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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Hybrid techniques for complex aerospace electromagnetics problems

Important aerospace electromagnetics problems include the evaluation of antenna performance on aircraft and the prediction and control of the aircraft's electromagnetic signature. Due to the ever increasing complexity and expense of aircraft design, aerospace engineers have become increasingly dependent on computer solutions. Traditionally, computational electromagnetics (CEM) has relied primarily on four disparate techniques: the method of moments (MoM), the finite-difference time-domain (FDTD) technique, the finite element method (FEM), and high frequency asymptotic techniques (HFAT) such as ray tracing. Each of these techniques has distinct advantages and disadvantages, and no single technique is capable of accurately solving all problems of interest on computers that are available now or will be available in the foreseeable future. As a result, new approaches that overcome the deficiencies of traditional techniques are beginning to attract a great deal of interest in the CEM community. Among these new approaches are hybrid methods which combine two or more of these techniques into a coherent model. During the ASEE Summer Faculty Fellowship Program a hybrid FEM/MoM computer code was developed and applied to a geometry containing features found on many modern aircraft.

Aberle, Jim↗
NASA NTRS1997

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick↗
NASA NTRS2002

Predicting Print-thru for the Sub-scale Beryllium Mirror Demonstrator (SBMD)

This document presents a finite element method for predicting print-thru or quilting for a lightweight mirror in a low temperature environment. The mirror is represented with quadrilateral and triangular plate finite elements. The SBMD (Sub-scale Beryllium Mirror Demonstrator) is circular with a diameter of 50 cm and one flat side. The mirror structure is a thin-wall triangular cell core with a single facesheet. There is a 4 mm radius fillet between the facesheet and cell walls. It is made entirely of Beryllium. It is assumed that polishing the mirror surface creates a thin surface layer with different material properties. Finite element results are compared with measured values at cryogenic temperatures.

Craig, Larry↗
NASA NTRS1991

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Cockburn, Bernardo↗
NASA NTRS1997

Modeling of Structural-Acoustic Interaction Using Coupled FE/BE Method and Control of Interior Acoustic Pressure Using Piezoelectric Actuators

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural-acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the acoustic domain. Results for a system consisting of an isotropic panel and a cubic cavity are in good agreement with exact solutions and experiment data. The response of a composite panel backed cavity is then obtained. The results show that the mass and stiffness of piezoelectric layers have to be considered. The coupled finite element and boundary element equations are transformed into modal coordinates, which is more convenient for transient excitation. Several transient problems are solved based on this formulation. Two control designs, a linear quadratic regulator (LQR) and a feedforward controller, are applied to reduce the acoustic pressure inside the cavity based on the equations in modal coordinates. The results indicate that both controllers can reduce the interior acoustic pressure and the plate deflection.

Mei, Chuh↗
NASA NTRS1978

Planar scarf joints in composite repair

This study examined the effects of varying certain important geometric parameters on the stresses in an adhesive repair of a thin composite laminate. The repair, a planar scarf joint with a doubler, was studied using finite element methods at scarf angles of 6 deg and 12 deg, damage lengths between 2.5 mm and 25 mm and doubler overlaps between 10 mm and 40 mm. Finite element models also showed that significant stress peaks occur at the ends of the scarf joint adhesive, similar to shear lag phenomena in lap joints. A bending model of the planar scarf joint with a doubler, based on mechanics of materials theory, was also developed.

Adkins, D. W.↗
NASA NTRS1987

Design of Software for Design of Finite Element for Structural Analysis

The concepts of software engineering which allow a user of the finite element method to describe a model, to collect and to check the model data in a data base as well as to form the matrices required for a finite element calculation are examined. Next the components of the model description are conceived including the mesh tree, the topology, the configuration, the kinematic boundary conditions, the data for each element, and the loads. The possibilities for description and review of the data are considered. The concept of the segments for the modularization of the programs follows the components of the model description. The significance of the mesh tree as a globular guiding structure will be understood in view of the principle of the unity of the model, the mesh tree, and the data base. The user-friendly aspects of the software system will be summarized: the principle of language communication, the data generators, error processing, and data security.

