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At least 433 records · Page 24

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NASA NTRS1980

A new look at numerical analyses of free-edge stresses in composite laminates

The edge stress problem for a + or - 45 deg graphite/epoxy laminate was examined. The reliability of the displacement formulated finite element method in analyzing the edge stress problem was investigated. Analyses of two well known elasticity problems, one involving a stress discontinuity and one a singularity, showed that the finite element analysis yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity of singularity. Stress distributions for a + or - 45 deg laminate showed the same behavior near the singularity found in the well known problems with exact solutions. The displacement formulated finite element method appears to be a highly accurate technique for calculating interlaminar stress in composite laminates. The disagreement among the numerical methods was attributed to the unsymmetric stress tensor at the singularity.

Raju, I. S.↗

NASA NTRS1981

Pull-out fibers from composite materials at high rate of loading

Numerical and experimental results are presented on the pullout phenomenon in composite materials at a high rate of loading. The finite element method was used, taking into account the existence of a virtual shear deformation layer as the interface between fiber and matrix. Experimental results agree well with those obtained by the finite element method. Numerical results show that the interlaminar shear stress is time dependent, in addition, it is shown to depend on the applied load time history. Under step pulse loading, the interlaminar shear stress fluctuates, finally decaying to its value under static loading.

Amijima, S.↗

NASA NTRS1986

An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry

High-order (p-type) finite element methods combine the geometric flexibility of standard low-order finite element (or finite volume) techniques with the rapid convergence properties of spectral methods. Various p-type schemes have been proposed for elliptic problems. However, an application of p-type methods to more complex equations, in particular the passive scalar or Navier-Stokes equations, is complicated by the nature of the equations and by efficiency considerations as regards the solution procedure. Patera (1984) has proposed a p-type method for the Navier-Stokes equations, taking into account the arising additional complications. The present study is concerned with an isoparametric spectral element discretization for the solution of flow problems in fully general, curvy geometries. Attention is given to the isoparametric formulation for elliptic equations and a time-splitting scheme for the Navier-Stokes equations.

Korczak, K. Z.↗

NASA NTRS1993

The NASA/industry Design Analysis Methods for Vibrations (DAMVIBS) program: Boeing Helicopters airframe finite element modeling

Mathematical models based on the finite element method of structural analysis, as embodied in the NASTRAN computer code, are routinely used by the helicopter industry to calculate airframe static internal loads used for sizing structural members. Historically, less reliance has been placed on the vibration predictions based on these models. Beginning in the early 1980's NASA's Langley Research Center initiated an industry wide program with the objective of engendering the needed trust in vibration predictions using these models and establishing a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process. Emphasis in this paper is placed on the successful modeling of the Army/Boeing CH-47D which showed reasonable correlation with test data. A principal finding indicates that improved dynamic analysis requires greater attention to detail and perhaps a finer mesh, especially the mass distribution, than the usual stress model. Post program modeling efforts show improved correlation placing key modal frequencies in the b/rev range with 4 percent of the test frequencies.

Gabel, R.↗

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 NTRS2004

A Discontinuous Galerkin Method for Parabolic Problems with Modified hp-Finite Element Approximation Technique

A recent paper is generalized to a case where the spatial region is taken in R(sup 3). The region is assumed to be a thin body, such as a panel on the wing or fuselage of an aerospace vehicle. The traditional h- as well as hp-finite element methods are applied to the surface defined in the x - y variables, while, through the thickness, the technique of the p-element is employed. Time and spatial discretization scheme based upon an assumption of certain weak singularity of double vertical line u(sub t) double vertical line 2, is used to derive an optimal a priori error estimate for the current method.

Kaneko, Hideaki↗

NASA NTRS2002

Meshless Local Petrov-Galerkin Method for Bending Problems

Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.

