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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Analytic method for calculating properties of random walks on networks

A method for calculating the properties of discrete random walks on networks is presented. The method divides complex networks into simpler units whose contribution to the mean first-passage time is calculated. The simplified network is then further iterated. The method is demonstrated by calculating mean first-passage times on a segment, a segment with a single dangling bond, a segment with many dangling bonds, and a looplike structure. The results are analyzed and related to the applicability of the Einstein relation between conductance and diffusion.

Goldhirsch, I.↗
NASA NTRS1987

A quasi-analytical method for non-iterative computation of nonlinear controls

An optimal control solution process was developed for a general class of nonlinear dynamical systems. The method combines control theory, perturbation methods, and Van Loan's recent matrix exponential results. A variety of applications support the practical utility of this method. Nonlinear rigid body optimal maneuvers are routinely solved. Flexible body dynamical systems of an order greater than 40 were solved. The method fails occasionally due to poor convergence of the perturbation expansion or numerical difficulties associated with computing the matrix exponential. The method is attractive because it appears to be a good candidate for semi-automation; no initial guess is required, and it usually converges at 2nd or 3rd order in minutes of machine time.

Junkins, J. L.↗
NASA NTRS1987

An approximate semi-analytical method for prediction of interlaminar shear stresses in an arbitrarily laminated thick plate

An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.

Chaudhuri, Reaz A.↗
NASA NTRS1988

Accuracy analysis of the semi-analytical method for shape sensitivity calculation

The semianalytical method, widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements, is studied in this paper. The paper shows that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. The errors are shown to be associated with the structural model. An error index is developed to test the accuracy of the semianalytical method. It characterizes the difference in errors between a general finite-difference method and the semianalytical method. Moreover, a method for improving the accuracy of the semianalytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.

Barthelemy, Bruno↗
NASA NTRS1990

Accuracy analysis of the semi-analytical method for shape sensitivity calculation

The semianalytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semianalytical method. It characterizes the difference in errors between a general finite-difference method and the semianalytical method. A method for improving the accuracy of the semianalytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.

Barthelemy, Bruno↗
NASA NTRS1992

Development of an analytical method to predict helicopter main rotor performance in icing conditions

Historically, certification of a helicopter for flight into known icing conditions was a problem. This is because of the current emphasis on flight testing for verification of system performance. Flight testing in icing conditions is difficult because, in addition to being dangerous and expensive, many times conditions which are sought after cannot be readily found in nature. The problem is compounded for helicopters because of their small range in comparison to many fixed wing aircraft. Thus, helicopters are forced to wait for conditions to occur in a certain region rather than seeking them out. These and other drawbacks to flight testing prompted extreme interest in developing validated alternatives to flight testing. One such alternative is theoretical prediction. It is desirable to have the ability to predict how a helicopter will perform when subjected to icing conditions. Herein, calculations are restricted to the main rotor, and are illustrated. The computational tool used to obtain performance is the lifting line analysis of B65. B65 incorporates experimental data into data banks in order to determine the section lift, drag, and moment characteristics of various airfoils at different Mach numbers and angles of attack. The local flow angle is calculated at user specified radial locations. This flow angle, along with the local Mach number is then cross referenced with the airfoil tables to obtain the local section characteristics. The local characteristics are then integrated together to obtain the entire rotor attributes. Once the clean performance is known, characterization of the type and shape of ice which accretes on the rotor blades is obtained using the analysis of LEWICE. The Interactive Boundary Layer (IBL) method then calculates the 2-D characteristics of the iced airfoil for input into the airfoil data bank of B65. Calculations are restricted to natural ice shedding and it is assumed that no de-icing takes place. Once the new lift, drag, and moment characteristics are known for the entire blade radius, this information is fed into B65, where the iced performance is then calculated.

Britton, Randall K.↗
NASA NTRS1993

Analytic methods for design of wave cycles for wave rotor core engines

A procedure to design a preliminary wave rotor cycle for any application is presented. To complete a cycle with heat addition there are two separate but related design steps that must be followed. The 'wave' boundary conditions determine the allowable amount of heat added in any case and the ensuing wave pattern requires certain pressure discharge conditions to allow the process to be made cyclic. This procedure, when applied, gives a first estimate of the cycle performance and the necessary information for the next step in the design process, namely the application of a characteristic based or other appropriate detailed one dimensional wave calculation that locates the proper porting around the periphery of the wave rotor. Four examples of the design procedure are given to demonstrate its utility and generality. These examples also illustrate the large gains in performance that could be realized with the use of wave rotor enhanced propulsion cycles.

Resler, Edwin L., Jr.↗
NASA NTRS1921

Analytical methods for computing the polar curves of airplanes

This report presents a method of calculating polar curves which is at least as precise as graphical methods, but it more rapid. Knowing the wind tunnel test of a wing and the performances of an airplane of the same profile, it is easy to verify the characteristic coefficients and, at the same time, the methods determining induced resistances.

LE SUEUR↗
NASA NTRS1945

Graphical and analytical methods for the determination of a flow of a compressible fluid around an obstacle

Chaplygin introduced the hodograph method in the theory of compressible fluid flows and developed a method for constructing stream functions of such flows. This method, which has been extensively used in investigation of compressible fluid flows, is limited in certain respects. The expression for the stream function obtained in this manner can represent only certain types of flow patterns. In general, flow patterns obtained in this way cannot represent the whole flow around an obstacle, but only a part of such a flow, and therefore several expressions are needed in order to obtain the whole flow. On the other hand, in many instances it is important to have a single expression representing the whole flow. Recently Von Karman and Tsien constructed more general types of stream functions, but only by replacing the true pressure density relation by the linear pressure-specific volume relation so that their method is essential limited to flows the maximum Mach number of which is not too large. In a companion report the author derived a new formula for stream functions based on the true pressure density relation. It is not subject to the limitations of the Chaplygin method. In the present report this formula is employed to construct two-dimensional subsonic compressible fluid flows around a body similar in shape to a given symmetric obstacle. The methods described in the report are illustrated by numerical examples.

FLOW, COMPRESSIBLE-MEASUREMENT↗