Iterative solution of nonlinear optimal control problems.
Mathematical programming methods for solving nonlinear state-constrained discrete optimal control problems
DYNAMIC PROGRAMMING↗
SEARCH · Engineering Papers
Results for “Mathematical methods”
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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On the thermodynamics and approximation theory of viscoelastic materials.
Thermodynamics and approximation theory of viscoelastic materials, developing Coleman-Noll theory, thermodynamic theory for fluids, etc
MATERIALS SCIENCE↗
Development of multivariate function models by least squares
Multivariate functional models for least squares approximation of error tolerance
LEAST SQUARES METHOD↗
Analytical methods for bacterial kinetics studies
Methods utilize mathematical equations and models and specialized computer techniques. Techniques apply to food production, complex chemicals production, and polluted water purification.
Edwards, V. E.↗
Application of positive-real functions in hyperstable discrete model-reference adaptive system design.
Proposal of an algorithmic procedure, based on mathematical programming methods, to design compensators for hyperstable discrete model-reference adaptive systems (MRAS). The objective of the compensator is to render the MRAS insensitive to initial parameter estimates within a maximized hypercube in the model parameter space.
Karmarkar, J. S.↗
Measurements, modeling, control and simulation - as applied to the human left ventricle for purposeful physiological monitoring.
Interdisciplinary engineering research effort in studying the intact human left ventricle has been employed to physiologically monitor the heart and to obtain its 'state-of-health' characteristics. The left ventricle was selected for this purpose because it plays a key role in supplying energy to the body cells. The techniques for measurement of the left ventricular geometry are described; the geometry is effectively displayed to bring out the abnormalities in cardiac function. Methods of mathematical modeling, which make it possible to determine the performance of the intact left ventricular muscle, are also described. Finally, features of a control system for the left ventricle for predicting the effect of certain physiological stress situations on the ventricle performance are discussed.
Ghista, D. N.↗
Automated procedure for design of wing structures to satisfy strength and flutter requirements
A pilot computer program was developed for the design of minimum mass wing structures under flutter, strength, and minimum gage constraints. The wing structure is idealized by finite elements, and second-order piston theory aerodynamics is used in the flutter calculation. Mathematical programing methods are used for the optimization. Computation times during the design process are reduced by three techniques. First, iterative analysis methods used to reduce significantly reanalysis times. Second, the number of design variables is kept small by not using a one-to-one correspondence between finite elements and design variables. Third, a technique for using approximate second derivatives with Newton's method for the optimization is incorporated. The program output is compared witH previous published results. It is found that some flutter characteristics, such as the flutter speed, can display discontinous dependence on the design variables (which are the thicknesses of the structural elements). It is concluded that it is undesirable to use such quantities in the formulation of the flutter constraint.
Haftka, R. T.↗
A comparison of two types of structural optimization procedures for satisfying flutter requirements
A comparison is made of results obtained from mathematical programming and optimality criteria procedures for the minimum-mass design of typical aircraft wing structures to satisfy prescribed flutter requirements. The mathematical programming method is based on an interior penalty function approach. A rigorous optimality criterion and an intuitive optimality criterion based on uniform strain energy density are considered. An intuitive resizing procedure is used for both optimality criterion solutions. All results are calculated using the same computer program, changing only the optimization procedure. Both high- and low-aspect-ratio wings are examined. Finite elements are used for structural modeling, and the generalized coordinates for the flutter solution are based on the natural vibration modes of the structure.
Haftka, R. T.↗
Liquefaction dynamics of n-octadecane in cylindrical coordinates
The study presents one method of mathematically modeling the effects of gravity-induced free convection upon the melting phenomena of a finite paraffin slab. The theoretical model is based on the numerical computer solution of the solid phase and liquid phase energy equations, coupled with an imposed ideal-viscous flow approximation. An implicit alternating-direction technique is used as the finite-difference approximation for the basic energy equations in the numerical solution. The theoretical predictions are compared to experimental data from an annular test cell, in which n-octadecane, C18H38, was used as the test material. The results show that the model is a good first approximation to the solution of solid-liquid phase change involving gravity-induced free convection.
