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NASA NTRS1988

A fine grid finite element computation of two-dimensional high Reynolds number flows

A velocity-pressure-integrated mixed-interpolation Galerkin finite-element computation of the Navier-Stokes equations using the grids is presented. The velocity variables are interpolated using complete quadratic shape functions, and the pressure was interpolated using linear shape functions defined on a triangular element which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow at Reynolds number Re = 400-10,000 and a laminar backward-facing step flow at Re = 100-900 are presented. Many high-Re flows involve convection-dominated motion as well as diffusion-dominated motion in the flow domain. The computational results for both of the fluid motions compared favorably with high-accuracy finite-difference computational results and/or experimental data.

Kim, Sang-Wook↗

NASA NTRS1988

A unique set of micromechanics equations for high-temperature metal matrix composites

A unique set of micromechanic equations is presented for high-temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Hopkins, Dale A.↗

NASA NTRS1991

Gain in computational efficiency by vectorization in the dynamic simulation of multi-body systems

An improved technique for the identification and extraction of the exact quantities associated with the degrees of freedom at the element as well as the flexible body level is presented. It is implemented in the dynamic equations of motions based on the recursive formulation of Kane et al. (1987) and presented in a matrix form, integrating the concepts of strain energy, the finite-element approach, modal analysis, and reduction of equations. This technique eliminates the CPU intensive matrix multiplication operations in the code's hot spots for the dynamic simulation of the interconnected rigid and flexible bodies. A study of a simple robot with flexible links is presented by comparing the execution times on a scalar machine and a vector-processor with and without vector options. Performance figures demonstrating the substantial gains achieved by the technique are plotted.

Amirouche, F. M. L.↗

NASA NTRS1986

A general low frequency acoustic radiation capability for NASTRAN

A new capability called NASHUA is described for calculating the radiated acoustic sound pressure field exterior to a harmonically-excited arbitrary submerged 3-D elastic structure. The surface fluid pressures and velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After the fluid impedance is calculated, most of the required matrix operations are performed using the general matrix manipulation package (DMAP) available in NASTRAN. Far field radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. Other output quantities include the maximum sound pressure levels in each of the three coordinate planes, the rms and average surface pressures and normal velocities, the total radiated power and the radiation efficiency. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both uniform and nonuniform applied loads.

Everstine, G. C.↗

NASA NTRS1985

On the impact of initially stressed composite laminates

The impact response behavior of initially stressed composite laminates is investigated using the finite element method. An experimentally established contact law is incorporated into the finite element program. The Newmark time integration algorithm is used for solving the time dependent equations of the plate and the impactor. Numerical results, including the contact force history, deflection, and strain in the plate, are presented. Effects of impact velocity, initial stress, and the mass and size of the impactor are discussed.

Sun, C. T.↗

NASA NTRS1987

Coupled NASTRAN/boundary element formulation for acoustic scattering

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Everstine, Gordon C.↗

NASA NTRS1989

Finite element flow-thermal-structural analysis of aerodynamically heated leading edges

Hypersonic vehicles operate in a hostile aerothermal environment which has a significant impact on their aerothermostructural performance. Significant coupling occurs between the aerodynamic flow field, structural heat transfer, and structural response creating a multidisciplinary interaction. A long term goal of the Aerothermal Loads Branch at the NASA Langley Research Center is to develop a computational capability for integrated fluid, thermal and structural analysis of aerodynamically heated structures. The integrated analysis capability includes the coupling between the fluid and the structure which occurs primarily through the thermal response of the structure, because: (1) the surface temperature affects the external flow by changing the amount of energy absorbed by the structure, and (2) the temperature gradients in the structure result in structural deformations which alter the flow field and attendant surface pressures and heating rates. In the integrated analysis, a finite element method is used to solve: (1) the Navier-Stokes equations for the flow solution, (2) the energy equation of the structure for the temperature response, and (3) the equilibrium equations of the structure for the structural deformation and stresses.

Dechaumphai, Pramote↗

NASA NTRS1993

Shear and compression buckling analysis for anisotropic panels with centrally located elliptical cutouts

An approximate analysis for buckling of biaxial- and shear-loaded anisotropic panels with centrally located elliptical cutouts is presented in the present paper. The analysis is composed of two parts, a prebuckling analysis and a buckling analysis. The prebuckling solution is determined using Lekhnitskii's complex variable equations of plane elastostatics combined with a Laurent series approximation and a boundary collocation method. The buckling solution is obtained using the principle of minimum potential energy. A by-product of the minimum potential energy equation is an integral equation which is solved using Gaussian quadrature. Comparisons with documented experimental results and finite element analyses indicate that the approximate analysis accurately predicts the buckling loads of square biaxial- and shear-loaded panels having elliptical cutouts with major axes up to sixty percent of the panel width. Results of a parametric study are presented for shear- and compression-loaded rectangular anisotropic panels with elliptical cutouts. The effects of panel aspect ratio, cutout shape, cutout size, cutout orientation, laminate anisotropy, and combined loading on the buckling load are examined.

Britt, V. O.↗

NASA NTRS2001

Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis

Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.

Shertzer, J.↗

NASA NTRS1988

A constitutive material model for nonlinear finite element structural analysis using an iterative matrix approach

A unified numerical method for the integration of stiff time dependent constitutive equations is presented. The solution process is directly applied to a constitutive model proposed by Bodner. The theory confronts time dependent inelastic behavior coupled with both isotropic hardening and directional hardening behaviors. Predicted stress-strain responses from this model are compared to experimental data from cyclic tests on uniaxial specimens. An algorithm is developed for the efficient integration of the Bodner flow equation. A comparison is made with the Euler integration method. An analysis of computational time is presented for the three algorithms.

