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NASA NTRS1991

A study of the response of nonlinear springs

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Hyer, M. W.↗

NASA NTRS1984

Application of Iosipescu specimen geometry to determination of shear strength in unidirectional composites

The Iosipescu (1967) test method, in conjunction with a finite element analysis of anisotropic, unidirectionally reinforced composite specimens, can be used to derive composite shear strength values despite the small size of the samples used. When such a specimen is loaded parallel to the fiber direction, fracture occurs by shear within a narrow region near the center of the specimen; this is consistent with the maximum shear area determined by finite element analysis. The resulting fracture surface, as observed, is characteristic of shear failure, occurring either within the matrix or at the fiber-matrix interface. Problems of compressive and mixed mode failure which accrue to short beam shear specimens are by the present method precluded.

Hurwitz, F. I.↗

NASA NTRS1984

The solution of non-linear hyperbolic equation systems by the finite element method

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Loehner, R.↗

NASA NTRS1998

Simulation of Conformal Spiral Slot Antennas on Composite Platforms

During the course of the grant, we wrote and distributed about 12 reports and an equal number of journal papers supported fully or in part by this grant. The list of reports (title & abstract) and papers are given in Appendices A and B. This grant has indeed been instrumental in developing a robust hybrid finite element method for the analysis of complex broadband antennas on doubly curved platforms. Previous to the grant, our capability was limited to simple printed patch antennas on mostly planar platforms. More specifically: (1) mixed element formulations were developed and new edge-based prisms were introduced; (2) these elements were important in permitting flexibility in geometry gridding for most antennas of interest; (3) new perfectly matched absorbers were introduced for mesh truncations associated with highly curved surfaces; (4) fast integral algorithms were introduced for boundary integral truncations reducing CPU time from O(N-2) down to O(N-1.5) or less; (5) frequency extrapolation schemes were developed for efficient broadband performance evaluations. This activity has been successfully continued by NASA researchers; (6) computer codes were developed and extensively tested for several broadband configurations. These include FEMA-CYL, FEMA-PRISM and FEMA-TETRA written by L. Kempel, T. Ozdemir and J. Gong, respectively; (7) a new infinite balun feed was designed nearly constant impedance over the 800-3000 MHz operational band; (8) a complete slot spiral antenna was developed, fabricated and tested at NASA Langley. This new design is a culmination of the projects goals and integrates the computational and experimental efforts. this antenna design resulted in a U.S. patent and was revised three times to achieve the desired bandwidth and gain requirements from 800-3000 MHz.

Volakis, J. L.↗

NASA NTRS1986

Interlaminar analysis of laminated composites using a sublaminate approach

A simple analysis method based upon a transverse shear deformation theory and a sublaminate approach is utilized to analyze a Mixed-Mode edge delamination specimen. The analysis provides a closed form distribution of the interlaminar shear stresses ahead of the crack, and the parameters controlling the behavior are identified. The effect of specimen stacking sequence and delamination interface on the strain energy release rate components is investigated. Results are compared with a finite element simulation for reference. The simple nature of the method makes it suitable for preliminary design analyses which require a large number of configurations to be evaluated quickly and economically.

Armanios, E. A.↗

NASA NTRS2022

A Cohesive Element Formulation for Simulation of General Mode I, II and III Delamination

Cohesive element formulations proposed thus far have assumed that Mode II and Mode III fracture processes, and hence traction-separation laws, are identical. However, experimental observations suggest that such an assumption may not hold in general. The approach described herein consists of a cohesive element formulation in which the assumption of identical Mode II and Mode III fracture processes is not required. This assumption is alleviated by estimating the normal to the delamination front based on the gradient of the displacement jumps determined within each element. The estimated normal is used to rotate the cohesive element coordinate system. Determining the displacement jumps in the rotated coordinate system enables the distinction between Mode II sliding, and Mode III tearing. This information is subsequently used to extend a recently proposed cohesive formulation, resulting in an approach that can simulate mixed-mode I/II/III fracture via prescribing piecewise-linear traction-separation laws combined with a 3D mixed-mode fracture criteria.

