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NASA NTRS1988

Spectral element methods - Algorithms and architectures

Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered; the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling.

Fischer, Paul↗

NASA NTRS1991

User's guide to a system of finite-element supersonic panel flutter programs

The utilization and operation of a set of six computer programs for the prediction of panel flutter at supersonic speeds by finite element methods are described. The programs run individually to determine the flutter behavior of a flat panel where the finite elements which model the panel each have four degrees of freedom (DOF), a curved panel where the finite elements each have four DOF, and a curved panel where the finite elements each have six DOF. The panels are assumed to be of infinite aspect ratio and are subjected to either simply-supported or clamped boundary conditions. The aerodynamics used by these programs are based on piston theory. Application of the program is illustrated by sample cases where the number of beam finite elements equals four, the in-plane tension parameter is 0.0, the maximum camber to panel length ratio for a curved panel case is 0.05, and the Mach number is 2.0. This memorandum provides a user's guide for these programs, describes the parameters that are used, and contains sample output from each of the programs.

Woolley, Christine L.↗

NASA NTRS2003

Modeling of 3-D Woven Ceramic Matrix Composites

Three different approaches are being pursued at the NASA Glenn Research Center to predict the nanostructural behavior of three-dimensional woven ceramic matrix composites. These are: a micromechanics-based approach using W-CEMCAN (Woven Ceramic Matrix Composite Analyzer), a laminate analogy method and a structural frame approach (based on the finite element method). All three techniques are applied to predict the thermomechanical properties of a three-dimensional woven angle interlock C/SiC composite. The properties are predicted for room temperature and 1100 C and the predicted properties are compared to measurements. General observations regarding the three approaches for three-dimensional composite modeling are discussed.

Murthy, Pappu L. N.↗

NASA NTRS2005

Multiscale Modeling for the Analysis for Grain-Scale Fracture Within Aluminum Microstructures

Multiscale modeling methods for the analysis of metallic microstructures are discussed. Both molecular dynamics and the finite element method are used to analyze crack propagation and stress distribution in a nanoscale aluminum bicrystal model subjected to hydrostatic loading. Quantitative similarity is observed between the results from the two very different analysis methods. A bilinear traction-displacement relationship that may be embedded into cohesive zone finite elements is extracted from the nanoscale molecular dynamics results.

Glaessgen, Edward H.↗

NASA NTRS1988

Three-dimensional inelastic approximate analysis code (MOMM)

The Mechanics of Materials Model (MOMM) is one of a series of new stand-alone three dimensional nonlinear structural analysis codes. Incorporation of a general purpose finite element computer code into the hot section design process was severely limited by the high costs involved. MOMM is a stiffness method finite element code that uses an internally generated network of beams to characterize hot section component behavior. The method was proposed as a fast, easy to use, computationally efficient tool for approximate analyses. MOMM incorporates a wide variety of analysis capabilities, material models, and load type specifiers instrumental for the analysis of hot section components.

Meister, Jeffrey P.↗

NASA NTRS1988

Stability sensitivity analysis for the aeroelastic optimization of a helicopter rotor

A sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method. Structural design variables include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity, and blade bending stiffnesses (flap, lag and torsion). The formulation for blade steady response is based on a finite element method in space and time. The vehicle trim and blade steady response are calculated iteratively as one coupled solution using a modified Newton method. Eigenvalues corresponding to different blade modes are calculated using Floquet transition matrix theory. The formulation for derivatives of the eigenvalues with respect to design variables is implemented using a direct analytical approach (chain rule differentiation), and constitutes an integral part of the regular stability analysis. The stability sensitivity derivatives were obtained at a fraction of computation time compared to the frequently adopted finite difference method. A parametric study showed that nonstructural mass and chordwise cg offset of outboarad elements, and lag bending stiffness of inboard elements, have powerful influence on blade stability.

