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NASA NTRS1992

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗

NASA NTRS1973

An approach to the analysis of performance of quasi-optimum digital phase-locked loops.

An approach to the analysis of performance of quasi-optimum digital phase-locked loops (DPLL's) is presented. An expression for the characteristic function of the prior error in the state estimate is derived, and from this expression an infinite dimensional equation for the prior error variance is obtained. The prior error-variance equation is a function of the communication system model and the DPLL gain and is independent of the method used to derive the DPLL gain. Two approximations are discussed for reducing the prior error-variance equation to finite dimension. The effectiveness of one approximation in analyzing DPLL performance is studied.

Polk, D. R.↗

NASA NTRS1983

A refined finite element for vibration analysis of twisted blades based on beam theory

A finite element method of discretizing beam segments of pretwisted rotating blades is presented. Employing the matrix displacement method, stiffness and mass properties are developed from basic mechanics of a pretwisted beam theory. By introducing the proper displacement functions, the effect of rotor blade rotational motion on the stiffness matrix is obtained systematically from the kinetic energy expression. Comparing with other beam elements the derivation of this element is more fundamental. This allows one to apply the same approach to more complicated problems including nonlinear effects or complex dynamic motions. Illustrative examples are given comparing numerical results with available data and other numerical solutions from rotating and nonrotating force fields. These examples show that accurate prediction of vibration frequencies for pretwisted blades can be obtained by employing a quite modest number of degrees of freedom.

Sisto, F.↗

NASA NTRS1989

Reflection of solar radiation by a cylindrical cloud

Potential applications of an analytic method for computing the solar radiation reflected by a cylindrical cloud are discussed, including studies of radiative transfer within finite clouds and evaluations of these effects on other clouds and on remote sensing problems involving finite clouds. The pattern of reflected sunlight from a cylindrical cloud as seen at a large distance has been considered and described by the bidirectional function method for finite cloud analysis, as previously studied theoretically for plane-parallel atmospheres by McKee and Cox (1974); Schmetz and Raschke (1981); and Stuhlmann et al. (1985). However, the lack of three-dimensional radiative transfer solutions for anisotropic scattering media have hampered theoretical investigations of bidirectional functions for finite clouds. The present approach permits expression of the directional variation of the radiation field as a spherical harmonic series to any desired degree and order.

Smith, G. L.↗

NASA NTRS1993

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Menart, J. A.↗

NASA NTRS2002

Fidelity of the Integrated Force Method Solution

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Hopkins, Dale↗

NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Shertzer, Janine↗

NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Shertzer, J.↗

NASA NTRS1984

A performability solution method for degradable nonrepairable systems

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

Furchtgott, D. G.↗

NASA NTRS1980

Nonlinear finite element analysis: An alternative formulation

A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.

Merazzi, S.↗

NASA NTRS1995

Advanced Multi-phase Flow CFD Model Development for Solid Rocket Motor Flowfield Analysis

A Navier-Stokes code, finite difference Navier-Stokes (FDNS), is used to analyze the complicated internal flowfield of the SRM (solid rocket motor) to explore the impacts due to the effects of chemical reaction, particle dynamics, and slag accumulation on the solid rocket motor (SRM). The particulate multi-phase flowfield with chemical reaction, particle evaporation, combustion, breakup, and agglomeration models are included in present study to obtain a better understanding of the SRM design. Finite rate chemistry model is applied to simulate the chemical reaction effects. Hermsen correlation model is used for the combustion simulation. The evaporation model introduced by Spalding is utilized to include the heat transfer from the particulate phase to the gase phase due to the evaporation of the particles. A correlation of the minimum particle size for breakup expressed in terms of the Al/Al2O3 surface tension and shear force was employed to simulate the breakup of particles. It is assumed that the breakup occurs when the Weber number exceeds 6. A simple L agglomeration model is used to investigate the particle agglomeration. However, due to the large computer memory requirements for the agglomeration model, only 2D cases are tested with the agglomeration model. The VOF (Volume of Fluid) method is employed to simulate the slag buildup in the aft-end cavity of the redesigned solid rocket motor (RSRM). Monte Carlo method is employed to calculate the turbulent dispersion effect of the particles. The flowfield analysis obtained using the FDNS code in the present research with finite rate chemical reaction, particle evaporation, combustion, breakup, agglomeration, and VOG models will provide a design guide for the potential improvement of the SRM including the use of materials and the shape of nozzle geometry such that a better performance of the SRM can be achieved. The simulation of the slag buildup in the aft-end cavity can assist the designer to improve the design of the RSRM geometry.