Delamination↗

NASA NTRS1987

Petrov-Galerkin methods for natural convection in directional solidification of binary alloys

A Petrov-Galerkin finite element method is presented for calculation of the steady, axisymmetric thermosolutal convection and interface morphology in a model for vertical Bridgman crystal growth of nondilute binary alloys. The Petrov-Galerkin method is based on the formulation for biquadratic elements developed by Heinrich and Zienkiewicz and is introduced into the calculation of the velocity, temperature and concentration fields. The algebraic system is solved simultaneously for the field variables and interface shape by Newton's method. The results of the Petrov-Galerkin method are compared critically with those of Galerkin's method using the same finite element grids. Significant improvements in accuracy are found with the Petrov-Galerkin method only when the mesh is refined and when the formulation of the residual equations is modified to account for the mixed boundary conditions that arise at the solidification interface. Calculations for alloys with stable and unstable solute gradients show the occurrence of classical flow transitions and morphological instabilities in the solidification system.

Adornato, Peter M.↗

NASA NTRS1982

Finite element models for predicting crack growth characteristics in composite materials

Two dimensional and quasi-three dimensional, linear elastic finite element models for the prediction of crack growth characteristics, including crack growth direction, in laminated composite materials are presented. Mixed mode crack growth in isotropic materials, unidirectional and laminated composites is considered. The modified crack closure method is used to predict the applied load level for crack extension and two failure theories, modifications of the point stress and the Hashin failure criteria, are proposed to predict the direction of crack extension in composites. Comparisons are made with the Tsai-Wu failure criterion and the Sih strain energy density criterion as well as with experimental results. It is shown that the modified versions of point stress and Hashin criteria compare well with experiment.

Buczek, M. B.↗

NASA NTRS1990

Numerical Analysis Of Flows With FIDAP

Report presents an evaluation of accuracy of Fluid Dynamics Package (FIDAP) computer program. Finite-element code for analysis of flows of incompressible fluids and transfers of heat in multidimensional domains. Includes both available methods for treatment of spurious numerical coupling between simulated velocity and simulated pressure; namely, penalty method and mixed-interpolation method with variable choices of interpolation polynomials for velocity and pressure. Streamwise upwind (STU) method included as option for flows dominated by convection.

Sohn, Jeong L.↗

NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problems

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method, and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Jiang, Bo-Nan↗

NASA NTRS1992

A least-squares finite element method for incompressible Navier-Stokes problems

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Jiang, Bo-Nan↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

A highly efficient, edge-based viscous (EBV) discretization method has been recently implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver and evaluated for Reynolds-averaged Navier-Stokes (RANS) formulations. In comparison to a well-established cell-based viscous (CBV) method, the EBV method has demonstrated multifold acceleration of all viscous-kernel computations on general unstructured mixed-element grids. The viscous kernels include evaluation of viscous fluxes, diffusion terms in turbulence models, and the corresponding Jacobian terms. In this paper, an EBV implementation of a nonlinear extension of the Spalart-Allmaras turbulence model, SA-neg-QCR2000, is presented and verified. The SA-neg-QCR2000 model is used for simulating turbulent corner flows. Previously reported EBV computations have been conducted on traditional computing architectures based on central processing units (CPU). This paper assesses benefits of the EBV method on modern high-performance computing architectures based on graphics processing units (GPU). The GPU implementations of the CBV and EBV methods are verified by comparing solutions and iterative convergence with those observed in CPU computations on the same grids. A comprehensive assessment of the EBV speedup on CPU and GPU architectures is presented for established benchmark corner flows, namely, a supersonic flow through a long square duct and a subsonic flow around a NASA juncture flow model.

