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NASA NTRS2006

Fatigue Life Methodology for Tapered Hybrid Composite Flexbeams

Nonlinear-tapered flexbeam specimens from a full-size composite helicopter rotor hub flexbeam were tested under combined constant axial tension and cyclic bending loads. Two different graphite/glass hybrid configurations tested under cyclic loading failed by delamination in the tapered region. A 2-D finite element model was developed which closely approximated the flexbeam geometry, boundary conditions, and loading. The analysis results from two geometrically nonlinear finite element codes, ANSYS and ABAQUS, are presented and compared. Strain energy release rates (G) associated with simulated delamination growth in the flexbeams are presented from both codes. These results compare well with each other and suggest that the initial delamination growth from the tip of the ply-drop toward the thick region of the flexbeam is strongly mode II. The peak calculated G values were used with material characterization data to calculate fatigue life curves for comparison with test data. A curve relating maximum surface strain to number of loading cycles at delamination onset compared well with the test results.

urri, Gretchen B.↗

NASA NTRS1987

Finite element modeling of electromagnetic propagation in composite structures

A finite element Galerkin formulation has been developed to study electromagnetic propagation in complex two-dimensional absorbing ducts. The reflection and transmission at entrance and exit boundaries are determined by coupling the finite element solutions at the entrance and exit to the eigenfunctions of an infinite uniform perfect conducting duct. Example solutions are presented for electromagnetic propagation with absorbing duct walls and propagating through dielectric-metallic matrix materials.

Baumeister, K. J.↗

NASA NTRS1994

Analysis of new composite architectures

Global/local method in conjunction with a special macro finite element is used to gain computational efficiency in the simulation of textile composites behavior. Results are included to demonstrate the effectiveness of the method. Also, 2D finite elements are used to study boundary effects in plain weave composite specimens subjected to extension, shear, and flexure loads. Effective extension, shear, and flexural moduli were found to be quite sensitive to specimen size. For extension and flexure loads stress distributions were affected by a free surface, but the free surface boundary effect did not appear to propagate very far into the interior. For shear load, the boundary effect appeared to propagate much further into the interior. The report is in the form of two technical articles, the first describes the global/local method while the second describes the use of the 2D finite elements.

Whitcomb, John D.↗

NASA NTRS1998

A Geodynamic Framework for Eastern Mediterranean Kinematics

We use a finite element model incorporating plate motion boundary conditions, fault constraints, and space geodetic velocities to calculate eastern Mediterranean plate kinematics and to estimate the motion of the region's major faults.

Plate↗

NASA NTRS1991

An improved error analysis of finite element solutions for postbuckled plates

The accurate calculation of stresses at boundaries and interfaces where FEM analysis may be unreliable is presently undertaken by an error analysis that derives a continuous approximation to discrete finite-element data, which can be differentiated to compute continuous stresses for component-failure predictions. An evaluation is conducted of this approximation in the context of the nonlinear PDEs. A novel interpolation formula which is a simple modification of the double Fourier sine series is used to reduce truncation errors near the rectangular plate boundary by means of an 'extended grid'. Results are presented from a FEM solution, a conventional double-Fourier series' continuous approximation, and a solution applying interpolation on the extended grid, which yields superior convergence properties near the plate boundaries.

Sistla, Rajaram↗

NASA NTRS1993

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Day, Brad A.↗

NASA NTRS1981

Numerical algorithms for finite element computations on arrays of microprocessors

The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.

Ortega, J. M.↗

NASA NTRS1993

The Design of Mechanically Compatible Fasteners for Human Mandible Reconstruction