Koenig, Herbert A.↗

NASA NTRS1991

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility being the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements. Recent efforts have focused on reducing run time, improving accuracy and adding more boundary condition choices.

Klang, Eric C.↗

NASA NTRS1990

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility is the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements.

Owen, Vicki L.↗

NASA NTRS1990

Boundary element analysis of sound scattered by a moving surface

A solution for the acoustic field scattered from a uniformly moving rigid body in the presence of a harmonic incident source has been obtained using a boundary integral method. A derivation of the Kirchhoff formula given by Farassat and Myers (1988) for moving surfaces forms the basis for the analysis, and the development of a boundary integral method for the solution of scattering problems from moving rigid bodies is described. Finite elements are used in conjunction with the Galerkin method in order to solve the integral equation that results from the Kirchhoff formula when the observer point is placed on the moving body surface. Once appropriate surface field values are known they are inserted back into the formula in order to predict the field scattered off the body. Tests, including the so called superposition method, are carried out in order to validate the technique and to establish some confidence in its accuracy. Application of the superposition method to moving bodies is presented, and results of the two approaches are discussed. Sample calculations of scattering from a simple body are presented to illustrate the effects of variations in relevant parameters.

Myers, M. K.↗

NASA NTRS2003

A New Modular Approach for Tightly Coupled Fluid/Structure Analysis

Static aeroelastic computations are made using a C++ executive suitable for closely coupled fluid/structure interaction studies. The fluid flow is modeled using the Euler/Navier Stokes equations and the structure is modeled using finite elements. FORTRAN based fluids and structures codes are integrated under C++ environment. The flow and structural solvers are treated as separate object files. The data flow between fluids and structures is accomplished using I/O. Results are demonstrated for transonic flow over partially flexible surface that is important for aerospace vehicles. Use of this development to accurately predict flow induced structural failure will be demonstrated.

Guruswamy, Guru↗

NASA NTRS2003

An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design

A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.

Provenza, Andrew J.↗

NASA NTRS1995

A Hybrid Finite Element Method for Axisymmetric Waveguide fed Horns

A new method for finding radiation patterns and the reflection coefficients associated with an axisymmetric waveguide fed horn is presented. The approach is based on a hybrid finite element method (FEM) wherein the electromagnetic fields in the FEM region are coupled to the fields outside by two surface integral equations. Because of the local nature of the FEM, this formalism allows for the presence of inhomogeneities to be included in the problem domain. The matrix equation which results from the application of this method is shown to be complex-symmetric. It is, furthermore, diagonally dominant and sparse. Comparisons of calculated and measured data for two different horns show good agreement.

Hybrid↗

NASA NTRS2001

Integrated Thermal Response Tool for Earth Entry Vehicles

A system is presented for multi-dimensional, fully-coupled thermal response modeling of hypersonic entry vehicles. The system consists of a two-dimensional implicit thermal response, pyrolysis and ablation program (TITAN), a commercial finite-element thermal and mechanical analysis code (MARC), and a high fidelity Navier-Stokes equation solver (GIANTS). The simulations performed by this integrated system include hypersonic flow-field, fluid and solid interaction, ablation, shape change, pyrolysis gas generation and flow, and thermal response of heatshield and structure. The thermal response of the ablating and charring heatshield material is simulated using TITAN, and that of the underlying structural is simulated using MARC. The ablating heatshield is treated as an outer boundary condition of the structure, and continuity conditions of temperature and heat flux are imposed at the interface between TITAN and MARC. Aerothermal environments with fluid and solid interaction are predicted by coupling TITAN and GIANTS through surface energy balance equations. With this integrated system, the aerothermal environments for an entry vehicle and the thermal response of both the heatshield and the structure can be obtained simultaneously. Representative computations for a proposed blunt body earth entry vehicle are presented and discussed in detail.

Chen, Y.-K.↗

NASA NTRS2011

Large Ka-Band Slot Array for Digital Beam-Forming Applications

This work describes the development of a large Ka Band Slot Array for the Glacier and Land Ice Surface Topography Interferometer (GLISTIN), a proposed spaceborne interferometric synthetic aperture radar for topographic mapping of ice sheets and glaciers. GLISTIN will collect ice topography measurement data over a wide swath with sub-seasonal repeat intervals using a Ka-band digitally beamformed antenna. For technology demonstration purpose a receive array of size 1x1 m, consisting of 160x160 radiating elements, was developed. The array is divided into 16 sticks, each stick consisting of 160x10 radiating elements, whose outputs are combined to produce 16 digital beams. A transmit array stick was also developed. The antenna arrays were designed using Elliott's design equations with the use of an infinite-array mutual-coupling model. A Floquet wave model was used to account for external coupling between radiating slots. Because of the use of uniform amplitude and phase distribution, the infinite array model yielded identical values for all radiating elements but for alternating offsets, and identical coupling elements but for alternating positive and negative tilts. Waveguide-fed slot arrays are finding many applications in radar, remote sensing, and communications applications because of their desirable properties such as low mass, low volume, and ease of design, manufacture, and deployability. Although waveguide-fed slot arrays have been designed, built, and tested in the past, this work represents several advances to the state of the art. The use of the infinite array model for the radiating slots yielded a simple design process for radiating and coupling slots. Method of moments solution to the integral equations for alternating offset radiating slots in an infinite array environment was developed and validated using the commercial finite element code HFSS. For the analysis purpose, a method of moments code was developed for an infinite array of subarrays. Overall the 1x1 m array was found to be successful in meeting the objectives of the GLISTIN demonstration antenna, especially with respect to the 0.042deg, 1/10th of the beamwidth of each stick, relative beam alignment between sticks.

Rengarajan, Sembiam↗