CFD↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

CFD↗

NASA NTRS1986

Sublaminate analysis of interlaminar fracture in composites

A simple analysis method based upon a transverse shear deformation theory and a sublaminate approach is utilized to analyze a mixed-mode edge delamination specimen. The analysis provides closed form expressions for the interlaminar shear stresses ahead of the crack, the total energy release rate, and the energy release rate components. The parameters controlling the behavior are identified. The effect of specimen stacking sequence and delamination interface on the strain energy release rate components is investigated. Results are compared with a finite element simulation for reference. The simple nature of the method makes it suitable for preliminary design analyses which require a large number of configurations to be evaluated quickly and economically.

Armanios, E. A.↗

NASA NTRS1990

Theoretical and numerical difficulties in 3-D vector potential methods in finite element magnetostatic computations

This paper describes the results of application of three well known 3D magnetic vector potential (MVP) based finite element formulations for computation of magnetostatic fields in electrical devices. The three methods were identically applied to three practical examples, the first of which contains only one medium (free space), while the second and third examples contained a mix of free space and iron. The first of these methods is based on the unconstrained curl-curl of the MVP, while the second and third methods are predicated upon constraining the divergence of the MVP 10 zero (Coulomb's Gauge). It was found that the two latter methods cease to give useful and meaningful results when the global solution region contains a mix of media of high and low permeabilities. Furthermore, it was found that their results do not achieve the intended zero constraint on the divergence of the MVP.

Demerdash, N. A.↗

NASA NTRS2001

Consideration of Moving Tooth Load in Gear Crack Propagation Predictions

Robust gear designs consider not only crack initiation, but crack propagation trajectories for a fail-safe design. In actual gear operation, the magnitude as well as the position of the force changes as the gear rotates through the mesh. A study to determine the effect of moving gear tooth load on crack propagation predictions was performed. Two-dimensional analysis of an involute spur gear and three-dimensional analysis of a spiral-bevel pinion gear using the finite element method and boundary element method were studied and compared to experiments. A modified theory for predicting gear crack propagation paths based on the criteria of Erdogan and Sih was investigated. Crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction techniques using a simple static analysis in which the tooth load was located at the highest point of single tooth contact was validated. For three-dimensional analysis, however, the analysis was valid only as long as the crack did not approach the contact region on the tooth.

Lewicki, David G.↗

NASA NTRS1993

A new approach to mixed H2/H infinity controller synthesis using gradient-based parameter optimization methods

In the past few years, the mixed H(sub 2)/H-infinity control problem has been the object of much research interest since it allows the incorporation of robust stability into the LQG framework. The general mixed H(sub 2)/H-infinity design problem has yet to be solved analytically. Numerous schemes have considered upper bounds for the H(sub 2)-performance criterion and/or imposed restrictive constraints on the class of systems under investigation. Furthermore, many modern control applications rely on dynamic models obtained from finite-element analysis and thus involve high-order plant models. Hence the capability to design low-order (fixed-order) controllers is of great importance. In this research a new design method was developed that optimizes the exact H(sub 2)-norm of a certain subsystem subject to robust stability in terms of H-infinity constraints and a minimal number of system assumptions. The derived algorithm is based on a differentiable scalar time-domain penalty function to represent the H-infinity constraints in the overall optimization. The scheme is capable of handling multiple plant conditions and hence multiple performance criteria and H-infinity constraints and incorporates additional constraints such as fixed-order and/or fixed structure controllers. The defined penalty function is applicable to any constraint that is expressible in form of a real symmetric matrix-inequity.

Ly, Uy-Loi↗

NASA NTRS1979

Application of the method of integral relations to unsteady fluid flow problems with shocks

A mixed method using both the method of integral relations and the finite difference technique is developed for the solution of unsteady flow problems. The integral relations method is based upon a chosen interpolating function dependent only on the time domain. The resulting local semidiscrete finite element equations obtained are assembled into a global form. The spatial derivatives at the nodes are replaced by finite difference operators and the discretized nonlinear algebraic system is solved by an iterative scheme. Solutions are obtained for the one-dimensional gasdynamics equation, the one-dimensional wave equation and Burger's model of turbulence. Agreement with other numerical and analytical solutions is excellent for the gasdynamics problem and satisfactory for the Burger equation in cases of small viscous effects.

Wadia, A. R.↗