Mechanically compatible fasteners for use with thin or weakened bone sections in the human mandible are being developed to help reduce large strain discontinuities across the bone/implant interface. Materials being considered for these fasteners are a polyetherertherketone (PEEK) resin with continuous quartz or carbon fiber for the screw. The screws were designed to have a shear strength equivalent to that of compact/trabecular bone and to be used with a conventional nut, nut plate, or an expandable shank/blind nut made of a ceramic filled polymer. Physical and finite element models of the mandible were developed in order to help select the best material fastener design. The models replicate the softer inner core of trabecular bone and the hard outer shell of compact bone. The inner core of the physical model consisted of an expanding foam and the hard outer shell consisted of ceramic particles in an epoxy matrix. This model has some of the cutting and drilling attributes of bone and may be appropriate as an educational tool for surgeons and medical students. The finite element model was exercised to establish boundary conditions consistent with the stress profiles associated with mandible bite forces and muscle loads. Work is continuing to compare stress/strain profiles of a reconstructed mandible with the results from the finite element model. When optimized, these design and fastening techniques may be applicable, not only to other skeletal structures, but to any composite structure.

Roberts, Jack C.↗

NASA NTRS1972

Finite elements of nonlinear continua.

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Oden, J. T.↗

NASA NTRS2020

Stochastic Simulation of Mudcrack Damage Formation in an Environmental Barrier Coating

The FEAMAC/CARES program, which integrates finite element analysis (FEA) with the MAC/GMC (Micromechanics Analysis Code with Generalized Method of Cells) and the CARES/Life (Ceramics Analysis and Reliability Evaluation of Structures / Life Prediction) programs, was used to simulate the formation of mudcracks during the cooling of a multilayered environmental barrier coating (EBC) deposited on a silicon carbide substrate. FEAMAC/CARES combines the MAC/GMC multiscale micromechanics analysis capability (primarily developed for composite materials) with the CARES/Life probabilistic multiaxial failure criteria (developed for brittle ceramic materials) and Abaqus (Dassault Systèmes) FEA. In this report, elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio elements enabled the formation of crack boundaries, leading to development of mudcrack-patterned damage. Finite element models of a disk-shaped three-dimensional specimen and a twodimensional model of a through-the-thickness cross section subjected to progressive cooling from 1,300 °C to an ambient temperature of 23 °C were made. Mudcrack damage in the coating resulted from the buildup of residual tensile stresses between the individual material constituents because of thermal expansion mismatches between coating layers and the substrate. A two-parameter Weibull distribution characterized the coating layer stochastic strength response and allowed the effect of the Weibull modulus on the formation of damage and crack segmentation lengths to be studied. The spontaneous initiation of cracking and crack coalescence resulted in progressively smaller mudcrack cells as cooling progressed, consistent with a fractal-behaved fracture pattern. Other failure modes such as delamination, and possibly spallation, could also be reproduced. The physical basis assumed and the heuristic approach employed, which involves a simple stochastic cellular automaton methodology to approximate the crack growth process, are described. The results ultimately show that a selforganizing mudcrack formation can derive from a Weibull distribution that is used to describe the stochastic strength response of the bulk brittle ceramic material layers of an EBC.

Nemeth, Noel N.↗

NASA NTRS2017

Integrated Model of the Eye/Optic Nerve Head Biomechanical Environment

Visual Impairment and Intracranial Pressure (VIIP) syndrome is a concern for long-duration space flight. Previously, it has been suggested that ocular changes observed in VIIP syndrome are related to the cephalad fluid shift that results in altered fluid pressures [1]. We are investigating the impact of changes in intracranial pressure (ICP) using a combination of numerical models, which simulate the effects of various environment conditions, including finite element (FE) models of the posterior eye. The specific interest is to understand how altered pressures due to gravitational changes affect the biomechanical environment of tissues of the posterior eye and optic nerve sheath. METHODS: Additional description of the numerical modeling is provided in the IWS abstract by Nelson et al. In brief, to simulate the effects of a cephalad fluid shift on the cardiovascular and ocular systems, we utilized a lumped-parameter compartment model of these systems. The outputs of this lumped-parameter model then inform boundary conditions (pressures) for a finite element model of the optic nerve head (Figure 1). As an example, we show here a simulation of postural change from supine to 15 degree head-down tilt (HDT), with primary outcomes being the predicted change in strains at the optic nerve head (ONH) region, specifically in the lamina cribrosa (LC), retrolaminar optic nerve, and prelaminar neural tissue (PLNT). The strain field can be decomposed into three orthogonal components, denoted as the first, second and third principal strains. We compare the peak tensile (first principal) and compressive (third principal) strains, since elevated strain alters cell phenotype and induces tissue remodeling. RESULTS AND CONCLUSIONS: Our lumped-parameter model predicted an IOP increase of c. 7 mmHg after 21 minutes of 15 degree HDT, which agreed with previous reports of IOP in HDT [1]. The corresponding FEM simulations predicted a relative increase in the magnitudes of the peak tensile and compressive strains in the lamina cribrosa of 42 and 43, respectively (Fig. 2). The corresponding changes in the optic nerve strains were 17 and 39, while in the PLNT they were 47 and 43. These magnitudes of relative elevations in peak strains may induce a phenotypic response in resident mechano-responsive resident cells [2]. This approach may be expanded to investigate other environmental changes (e.g. parabolic flight). Through our VIIP SCHOLAR project, we will validate and improve these integrated models by measuring patient-specific changes in optic nerve sheath geometry in patients with idiopathic intracranial hypertension before and after lumbar puncture and CSF removal.

