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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Elasto-plastic flow in cracked bodies using a new finite element model

Cracked geometries were studied by finite element techniques with the aid of a new special element embedded at the crack tip. This model seeked to accurately represent the singular stresses and strains associated with the elasto-plastic flow process. The present model was not restricted to a material type and did not predetermine a singularity. Rather the singularity was treated as an unknown. For each step of the incremental process the nodal degrees of freedom and the unknown singularity were found through minimization of an energy-like functional. The singularity and nodal degrees of freedom were determined by means of an iterative process.

Karabin, M. E., Jr.↗
NASA NTRS1977

The finite element method in computational fluid mechanics

A finite element solution algorithm is established for a general statement of the time-averaged Navier-Stokes equations governing multi-dimensional turbulent flows. Numerical results are presented which evaluate factors affecting solution accuracy for a broad spectrum of linear and non-linear problem classes.

Baker, A. J.↗
NASA NTRS1982

A comparison of the finite difference and finite element methods for heat transfer calculations

The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.

Emery, A. F.↗
NASA NTRS1981

Finite element modeling of nonisothermal polymer flows

A finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer are important is described, and the numerical model is illustrated by means of computer experiments using extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments.

Roylance, D.↗
NASA NTRS1983

A finite element approach for predicting nozzle admittances

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 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 by using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. The boundary conditions are described for both straight and curved sonic lines. A two dimensional FEM with 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 NTRS1984

A triangular finite element for thin plates and shells

A finite element modeling technique which utilizes a triangular element called TSHEL with 45 degrees of freedom and seven point integration was tested for analysis of thin plate and shell structures. The element formulation is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. The effectiveness of the present modeling technique which features combined use of elements with kinematic modes and those without kinematic modes to eliminate both locking and spurious kinematic modes at the global structural levels are shown.

Lee, S. W.↗
NASA NTRS1983

Finite element or Galerkin type semidiscrete schemes

A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.

Durgun, K.↗
NASA NTRS1986

Survey of the status of finite element methods for partial differential equations

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Temam, Roger↗
NASA NTRS1987

An adaptive finite element strategy for complex flow problems

Adaptive finite element methods for steady and unsteady flow problems in two-dimensional domains are described. Details of a data management scheme are given that provide for the rapid implementation of various CFD algorithms on changing unstructured meshes. The results of several numerical experiments on subsonic and supersonic flow problems are discussed.

Oden, J. T.↗
NASA NTRS1988

Efficient assembly of finite-element subsystems with large relative rotations

A finite element approach is presented for the modeling of rotorcraft undergoing elastic deformation in addition to large rigid body motion with respect to inertial space, with particular attention given to the coupling of the rotor and fuselage subsystems subject to large relative rotations. The component synthesis technique used here allows the coupling of rotors to the fuselage for different rotorcraft configurations. The formulation is general and applicable to any rotorcraft vibration, aeroelasticity, and dynamics problem.

Fuh, Jon-Shen↗
NASA NTRS1990

A variational justification of the assumed natural strain formulation of finite elements. I - Variational principles. II - The C(0) four-node plate element

The assumed natural strain formulation of finite elements is interpreted from a variational standpoint. The approach is based on hybrid extensions of the Reissner-type functional which uses the strains and displacements as independent fields. Consideration is restricted to linear elasticity. The four-node C(0) plate-bending quadrilateral is used as a specific example to illustrate the application of the present interpretation. A key finding is that any change in the strain-displacement interpolation from the variationally consistent interpolation must be associated in some way to the addition of incompatible displacement modes.

Militello, Carmelo↗
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 NTRS1990

Bending and stretching finite element analysis of anisotropic viscoelastic composite plates

Finite element algorithms have been developed to analyze linear anisotropic viscoelastic plates, with or without holes, subjected to mechanical (bending, tension), temperature, and hygrothermal loadings. The analysis is based on Laplace transforms rather than direct time integrations in order to improve the accuracy of the results and save on extensive computational time and storage. The time dependent displacement fields in the transverse direction for the cross ply and angle ply laminates are calculated and the stacking sequence effects of the laminates are discussed in detail. Creep responses for the plates with or without a circular hole are also studied. The numerical results compare favorably with analytical solutions, i.e. within 1.8 percent for bending and 10(exp -3) 3 percent for tension. The tension results of the present method are compared with those using the direct time integration scheme.

Hilton, Harry H.↗
NASA NTRS1995

Electromagnetic scattering analysis of a three-dimensional-cavity-backed aperture in an infinite ground plane using a combined finite element method/method of moments approach

A combined finite element method/method of moments (FEM/MoM) approach is used to analyze the electromagnetic scattering properties of a three-dimensional-cavity-backed aperture in an infinite ground plane. The FEM is used to formulate the fields inside the cavity, and the MoM (with subdomain bases) in both spectral and spatial domains is used to formulate the fields above the ground plane. Fields in the aperture and the cavity are solved using a system of equations resulting from the combination of the FEM and the MoM. By virtue of the FEM, this combined approach is applicable to all arbitrarily shaped cavities with inhomogeneous material fillings, and because of the subdomain bases used in the MoM, the apertures can be of any arbitrary shape. This approach leads to a partly sparse and partly full symmetric matrix, which is efficiently solved using a biconjugate gradient algorithm. Numerical results are presented to validate the analysis.

Reddy, C. J.↗
NASA NTRS1993

Finite element calculations of transonic flutter in cascades

Aeroelastic stability and response of turbomachinery cascades operating in the transonic regime are explored using a new computational approach. The two-dimensional unsteady Euler equations are used to model the transonic cascade flows, and the cascade blades are modeled as thin plates. To minimize the discretization incompatibility, both the fluid and the solid domains are discretized using finite element procedures. The fluid and the structural models are coupled at the element level by introducing a channel theory, which is analogous to a strip theory in the classical sense. The system of space-discretized equations is marched forward in time using an explicit four-stage Runge-Kutta scheme. Results of free vibration analyses of typical blades are presented and compared to published finite element and Rayleigh-Ritz results. Aeroelastic stability and response characteristics of several transonic cascades are investigated using the new quasi-3D model. These results demonstrate the present 3D finite element blade model is capable of capturing aeroelastic instabilities involving higher modes, including (plate-type) camber bending modes.

Hsiao, Chingteng↗
NASA NTRS1982

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Carlson, F. M.↗
NASA NTRS1973

Computational considerations in application of the finite element method for analysis of unsteady flow around airfoils.

Difficulties related to the application of the finite element method for numerical solution of the Navier-Stokes equation are discussed. The unsteady flow around a stationary and oscillating NACA 0012 airfoil was analyzed. In an effort to establish the range of applicability of the developed numerical method, the accuracy and stability problems in representing unsteady flow patterns and determining pressure distribution around the airfoil were investigated. Error involved in determining the velocity field and in the numerical integration of the discretized equations were analyzed in terms of geometry of the finite element gridwork, boundary conditions for stationary and oscillating airfoils, angles of attack and flow conditions.

Bratanow, T.↗
DOE OSTI2019

Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities

Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this study, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over the global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element.

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