Phillips, Dawn R.↗

DOE OSTI2025

A Domain-Decomposed A-ϕ Formulation Based on Lagrange Multipliers for Low-Frequency Problems

A domain-decomposed A-ϕ formulation based on Lagrange multipliers is proposed to simulate low-frequency elec- tromagnetic problems. This method partitions the computational domain into smaller subdomains, allowing each subdomain to be independently formulated using Lagrange multipliers as Dirichlet boundary conditions, while ensuring continuity of the fields across the interfaces. A mixed finite element method, utilizing both vector and scalar basis functions, is employed to discretize the formulation, resulting in a global system to be solved. The proposed method is validated using TEAM Problem 7 at 50 Hz, demonstrating its effectiveness in handling complex geometries and addressing the low-frequency breakdown issues commonly encountered in traditional finite element methods.

Hossain, Amzad↗

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 NTRS1988

Use of adjoint methods in the probabilistic finite element approach to fracture mechanics

The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.

Liu, Wing Kam↗

NASA NTRS1989

A Navier-Stokes solver for high speed equilibrium flows and application to blunt bodies

This paper presents a finite element method for the solution of Navier-Stokes equations with the assumption of thermodynamic and chemical equilibrium. The method employs an upwind finite element technique with an implicit time-marching scheme for the solution, and uses an adaptively generated unstructured triangular mesh with several layers of quadrilateral elements near solid walls. The complexity associated with the assumption that the flow is in equilibrium is treated consistently, and the inviscid flux Jacobian matrices are derived. Several problems involving inviscid and viscous hypersonic flow past blunt are solved. Results are compared with other numerical results and experimental data, and generally good agreement is observed.

Prabhu, Ramadas K.↗

NASA NTRS2001

Comparison of Two Acoustic Waveguide Methods for Determining Liner Impedance

Acoustic measurements taken in a flow impedance tube are used to assess the relative accuracy of two waveguide methods for impedance eduction in the presence of grazing flow. The aeroacoustic environment is assumed to contain forward and backward-traveling acoustic waves, consisting of multiple modes, and uniform mean flow. Both methods require a measurement of the complex acoustic pressure profile over the length of the test liner. The Single Mode Method assumes that the sound pressure level and phase decay-rates of a single progressive mode can be extracted from this measured complex acoustic pressure profile. No a priori assumptions are made in the Finite Element. Method regarding the modal or reflection content in the measured acoustic pressure profile. The integrity of each method is initially demonstrated by how well their no-flow impedances match those acquired in a normal incidence impedance tube. These tests were conducted using ceramic tubular and conventional perforate liners. Ceramic tubular liners were included because of their impedance insensitivity to mean flow effects. Conversely, the conventional perforate liner was included because its impedance is known to be sensitive to mean flow velocity effects. Excellent comparisons between impedance values educed with the two waveguide methods in the absence of mean flow and the corresponding values educed with the normal incident impedance tube were observed. The two methods are then compared for mean flow Mach numbers up to 0.5, and are shown to give consistent results for both types of test liners. The quality of the results indicates that the Single Mode Method should be used when the measured acoustic pressure profile is clearly dominated by a single progressive mode, and the Finite Element Method should be used for all other cases.

Jones, Michael G.↗

NASA NTRS1992

Finite element simulations involving simultaneous multiple interface fronts in phase change problems

The present paper describes the simulation of phase change problems involving simultaneous multiple interface fronts employing the finite element method. Much of the past investigations employing finite elements have been restricted to primarily a single phase change situation. The existence of more than one phase, that is, the presence of multiple phase fronts poses certain challenges and further complications. However, the results provide a very interesting thermal behavior for this class of problems. In this paper, attention is focused on fixed grid methods and the trapezoidal family of one-step methods using the enthalpy formulations. Illustrative examples which handle simultaneous multiple fronts in phase change problems are presented.

