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NASA NTRS1994

Radiation and scattering from cylindrically conformal printed antennas

Microstrip patch antennas offer considerable advantages in terms of weight, aerodynamic drag, cost, flexibility, and observables over more conventional protruding antennas. These flat patch antennas were first proposed over thirty years ago by Deschamps in the United States and Gutton and Baisinot in France. Such antennas have been analyzed and developed for planar as well as curved platforms. However, the methods used in these designs employ gross approximations, suffer from extreme computational burden, or require expensive physical experiments. The goal of this thesis is to develop accurate and efficient numerical modeling techniques which represent actual antenna structures mounted on curved surfaces with a high degree of fidelity. In this thesis, the finite element method is extended to cavity-backed conformal antenna arrays embedded in a circular, metallic, infinite cylinder. Both the boundary integral and absorbing boundary mesh closure conditions will be used for terminating the mesh. These two approaches will be contrasted and used to study the scattering and radiation behavior of several useful antenna configurations. An important feature of this study will be to examine the effect of curvature and cavity size on the scattering and radiation properties of wraparound conformal antenna arrays.

Kempel, Leo C.↗

NASA NTRS1996

Development of a Higher Order Laminate Theory for Modeling Composites with Induced Strain Actuators

A refined higher order plate theory is developed to investigate the actuation mechanism of piezoelectric materials surface bonded or embedded in composite laminates. The current analysis uses a displacement field which accurately accounts for transverse shear stresses. Some higher order terms are identified by using the conditions that shear stresses vanish at all free surfaces. Therefore, all boundary conditions for displacements and stresses are satisfied in the present theory. The analysis is implemented using the finite element method which provides a convenient means to construct a numerical solution due to the discrete nature of the actuators. The higher order theory is computationally less expensive than a full three dimensional analysis. The theory is also shown to agree well with published experimental results. Numerical examples are presented for composite plates with thicknesses ranging from thin to very thick.

Chattopadhyay, Aditi↗

NASA NTRS2001

The Use of Non-Standard Devices in Finite Element Analysis

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Schur, Willi W.↗

NASA NTRS2014

High Fidelity CFD Analysis and Validation of Rotorcraft Gearbox Aerodynamics Under Operational and Oil-Out Conditions

This document represents the evolving formal documentation of the NPHASE-PSU computer code. Version 3.15 is being delivered along with the software to NASA in 2013.Significant upgrades to the NPHASE-PSU have been made since the first delivery of draft documentation to DARPA and USNRC in 2006. These include a much lighter, faster and memory efficient face based front end, support for arbitrary polyhedra in front end, flow-solver and back-end, a generalized homogeneous multiphase capability, and several two-fluid modelling and algorithmic elements. Specific capability installed for the NASA Gearbox Windage Aerodynamics NRA are included in this version: Hybrid Immersed Overset Boundary Method (HOIBM) [Noack et. al (2009)] Periodic boundary conditions for multiple frames of reference, Fully generalized immersed boundary method, Fully generalized conjugate heat transfer, Droplet deposition, bouncing, splashing models, and, Film transport and breakup.

Gears↗

NASA NTRS1985

Algorithmic and theoretical results on computation of incompressible viscous flows by finite element methods

Primitive variable as well as streamfunction-vorticity and pure streamfunction formulations are discussed. For the primitive variable case alternative choices of the viscous stress term are shown to produce natural boundary conditions which are well suited for matching to various far field conditions. For the other cases recent analytical results, including error estimates are described, and an optical algorithm for pressure recovery as well as treatment for multiply connected domains are given.