Liaw, Paul↗

NASA NTRS1982

Random element method for numerical modeling of diffusional processes

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Ghoniem, A. F.↗

NASA NTRS1998

Experimental Results and Issues on Equalization for Nonlinear Memory Channel: Pre-Cursor Enhanced Ram-DFE Canceler

This thesis investigates the effects of the High Power Amplifier (HPA) and the filters over a satellite or telemetry channel. The Volterra series expression is presented for the nonlinear channel with memory, and the algorithm is based on the finite-state machine model. A RAM-based algorithm operating on the receiver side, Pre-cursor Enhanced RAM-FSE Canceler (PERC) is developed. A high order modulation scheme , 16-QAM is used for simulation, the results show that PERC provides an efficient and reliable method to transmit data on the bandlimited nonlinear channel. The contribution of PERC algorithm is that it includes both pre-cursors and post-cursors as the RAM address lines, and suggests a new way to make decision on the pre-addresses. Compared with the RAM-DFE structure that only includes post- addresses, the BER versus Eb/NO performance of PERC is substantially enhanced. Experiments are performed for PERC algorithms with different parameters on AWGN channels, and the results are compared and analyzed. The investigation of this thesis includes software simulation and hardware verification. Hardware is setup to collect actual TWT data. Simulation on both the software-generated data and the real-world data are performed. Practical limitations are considered for the hardware collected data. Simulation results verified the reliability of the PERC algorithm. This work was conducted at NMSU in the Center for Space Telemetering and Telecommunications Systems in the Klipsch School of Electrical and Computer Engineering Department.

Yuan, Lu↗

NASA NTRS1988

Vibrational Power Flow Analysis of Rods and Beams

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

Wohlever, James Christopher↗

NASA NTRS1974

The diffusive idealization of charged particle transport in random magnetic fields

The transport of charged particles diffusing in a random magnetic field parallel to a relatively large guiding field is presented. The same coefficient of diffusion is obtained by three methods. Two corrections must be added to the expression in which the diffusive flux is proportional to the gradient of the density. Explicit expressions are given for a characteristic time and a characteristic length which describe the corrections. The well known divergence of the coefficient of diffusion, which is implied by the quasilinear analysis of pitch angle scattering, does not occur if the scattering rate is finite at 90 deg pitch angle. This effect is illustrated by formulas which give the coefficient of diffusion when the quasilinear expression is perturbed by a variable amount of isotropic scattering.

Earl, J. A.↗

NASA NTRS1987

Research in computational fluid dynamics

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Murman, Earll M.↗

NASA NTRS2020

Investigating Local Buckling and Plastic Collapse in Multifunctional Sandwich Composite Cores using a Unit Cell Method

The primary goal of developing analytical models of composite sandwich cores has been to obtain simple expressions for elastic and failure response to improve the rapid analysis of composite structures. An earlier investigation by the authors was made to verify the accuracy of widely-used analytical models that calculate equivalent elastic moduli of a uniform homogeneous single layer of material in place of the complex honeycomb core properties in sandwich composites. This transformation of elastic properties permits a coarsening of the finite element model (FEM) of the core to a fraction of the computational cost in simulating the original complex core architecture. In addition, the core was assumed constructed of multi-layered isotropic walls to support potential additional functionality beyond simple load-carrying capability.

Erik Saether↗

NASA NTRS1983

Sound radiation from a vibrating cylinder in flow

An alternative approach to the conventional manner of calculating net power output of a source by integrating the energy flux over a distant control surface is presented. The method gives a means of calculating source radiation by an integral only over the source region and eliminates the need for a possibly difficult flux integration. The radiator chosen here is a finite, open ended, cylindrical shell of negligible thickness in the presence of uniform axial flow. A homogeneous medium without external boundaries is assumed. An integral representation and, in the long wave length approximation, an analytical expression for the power radiated by the vibrating cylinder are obtained. The results show power radiation may be increased or decreased by the presence of flow, depending on the relationship between the wave number of the vibration and the size of the radiator. The result is compared with results for simpler geometries.

Smith, M.↗