Ouyang, Tianhong↗

NASA NTRS1988

Prediction of high temperature metal matrix composite ply properties

The application of the finite element method (superelement technique) in conjunction with basic concepts from mechanics of materials theory is demonstrated to predict the thermomechanical behavior of high temperature metal matrix composites (HTMMC). The simulated behavior is used as a basis to establish characteristic properties of a unidirectional composite idealized an as equivalent homogeneous material. The ply properties predicted include: thermal properties (thermal conductivities and thermal expansion coefficients) and mechanical properties (moduli and Poisson's ratio). These properties are compared with those predicted by a simplified, analytical composite micromechanics model. The predictive capabilities of the finite element method and the simplified model are illustrated through the simulation of the thermomechanical behavior of a P100-graphite/copper unidirectional composite at room temperature and near matrix melting temperature. The advantage of the finite element analysis approach is its ability to more precisely represent the composite local geometry and hence capture the subtle effects that are dependent on this. The closed form micromechanics model does a good job at representing the average behavior of the constituents to predict composite behavior.

Caruso, J. J.↗

NASA NTRS1973

An interactive graphics system to facilitate finite element structural analysis

The characteristics of an interactive graphics systems to facilitate the finite element method of structural analysis are described. The finite element model analysis consists of three phases: (1) preprocessing (model generation), (2) problem solution, and (3) postprocessing (interpretation of results). The advantages of interactive graphics to finite element structural analysis are defined.

Burk, R. C.↗

NASA NTRS1981

Finite element analyses of plane thermal entry-length flows

It is pointed out that the design of actively cooled engine and airframe structures for hypersonic flight requires strong interaction between fluid, thermal, and structural analyses. Research programs are being conducted to develop an integrated thermal-structural analysis capability based upon the finite element method. In connection with these programs, a finite element engineering approach has been developed based upon a number of assumptions customarily used in practical heat transfer analysis. An evaluation is conducted of the finite element engineering approach for entry-length flows. The evaluation makes use of an analysis of plane thermal entry-length flows by a finite element approach utilizing mean fluid temperatures with a convection coefficient. Another analysis is based on a finite element continuum approach, taking into account the rigorous momentum, mass, and energy equations of viscous, incompressible flow. The engineering approach was found to give excellent agreement with the rigorous continuum approach for Peclet number values not less than 100.

Thornton, E. A.↗

NASA NTRS1984

A spectral element method for fluid dynamics - Laminar flow in a channel expansion

A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

Patera, A. T.↗

NASA NTRS2003

Hierarchical Strategy for Rapid Analysis Environment

A new philosophy is developed wherein the hierarchical definition of data is made use of in creating a better environment to conduct analyses of practical problems. This system can be adapted to conduct virtually any type of analysis, since this philosophy is not bound to any specific kind of analysis. It provides a framework to manage different models and its results and more importantly, the interaction between the different models. Thus, it is ideal for many types of finite element analyses like globalAoca1 analysis and those that involve multiple scales and fields. The system developed during the course of this work is just a demonstrator of the basic concepts. A complete implementation of this strategy could potentially make a major impact on the way analyses are conducted. It could considerably reduce the time frame required to conduct the analysis of real-life problems by efficient management of the data involved and reducing the human effort involved. It also helps in better decision making because of more ways to interpret the results. The strategy has been currently implemented for structural analysis, but with more work it could be extended to other fields of science when the finite element method is used to solve the differential equations numerically. This report details the work that has been done during the course of this project and its achievements and results. The following section discusses the meaning of the word hierarchical and the different references to the term in the literature. It talks about the development of the finite element method, its different versions and how hierarchy has been used to improve the methodology. The next section describes the hierarchical philosophy in detail and explains the different concepts and terms associated with it. It goes on to describe the implementation and the features of the demonstrator. A couple of problems are analyzed using the demonstrator program to show the working of the system. The two problems considered are two dimensional plane stress analysis problems. The results are compared with those obtained using conventional analysis. The different challenges faced during the development of this system are discussed. Finally, we conclude with suggestions for future work to add more features and extend it to a wider range of problems.

Whitcomb, John↗