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At least 127 records · Page 7

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NASA NTRS1986

Arbitrarily laminated, anisotropic cylindrical shell under internal pressure

An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.

Chaudhuri, Reaz Z.↗

NASA NTRS1987

Laminar mixing in a small floating zone

The relationship between the flow and solute fields during steady mass transfer of a dilute component is analyzed for multi-cellular rotating flows in the floating zone process of semiconductor growth. When the recirculating flows are weak in relation to the rate of crystal growth, a closed-form solution clearly shows the link between the convection pattern in the melt and the solute distribution across the surface of the growing solid. In the limit of strong convection, finite element calculations demonstrate the tendency of the composition to become uniform over the majority of the melt. The solute segregation in the product crystal is greatest when the recirculating motion is comparable to the rate of crystal growth, and points to the danger in attempting to grow compositionally uniform materials from a nearly convectionless melt.

Harriott, George M.↗

NASA NTRS1993

A flux-limited treatment for the conductive evaporation of spherical interstellar gas clouds

In this work, we present and analyze a new analytic solution for the saturated (flux-limited) thermal evaporation of a spherical cloud. This work is distinguished from earlier analytic studies by allowing the thermal conductivity to change continuously from a diffusive to a saturated form, in a manner usually employed only in numerical calculations. This closed form solution will be of interest as a computational benchmark. Using our calculated temperature profiles and mass-loss rates, we model the thermal evaporation of such a cloud under typical interstellar medium (ISM) conditions, with some restrictions. We examine the ionization structure of the cloud-ISM interface and evaluate column densities of carbon, nitrogen, oxygen, neon, and silicon ions toward the cloud. In accord with other investigations, we find that ionization equilibrium is far from satisfied under the assumed conditions. Since the inclusion of saturation effects in the heat flux narrows the thermal interface relative to its classical structure, we also find that saturation effects tend to lower predicted column densities.

Dalton, William W.↗

NASA NTRS2013

Extended Analytic Device Optimization Employing Asymptotic Expansion

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

Thermoelectric Generators↗

NASA NTRS1991

Reliability and availability modeling of coupled communication networks - A simplified modeling approach

The network-complexity of LANs and of LANs that are interconnected by bridges and routers poses a challenging reliability-modeling problem. The present effort toward these problems' solution attempts to simplify them by reducing their number of states through truncation and state merging, as suggested by Shooman and Laemmel (1990). Through the use of state merging, it becomes possible to reduce the Bateman-Cortes 161 state model to a two state model with a closed-form solution. In the case of coupled networks, a technique which allows for problem-decomposition must be used.

Shooman, Martin L.↗

NASA NTRS1987

A higher-order theory for geometrically nonlinear analysis of composite laminates

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Reddy, J. N.↗

NASA NTRS1992

Exact solutions for laminated composite cylindrical shells in cylindrical bending

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Yuan, F. G.↗

NASA NTRS1992

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Kane, James H.↗

NASA NTRS1991

Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions

Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.

Kane, James H.↗

NASA NTRS1999

Reactive Infiltration of Silicon Melt Through Microporous Amorphous Carbon Preforms

The kinetics of unidirectional capillary infiltration of silicon melt into microporous carbon preforms have been investigated as a function of the pore morphology and melt temperature. The infiltrated specimens showed alternating bands of dark and bright regions, which corresponded to the unreacted free carbon and free silicon regions, respectively. The decrease in the infiltration front velocity for increasing infiltration distances, is in qualitative agreement with the closed-form solution of capillarity driven fluid flow through constant cross section cylindrical pores. However, drastic changes in the thermal response and infiltration front morphologies were observed for minute differences in the preforms microstructure. This suggests the need for a dynamic percolation model that would account for the exothermic nature of the silicon-carbon chemical reaction and the associated pore closing phenomenon.

Sangsuwan, P.↗

NASA NTRS1986

An exact solution for the solidification of a liquid slab of binary mixture

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

Antar, B. N.↗

NASA NTRS1987

Analytical approach to peel stresses in bonded composite stiffened panels

A closed-form solution was obtained for the stresses and displacements of two bonded beams. A system of two fourth-order and two second-order differential equations with the associated boundary equations was determined using a variational work approach. A FORTRAN computer program was devised to solve for the eigenvalues and eigenvectors of this system and to calculate the coefficients from the boundary conditions. The results were then compared with NASTRAN finite-element solutions and shown to agree closely.

Barkey, Derek A.↗

NASA NTRS1980

Induced drag ideal efficiency factor of arbitrary lateral-vertical wing forms

A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.