Lim, Joon W.↗

NASA NTRS1984

Performance of the h, p and h-p versions

There are three basic versions of the finite element method, called the h, p and h-p versions. They are characterized by the way in which the finite element meshes and polynomial degree of elements are chosen. They differ in computer implementation (program architecture) and mathematical analysis. The manner in which the meshes and polynomial degree of the elements affect the accuracy of finite element solutions is examined. The approach is to fix certain parameters and increase the number of degrees of freedom so that the finie element solutions converge to the exact solution. Such a systematic increase of the number of degrees of freedom is called extension because it can be interpreted as a systematic extension of finite element spaces.

Babuska, I.↗

NASA NTRS1996

Conceptual Design Oriented Wing Structural Analysis and Optimization

Airplane optimization has always been the goal of airplane designers. In the conceptual design phase, a designer's goal could be tradeoffs between maximum structural integrity, minimum aerodynamic drag, or maximum stability and control, many times achieved separately. Bringing all of these factors into an iterative preliminary design procedure was time consuming, tedious, and not always accurate. For example, the final weight estimate would often be based upon statistical data from past airplanes. The new design would be classified based on gross characteristics, such as number of engines, wingspan, etc., to see which airplanes of the past most closely resembled the new design. This procedure works well for conventional airplane designs, but not very well for new innovative designs. With the computing power of today, new methods are emerging for the conceptual design phase of airplanes. Using finite element methods, computational fluid dynamics, and other computer techniques, designers can make very accurate disciplinary-analyses of an airplane design. These tools are computationally intensive, and when used repeatedly, they consume a great deal of computing time. In order to reduce the time required to analyze a design and still bring together all of the disciplines (such as structures, aerodynamics, and controls) into the analysis, simplified design computer analyses are linked together into one computer program. These design codes are very efficient for conceptual design. The work in this thesis is focused on a finite element based conceptual design oriented structural synthesis capability (CDOSS) tailored to be linked into ACSYNT.

Lau, May Yuen↗

NASA NTRS1987

A finite element model for sound transmission through laminated composite plates

The finite element method is used to model the noise transmission through unstiffened and stiffened laminated composite panels of finite size into a closed cavity. Plate and acoustic finite elements are coupled and the frequencies of the coupled modes are determined. The model is then used to calculate the noise reduction of the panel. Results are compared to experimental values obtained at the NASA Langley Research Center. The purpose of this paper is to demonstrate the use of finite elements to model, for noise transmission calculations, complex structures, such as a stiffened composite panel or a composite panel with windows.

Ramakrishnan, J. V.↗

NASA NTRS1989

Computational Methods for Structural Mechanics and Dynamics

Topics addressed include: transient dynamics; transient finite element method; transient analysis in impact and crash dynamic studies; multibody computer codes; dynamic analysis of space structures; multibody mechanics and manipulators; spatial and coplanar linkage systems; flexible body simulation; multibody dynamics; dynamical systems; and nonlinear characteristics of joints.

Stroud, W. Jefferson↗

NASA NTRS2003

A Computationally Efficient Meshless Local Petrov-Galerkin Method for Axisymmetric Problems

The Meshless Local Petrov-Galerkin (MLPG) method is one of the recently developed element-free methods. The method is convenient and can produce accurate results with continuous secondary variables, but is more computationally expensive than the finite element method. To overcome this disadvantage, a simple Heaviside test function is chosen. The computational effort is significantly reduced by eliminating the domain integral for the axisymmetric potential problems and by simplifying the domain integral for the axisymmetric elasticity problems. The method is evaluated through several patch tests for axisymmetric problems and example problems for which the exact solutions are available. The present method yielded very accurate solutions. The sensitivity of several parameters of the method is also studied.

Raju, I. S.↗

NASA NTRS1975

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗

NASA NTRS1982

Development of a reduced basis technique for transient thermal analysis

A technique to reduce the degrees of freedom in static and dynamic problems, the reduced basis method, is described. The method combines the classical Rayleigh-Ritz approximation with contemporary finite element methods to retain modeling versatility as the degrees of freedom are reduced. Applications to a nonlinear dynamic response problem are discussed efforts to apply the method to nonlinear transient thermal response problems are summarized. The selection of basis vectors for reducing the system of equations is addressed.