Gunzburger, M. D.↗

NASA NTRS2004

A Simplified Mesh Deformation Method Using Commercial Structural Analysis Software

Mesh deformation in response to redefined or moving aerodynamic surface geometries is a frequently encountered task in many applications. Most existing methods are either mathematically too complex or computationally too expensive for usage in practical design and optimization. We propose a simplified mesh deformation method based on linear elastic finite element analyses that can be easily implemented by using commercially available structural analysis software. Using a prescribed displacement at the mesh boundaries, a simple structural analysis is constructed based on a spatially varying Young s modulus to move the entire mesh in accordance with the surface geometry redefinitions. A variety of surface movements, such as translation, rotation, or incremental surface reshaping that often takes place in an optimization procedure, may be handled by the present method. We describe the numerical formulation and implementation using the NASTRAN software in this paper. The use of commercial software bypasses tedious reimplementation and takes advantage of the computational efficiency offered by the vendor. A two-dimensional airfoil mesh and a three-dimensional aircraft mesh were used as test cases to demonstrate the effectiveness of the proposed method. Euler and Navier-Stokes calculations were performed for the deformed two-dimensional meshes.

Hsu, Su-Yuen↗

NASA NTRS1980

Theoretical determination of nozzle admittances using a finite element approach

A finite element method is used to predict the admittances of axisymmetric nozzles. It is assumed that the flow in the nozzle is isentropic and irrotational, and the disturbances are small so that linear analyses apply. An approximate, two dimensional compressible model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear wave equation. The differential form of the acoustic equation is transformed to an integral equation using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. A two-dimensional FEM using linear elements is used to solve the acoustic equation. A one dimensional FEM is also used to solve the reduced equation of Crocco, and the solution verifies the sufficiency of the boundary residual formulation. Comparison between computed admittances and experimental data is shown to be quite good.

Sigman, R. K.↗

NASA NTRS1993

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗

NASA NTRS1989

Prediction of the thermal environment and thermal response of simple panels exposed to radiant heat

A method of predicting the radiant heat flux distribution produced by a bank of tubular quartz heaters was applied to a radiant system consisting of a single unreflected lamp irradiating a flat metallic incident surface. In this manner, the method was experimentally verified for various radiant system parameter settings and used as a source of input for a finite element thermal analysis. Two finite element thermal analyses were applied to a thermal system consisting of a thin metallic panel exposed to radiant surface heating. A two-dimensional steady-state finite element thermal analysis algorithm, based on Galerkin's Method of Weighted Residuals (GFE), was formulated specifically for this problem and was used in comparison to the thermal analyzers of the Engineering Analysis Language (EAL). Both analyses allow conduction, convection, and radiation boundary conditions. Differences in the respective finite element formulation are discussed in terms of their accuracy and resulting comparison discrepancies. The thermal analyses are shown to perform well for the comparisons presented here with some important precautions about the various boundary condition models. A description of the experiment, corresponding analytical modeling, and resulting comparisons are presented.

Turner, Travis L.↗

NASA NTRS1995

Fast Multipole Methods for Three-Dimensional N-body Problems

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.

Koumoutsakos, P.↗

NASA NTRS1982

Acoustic propagation in rigid ducts with blockage

Acoustic levitation has been suggested for moving nonmagnetic material in furnaces for heat processing in space experiments. Basically, acoustic standing waves under resonant conditions are excited in the cavity of the furnace while the material blockage is located at a pressure node and thus at a maximum gradient. The position of the blockage is controlled by displacing the node as a result of frequency change. The present investigation is concerned with the effect of blockage on the longitudinal and transverse resonances of a cylindrical cavity, taking into account the results of a one-dimensional and three-dimensional (3-D) analysis. Based on a Green's function surface element method, 3-D analysis is tested experimentally and proved to be accurate over a wide range of geometric parameters and boundary shapes. The shift in resonance depends on the change in pressure gradient and duct shortening caused by the blockage.

El-Raheb, M.↗

NASA NTRS1984

3-D inelastic analysis methods for hot section components (base program)

A 3-D inelastic analysis methods program consists of a series of computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of combustor liners, turbine blades, and turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. These models are used to solve 3-D inelastic problems using linear approximations in the sense that stresses/strains and temperatures in generic modeling regions are linear functions of the spatial coordinates, and solution increments for load, temperature and/or time are extrapolated linearly from previous information. Three linear formulation computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), were developed and are described.