biomechanics↗

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 NTRS2000

Magnetic Field Suppression of Flow in Semiconductor Melt

One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.

Fedoseyev, A. I.↗

NASA NTRS1985

On the Interconnection of Incompatible Solid Finite Element Meshes Using Multipoint Constraints

Incompatible meshes, i.e., meshes that physically must have a common boundary, but do not necessarily have coincident grid points, can arise in the course of a finite element analysis. For example, two substructures may have been developed at different times for different purposes and it becomes necessary to interconnect the two models. A technique that uses only multipoint constraints, i.e., MPC cards (or MPCS cards in substructuring), is presented. Since the method uses only MPC's, the procedure may apply at any stage in an analysis; no prior planning or special data is necessary.

Fox, G. L.↗

NASA NTRS1988

Unsteady heat transfer in turbine blade ducts: Focus on combustor sources

Thermal waves generated by either turbine rotor blades cutting through nonuniform combustor temperature fields or unsteady burning could lead to thermal fatigue cracking in the blades. To determine the magnitude of the thermal oscillation in blades with complex shapes and material compositions, a finite element Galerkin formulation has been developed to study combustor generated thermal wave propagation in a model two-dimensional duct with a uniform plug flow profile. The reflection and transmission of the thermal waves at the entrance and exit boundaries are determined by coupling the finite element solutions at the entrance and exit to the eigenfunctions of an infinitely long adiabatic duct. Example solutions are presented. In general, thermal wave propagation from an air passage into a metallic blade wall is small and not a problem. However, if a thermal barrier coating is applied to a metallic surface under conditions of a high heat transfer, a good impedance match is obtained and a significant portion of the thermal wave can pass into the blade material.

Baumeister, Kenneth J.↗

NASA NTRS1988

Unsteady heat transfer in turbine blade ducts - Focus on combustor sources

Baumeister, K. J.↗

NASA NTRS1989

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗

NASA NTRS1992

Error analysis of finite element results on plates with nonuniform grids

Discrete Dirac delta functions in two dimensions and the governing plate differential equations are used to produce continuous approximations from discrete finite-element data on nonuniform grids. The resulting continuous approximation when compared to the discrete data provides an error analysis. Moreover, the continuous approximation can be differentiated to compute continuous stresses needed for component failure prediction. Stresses can then be calculated accurately at boundaries and at interfaces where finite-element analysis alone may not provide reliable results. The continuous solution along with the differential equations also provides a residual error which is used in the error analysis. This is a unique feature of this approach. Two application examples of the procedure are provided. One example involves the linear response of a clamped square plate under uniform transverse load. Results from finite-element analysis and the continuous solution from the present analysis are compared to a closed-form elasticity solution. The continuous solution is used in a Zienkiewicz-Zhu error estimator to assess the performance of the present analysis. The continuous solution is observed to dramatically correct the finite-element results. In a second example, results for the nonlinear response of a stiffened panel are compared to the finite-element solution.

Sistla, Rajaram↗