Shore, C. P.↗

NASA NTRS1987

A general method for dynamic analysis of structures overview

The presented research deals with the development of a dynamic analysis method for structural systems. The modeling approach is essentially a finite element method in the sense that the structure is divided into n elements. An element is defined as any structural unit whose degree of freedom (dofs) can be categorized as either interface or non-interface dofs. An element could be a fundamental unit such as a rod, a beam, a plate etc., or it could be an entire structural component. Furthermore, the parameters for the element could be distributed or lumped. The choice of elements is totally arbitrary and is a matter of user convenience. In particular, issues of accuracy and convergence do not enter on the level of example that bookkeeping is reduced to a minimum. Each element is modeled using a set of interface constraint modes (ICM) combined with a set of interface restrained normal models (IRNM). The next step is the solution of the system eigenvalue problem. The procedure calls for the sequential solution of a number of small eigenvalue problems based on a truncation principle for IRNM. In addition, the form of these eigenvalue problems is very simple such that an escalator type of eigenvalue problem solver can be used which is extremely cost-effective and fast.

Engels, Remi C.↗

NASA NTRS2003

Three-Dimensional Magnetic Analysis Technique Developed for Evaluating Stirling Convertor Linear Alternators

The Department of Energy, the Stirling Technology Company (STC), and the NASA Glenn Research Center are developing Stirling convertors for Stirling radioisotope generators to provide electrical power for future NASA deep space missions. STC is developing the 55-We technology demonstration convertor (TDC) under contract to the Department of Energy. The Department of Energy recently named Lockheed Martin as the system integration contractor for the Stirling radioisotope generator development project. Lockheed Martin will develop the Stirling radioisotope generator engineering unit and has contract options to develop the qualification unit and the first flight unit. Glenn s role includes an in-house project to provide convertor, component, and materials testing and evaluation in support of the overall power system development. As a part of this work, Glenn has established an in-house Stirling research laboratory for testing, analyzing, and evaluating Stirling machines. STC has built four 55-We convertors for NASA, and these are being tested at Glenn. A cross-sectional view of the 55-We TDC is shown in the figure. Of critical importance to the successful development of the Stirling convertor for space power applications is the development of a lightweight and highly efficient linear alternator. In support, Glenn has been developing finite element analysis and finite element method tools for performing various linear alternator thermal and electromagnetic analyses and evaluating design configurations. A three-dimensional magnetostatic finite element model of STC's 55-We TDC linear alternator was developed to evaluate the demagnetization fields affecting the alternator magnets. Since the actual linear alternator hardware is symmetric to the quarter section about the axis of motion, only a quarter section of the alternator was modeled. The components modeled included the mover laminations, the neodymium-iron-boron magnets, the stator laminations, and the copper coils. The three-dimensional magnetostatic model was then coupled with a circuit simulator model of the alternator load and convertor controller. The coupled model was then used to generate alternator terminal voltage and current predictions. The predicted voltage and current waveforms agreed well with the experimental data, which tended to validate the accuracy of the coupled model. The model was then used to generate predictions of the demagnetization fields acting on the alternator magnets for the alternator under load. The preliminary model predictions indicate that the highest potential for demagnetization is along the inside surface of the uncovered magnets. The demagnetization field for the uncovered magnets when the mover is positioned at the end of a stroke is higher than it is when the mover is at the position of maximum induced voltage or maximum alternator current. Assuming normal load conditions, the model predicted that the onset of demagnetization is most likely to occur for magnet temperatures above 101 C.

Geng, Steven M.↗

NASA NTRS2000

Determination of the Fracture Parameters in a Stiffened Composite Panel

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Lin, Chung-Yi↗

NASA NTRS1986

Least squares finite element simulation of transonic flows

Finite difference approximation of transonic flow problems is a well-developed and largely successful approach. Nevertheless, there is still a real need to develop finite element methods for applications arising from fluid-structure interactions and problems with complicated boundaries. In this paper a least squares based finite element scheme is introduced. It is shown that, if suitably formulated, such an approach can lead to physically meaningful results. Bottlenecks that arise from such schemes are also discussed.

Chen, T. F.↗

NASA NTRSDate not supplied

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