Wilson, R. B.↗

NASA NTRS1986

Preconditioned conjugate residual methods for the solution of spectral equations

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Wong, Y. S.↗

NASA NTRS1987

Advances in 3-D Inelastic Analysis Methods for hot section components

3-D Inelastic Analysis Methods are described. These methods consist of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, specialty finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this paper.

Chamis, Christos C.↗

NASA NTRS1992

Crustal deformation along the San Andreas, California

The goal is to achieve a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effects of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate, viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformation. Special focus is placed on the three dimensional time dependent surface deformation due to localized slippage in a elastic layer coupled to a visco-elastic substrate. The numerical analysis is based on a 3-D boundary element technique. Extension to visco-elastic coupling demands the derivation of 3-D time dependent Green's function. This method was applied to analyze the viscoelastic surface displacements due to a dislocated embedded patch. Surface uplift as a function of time and position are obtained. Comparisons between surface uplift for long and short dislocated patches are made.

Li, Victor C.↗

NASA NTRS1993

FEM/SINDA: Combining the strengths of NASTRAN, SINDA, I-DEAS, and PATRAN for thermal and structural analysis

This paper describes the interface/integration between FEM/SINDA, a general purpose geometry driven thermal analysis code, and the FEM software: I-DEAS, PATRAN, and NASTRAN. FEM/SINDA brings together the advantages of the finite element method to model arbitrary geometry and anisotropic materials and SINDA's finite difference capability to model thermal properties, loads, and boundary conditions that vary with time or temperature. I-DEAS and PATRAN thermal entities are directly supported since FEM/SINDA uses the nodes of the FEM model as the point at which the temperature is determined. Output from FEM/SINDA (as well as the FEM/SINDA input deck) can be used directly by NASTRAN for structural analysis.

Zarda, P. Richard↗

NASA NTRS1995

Alaska Crustal Deformation: Finite Element Modeling Constrained by Geologic and Very Long Baseline Interferometry Data

We compute crustal motions in Alaska by calculating the finite element solution for an elastic spherical shell problem. The method we use allows the finite element mesh to include faults and very long baseline interferometry (VLBI) baseline rates of change. Boundary conditions include Pacific-North American (PA-NA) plate motions. The solution is constrained by the oblique orientation of the Fairweather-Queen Charlotte strike-slip faults relative to the PA-NA relative motion direction and the oblique orientation from normal convergence of the eastern Aleutian trench fault systems, as well as strike-shp motion along the Denali and Totschunda fault systems. We explore the effects that a range of fault slip constraints and weighting of VLBI rates of change has on the solution. This allows us to test the motion on faults, such as the Denali fault, where there are conflicting reports on its present-day slip rate. We find a pattern of displacements which produce fault motions generally consistent with geologic observations. The motion of the continuum has the general pattern of radial movement of crust to the NE away from the Fairweather-Queen Charlotte fault systems in SE Alaska and Canada. This pattern of crustal motion is absorbed across the Mackenzie Mountains in NW Canada, with strike-slip motion constrained along the Denali and Tintina fault systems. In south central Alaska and the Alaska forearc oblique convergence at the eastern Aleutian trench and the strike-shp motion of the Denali fault system produce a counterclockwise pattern of motion which is partially absorbed along the Contact and related fault systems in southern Alaska and is partially extruded into the Bering Sea and into the forearc parallel the Aleutian trench from the Alaska Peninsula westward. Rates of motion and fault slip are small in western and northern Alaska, but the motions we compute are consistent with the senses of strike-slip motion inferred geologically along the Kaltag, Kobuk Trench, and Thompson Creek faults and with the normal faulting observed in NW Alaska near Nome. The nonrigid behavior of our finite element solution produces patterns of motion that would not have been expected from rigid block models: strike-slip faults can exist in a continuum that has motion mostly perpendicular to their strikes, and faults can exhibit along-strike differences in magnitudes and directions.

Lundgren, Paul↗

NASA NTRS2006

Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method

Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.

Chang, Chau-Lyan↗