.

Park, K. C.↗

NASA NTRS1993

A variational method for finite element stress recovery and error estimation

A variational method for obtaining smoothed stresses from a finite element derived nonsmooth stress field is presented. The method is based on minimizing a functional involving discrete least-squares error plus a penalty constraint that ensures smoothness of the stress field. An equivalent accuracy criterion is developed for the smoothing analysis which results in a C sup 1-continuous smoothed stress field possessing the same order of accuracy as that found at the superconvergent optimal stress points of the original finite element analysis. Application of the smoothing analysis to residual error estimation is also demonstrated.

Tessler, A.↗

NASA NTRS1994

Airfoil optimization by the one-shot method

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (Governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Language multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

Kuruvila, G.↗

NASA NTRS1994

ASCA observations of SS Cygni during an anomalous outburst

SS Cygni was observed by the ASCA satellite on 1993 May 27, the first cataclysmic variable studied by ASCA. The observations were conducted while the system was in an outburst of the 'anomalous' variety. The SIS spectrum cannot be explained by two-temperature Raymond-Smith coronal plasma models as invoked in previous studies with lower spectral resolution. Significantly better agreement is found for models with plasma emission at kT = 0.8, 3.5 keV and thermal bremsstrahlung at kT = 18 keV. The gas imaging spectrometer (GIS) data are consistent with the solid state imaging spectrometer (SIS) data, showing evidence for Fe line emission but showing no evidence of pulsation over times ranging from seconds to minutes. These observations seem at variance with standard theory in two regards: we simultaneously see hard X-rays and optically thin soft X-rays while the system is in outburst, and we see a nonsmooth emission measure distribution. We speculate on possible scenarios which might resolve these differences.

Nousek, John A.↗