Helfrich, Reinhard↗
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1993

A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

Bey, Kim S.↗
NASA NTRS1993

A comparison of viscoelastic damping models

Modern finite element methods (FEM's) enable the precise modeling of mass and stiffness properties in what were in the past overwhelmingly large and complex structures. These models allow the accurate determination of natural frequencies and mode shapes. However, adequate methods for modeling highly damped and high frequency dependent structures did not exist until recently. The most commonly used method, Modal Strain Energy, does not correctly predict complex mode shapes since it is based on the assumption that the mode shapes of a structure are real. Recently, many techniques have been developed which allow the modeling of frequency dependent damping properties of materials in a finite element compatible form. Two of these methods, the Golla-Hughes-McTavish method and the Lesieutre-Mingori method, model the frequency dependent effects by adding coordinates to the existing system thus maintaining the linearity of the model. The third model, proposed by Bagley and Torvik, is based on the Fractional Calculus method and requires fewer empirical parameters to model the frequency dependence at the expense of linearity of the governing equations. This work examines the Modal Strain Energy, Golla-Hughes-McTavish and Bagley and Torvik models and compares them to determine the plausibility of using them for modeling viscoelastic damping in large structures.

Slater, Joseph C.↗
NASA NTRS1985

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Noor, A. K.↗
NASA NTRS1971

Design of optical mirror structures

The structural requirements for large optical telescope mirrors was studied with a particular emphasis placed on the three-meter Large Space Telescope primary mirror. Analysis approaches through finite element methods were evaluated with the testing and verification of a number of element types suitable for particular mirror loadings and configurations. The environmental conditions that a mirror will experience were defined and a candidate list of suitable mirror materials with their properties compiled. The relation of the mirror mechanical behavior to the optical performance is discussed and a number of suitable design criteria are proposed and implemented. A general outline of a systematic method to obtain the best structure for the three-meter diffraction-limited system is outlined. Finite element programs, using the STRUDL 2 analysis system, were written for specific mirror structures encompassing all types of active and passive mirror designs. Parametric studies on support locations, effects of shear deformation, diameter to thickness ratios, lightweight and sandwich mirror configurations, and thin shell active mirror needs were performed.

Soosaar, K.↗
NASA NTRS1985

Quantification of Saint-Venant's principle for a general prismatic member

A method to quantify Saint-Venant's principle for general prismatic members is described. Finite elements are used to model the member cross-section to allow the analysis of arbitrary geometries, material properties, and nonhomogeneities. The variation in the structural response along the member's length, away from the loaded end, is modelled with an exponential decay which has been established in the literature to be the correct form. Many analytic results exist in the literature for special cases. Because of its ability to handle arbitrary cross sectional geometries, this semi-analytic finite element method can provide a firm footing for the utilization of Saint-Venant's principle for whole new classes of problems. Results for several typical problems are given.

Goetschel, D. B.↗
NASA NTRS1990

ENSAERO - A multidisciplinary program for fluid/structural interaction studies of aerospace vehicles

A computational procedure is developed that uses a moving zonal grid concept to model complex flexible aerospace vehicles. The Euler/Navier-Stokes equations are used to model the flow, and computations are made using efficient methods based on both central and upwind schemes. The structure is represented by a finite element method which can model general aerospace vehicles. Provisions are made to accommodate other disciplines such as controls and thermal loads. The code is capable of computing unsteady flows on flexible wings with vortical flows. Adaptation of this procedure for parallel processing and validation for complete aerospace configurations is in progress.

Guruswamy, G. P.↗
NASA NTRS2014

Computational Design of Materials: Planetary Entry to Electric Aircraft and Beyond

NASA's projects and missions push the bounds of what is possible. To support the agency's work, materials development must stay on the cutting edge in order to keep pace. Today, researchers at NASA Ames Research Center perform multiscale modeling to aid the development of new materials and provide insight into existing ones. Multiscale modeling enables researchers to determine micro- and macroscale properties by connecting computational methods ranging from the atomic level (density functional theory, molecular dynamics) to the macroscale (finite element method). The output of one level is passed on as input to the next level, creating a powerful predictive model.

Materials Design↗
NASA NTRS1991

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Stoll, Frederick↗