Deyoung, J.↗

NASA NTRS1981

Sensitivity of optimum solutions to problem parameters

In an aircraft configuration optimization, the information of interest is the sensitivity of optimal block fuel consumption and wing aspect ratio and area, to variations of required range and payload. The objectives of this study are: (1) to show how the equations capable of yielding the sensitivity derivatives (the sensitivity equations) can be obtained for a constrained optimum regardless of the type of optimization algorithm that was used to arrive at the optimum point, (2) to review the solvability of the sensitivity equations and (3) to report on applications on structural optimization. Numerical examples, which demonstrate the sensitivity analysis, include a tubular column and a three-bar truss for which closed form solutions are obtained, a ten-bar truss that requires the use of a finite element analysis, and a thin-walled beam characterized by strongly nonlinear constraints for local buckling. It is concluded that a practically significant extrapolation accuracy may be obtained for a reasonably broad range of parameter changes; and that accuracy does not depend strongly on the degree of convergence of the optimum solution from which the sensitivity derivatives are obtained.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1992

Eigenvalue error analysis of viscously damped structures using a Ritz reduction method

The efficient solution of the eigenvalue problem that results from inserting passive dampers with variable stiffness and damping coefficients into a structure is addressed. Eigenanalysis of reduced models obtained by retaining a number of normal modes augmented with Ritz vectors corresponding to the static solutions resulting from the load patterns introduced by the dampers has been empirically shown to yield excellent approximations to the full eigenvalue problem. An analysis of this technique in the case of a single damper is presented. A priori and a posteriori error estimates are generated and tested on numerical examples. Comparison theorems with modally truncated models and a Markov parameter matching reduced-order model are derived. These theorems corroborate the heuristic that residual flexibility methods improve low-frequency approximation of the system. The analysis leads to other techniques for eigenvalue approximation. Approximate closed-form solutions are derived that include a refinement to eigenvalue derivative methods for approximation. An efficient Newton scheme is also developed. A numerical example is presented demonstrating the effectiveness of each of these methods.

Chu, Cheng-Chih↗

NASA NTRS2000

Transverse Stress Decay in a Specially Orthotropic Strip Under Localizing Normal Edge Loading

Solutions are presented for the stresses in a specially orthotropic infinite strip which is subjected to localized uniform normal loading on one edge while the other edge is either restrained against normal displacement only, or completely fixed. The solutions are used to investigate the diffusion of load into the strip and in particular the decay of normal stress across the width of the strip. For orthotropic strips representative of a broad range of balanced and symmetric angle-ply composite laminates, minimum strip widths are found that ensure at least 90% decay of the normal stress across the strip. In addition, in a few cases where, on the fixed edge the peak shear stress exceeds the normal stress in magnitude, minimum strip widths that ensure 90% decay of both stresses are found. To help in putting these results into perspective, and to illustrate the influence of material properties on load 9 orthotropic materials, closed-form solutions for the stresses in similarly loaded orthotropic half-planes are obtained. These solutions are used to generate illustrative stress contour plots for several representative laminates. Among the laminates, those composed of intermediate-angle plies, i.e., from about 30 degrees to 60 degrees, exhibit marked changes in normal stress contour shape with stress level. The stress contours are also used to find 90% decay distances in the half-planes. In all cases, the minimum strip widths for 90% decay of the normal stress exceed the 90% decay distances in the corresponding half-planes, in amounts ranging from only a few percent to about 50% of the half-plane decay distances. The 90% decay distances depend on both material properties and the boundary conditions on the supported edge.

Fichter, W. B.↗

NASA NTRS1989

First and second order convex approximation strategies in structural optimization

In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.

Fleury, C.↗

NASA NTRS1985

Downwash in the plane of symmetry of an elliptically loaded wing

A closed-form solution for the downwash in the plane of symmetry of an elliptically loaded line is given. This theoretical result is derived from Prandtl's lifting-line theory and assumes that: (1) a three-dimensional wing can be replaced by a straight lifting line, (2) this line is elliptically loaded, and (3) the trailing wake is a flat-sheet which does not roll up. The first assumption is reasonable for distances greater than about 1 chord from the wing aerodynamic center. The second assumption is satisfied by any combination of wing twist, spanwise camber variation, or planform that approximates elliptic loading. The third assumption is justified only for high-aspect-ratio wings at low lift coefficients and downstream distances less than about 1 span from the aerodynamic center. It is shown, however, that assuming the wake to be fully rolled up gives downwash values reasonably close to those of the flat-sheet solution derived in this paper. The wing can therefore be modeled as a single horseshoe vortex with the same lift and total circulation as the equivalent ellipticity loaded line, and the predicted downwash will be a close approximation independent of aspect ratio and lift coefficient. The flat-sheet equation and the fully rolled up wake equation are both one-line formulas that predict the upwash field in front of the wing, as well as the downwash field behind it. These formulas are useful for preliminary estimates of the complex aerodynamic interaction between two wings (i.e., canard, tandem wing, and conventional aircraft) including the effects of gap and stagger.

Phillips, J. D.↗