Bain, R. L.↗
Parameter estimation for terrain modeling from gradient data
This paper developes a method for mathematically modeling terrain surfaces for use on an unmanned Martian vehicle. The data collected by the vehicle consists of terrain height and two directional slopes at each data point. The parameters for the mathematical terrain model are stochastically determined by using least square approximations.-
Shen, C. N.↗
WINDOWAC (Wing Design Optimization With Aeroelastic Constraints): Program manual
User and programer documentation for the WIDOWAC programs is given. WIDOWAC may be used for the design of minimum mass wing structures subjected to flutter, strength, and minimum gage constraints. The wing structure is modeled by finite elements, flutter conditions may be both subsonic and supersonic, and mathematical programing methods are used for the optimization procedure. The user documentation gives general directions on how the programs may be used and describes their limitations; in addition, program input and output are described, and example problems are presented. A discussion of computational algorithms and flow charts of the WIDOWAC programs and major subroutines is also given.
Haftka, R. T.↗
An exact transformation from geocentric to geodetic coordinates for nonzero altitudes
An exact method for the nonzero altitude transformation from geocentric to geodetic coordinates is derived. The method is mathematically general and should serve as a primary standard.
Hedgley, D. R., Jr.↗
C super 1: Compatible interpolation over a triangle
An elementary derivation and a complete description is given of an algorithm for interpolation over a plane triangle when function values and first partial derivatives are given at the vertices. The method gives C1 continuity with neighboring triangles. The interpolation method is mathematically equivalent to one that has been discussed previously in the literature; however, the algorithmic form given here is more efficient than has previously been described.
Lawson, C. L.↗
Design of minimum-weight structures
Finite-element techniques, mathematical programming methods, and innovative collection of approximation techniques are combined in program for finding efficient minimum-weight optimum designs for significant class of structural synthesis problems.
Miura, H.↗
Water resources planning for rivers draining into Mobile Bay
The application of remote sensing, automatic data processing, modeling and other aerospace related technologies to hydrological engineering and water resource management are discussed for the entire river drainage system which feeds the Mobile Bay estuary. The adaptation and implementation of existing mathematical modeling methods are investigated for the purpose of describing the behavior of Mobile Bay. Of particular importance are the interactions that system variables such as river flow rate, wind direction and speed, and tidal state have on the water movement and quality within the bay system.
April, G. C.↗
Inclusion of explicit thermal requirements in optimum structural design
A finite-element based procedure is described for obtaining minimum mass designs of structures subjected to combined thermal and mechanical loading and both strength and thermal constraints. The procedure is based on a mathematical programming method using the Sequence of Unconstrained Minimizations Technique (SUMT) in which design requirements are incorporated by an exterior penalty function. The procedure is limited to steady-state temperatures which are controlled by structural sizing only. The optimization procedure is demonstrated by the design of a structural wing box with both mechanical loading and external heating, subject to design constraints on stress, minimum gage, and temperature. The final design for these conditions is compared with a corresponding design in which temperature constraints are omitted.
Adelman, H. M.↗
Impedance characteristics of coaxial and planar magnetoplasma capacitors
A theory has been developed for the impedance of a homogeneous magnetoplasma enclosed between two specular reflecting coaxial electrodes, with a static magnetic field parallel to the electrode axes. The parallel-plate magnetoplasma capacitor is treated as a sub-case. Starting with the Vlasov equation, an integral equation is derived for the electric field. Solving this equation, and integrating to obtain the voltage, gives the capacitor impedance. This includes a capacitive component, and a resistive component expressing the Landau damping associated with the open orbits of electrons reflected at the electrodes. A direct numerical solution of the field integral equation has been carried out for a range of values of magnetic field, plasma density, and signal frequency. The values of impedance so obtained are compared with the predictions of macroscopic theory, and of an approximate microscopic theory in which open orbits are ignored and solutions are obtained using finite Fourier transform methods. The mathematical relations between these theories are demonstrated.
Harker, K. J.↗
Development of methodology for optimum design of structures at elevated temperatures
This paper surveys a number of activities aimed at applying optimum design techniques to structures where high temperatures are important design considerations. An improved variant of fully-stressed design (FSD), denoted thermal fully-stressed design (TFSD), is described which converges significantly faster than FSD for problems where thermal stresses are comparable in magnitude to mechanical stresses. Second, an optimality criterion is described for sizing structures subjected to temperature constraints. Simultaneous requirements on strength and temperatures are handled by two different techniques: (1) a state-of-the-art mathematical programming method and (2) the optimality criterion technique for temperature constraints combined with FSD for strength constraints. A method is described to optimize the insulation and ply thicknesses of an insulated composite panel with a time-varying temperature applied to the outer surface of the insulation and a general set of in-plane loads applied to the panel.
Adelman, H. M.↗