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At least 199 records · Page 11

Free vibration analysis by BEM using particular integrals

A new method for the free-vibration analysis using the boundary element technique is presented. The method utilizes a fictitious vector function to approximate the inertia forces and then uses the well-known concept of complementary functions and particular integrals to solve the resulting governing differential equations. The necessary particular integrals are defined for the two and three-dimensional analyses, and the present formulation is applied to a number of two-dimensional problems to show its accuracy and efficiency in the solution of realistic engineering problems.

Ahmad, S.↗

Computational mechanics needs study

In order to assess the needs in computational mechanics over the next decade, we formulated a questionnaire and contacted computational mechanics researchers and users in industry, government, and academia. As expected, we found a wide variety of computational mechanics usage and research. This report outlines the activity discussed with those contacts, as well as that in our own organizations. It should be noted that most of the contacts were made before the recent decline of the defense industry. Therefore, areas which are strongly defense-oriented may decrease in relative importance. In order to facilitate updating of this study, names of a few key researchers in each area are included as starting points for future literature surveys. These lists of names are not intended to represent those persons doing the best research in that area, nor are they intended to be comprehensive. They are, as previously stated, offered as starting points for future literature searches. Overall, there is currently a broad activity in computational mechanics in this country, with the breadth and depth increasing as more sophisticated software and faster computers become more available. The needs and desires of the workers in this field are as diverse as their background and organizational products. There seems to be some degree of software development in any organization (although the level of activity is highly variable from one organization to another) which has any research component in its mission. It seems, however, that there is considerable use of commercial software in almost all organizations. In most industrial research organizations, it appears that very little actual software development is contracted out, but that most is done in-house, using a mixture of funding sources. Government agencies vary widely in the ratio of in-house to out-house ratio. There is a considerable amount of experimental verification in most, but not all, organizations. Generally, the amount of experimental verification is more than we expected. Of all the survey contacts, one or two believe that the resources they are allocated are sufficient, but most do not. Some believe they have only half the resources they need. Some see their resource deficits as short-term, while others see it as a trend which will continue or perhaps worsen. The pessimism is stronger in the defense and aerospace industry. When considering only the nonlinear development efforts, there appears to be an even mix of geometric and material nonlinearity. There is not much particular emphasis in linear analysis unless it is in extension of current analysis capabilities to larger problems. The primary exception is concern about modeling of composites, where proven methodologies have trailed element and computer hardware development. Most of the people we spoke to use finite element techniques, but there is some finite difference and boundary element work ongoing. There is also some interest in multiple methods. Coupling of finite elements and boundary elements appears to be of high interest, since the two analysis types are complementary.

Griffin, O. Hayden, Jr.↗

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Phillips, J. R.↗

A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

Collins, Jeffery D.↗

A new technique for simulating composite material

This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.

Volakis, John L.↗

Analysis of cracked laminates with holes using the boundary force method

The boundary force method is an indirect boundary element technique for the analysis of composite laminates with holes and cracks which uses the orthotropic elasticity solution for a concentrated horizontal and vertical force applied at a given point in a cracked infinite sheet. The orthotropic formulation of the method is verified by comparison with accepted solutions for a counter-crack specimen that is subjected to uniaxial tension. Parametric studies are conducted for two configurations for which no orthotropic solutions are available: cracks emanating from a circular hole, and a four-hole cracked specimen; both are loaded in uniaxial tension.

Tan, P. W.↗

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.↗

Methods for analysis of cracks in three-dimensional solids

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Raju, I. S.↗

Filament Wound Composite Analysis Using the NASA Multiscale Analysis Tool (NASMAT) and Finite Element Analysis

Fiber reinforced composite materials, owing to their tailorable thermomechanical and functional properties, allow one to produce a structure that is stronger, stiffer, and lighter than its metal counterpart while performing the same function, yielding a more efficient structure. This not only allows for the improvement of current technologies like aircraft structures, but also enables new technologies like gaseous hydrogen storage for mobility applications, which are otherwise impractical when manufactured using traditional metals due to weight and space restrictions or material embrittlement. However, the use of composites imposes greater design and manufacturing challenges on an engineer, since they are heterogenous, having a distinct structure across multiple length scale, behave generally anisotropically at the structural level and require complex manufacturing and processing methods. Capturing this complex behavior requires detailed numerical simulations, including the modeling of microstructural features like undulations, voids, and fiber alignment. In this paper, multiple repeating unit cells (RUCs), representing filament wound composites, are developed (via a script provided in the Appendix) and analyzed. The refinement of these RUCs is varied, and the analyses are performed using both the Abaqus finite element software and the NASA Multiscale Analysis Tool (NASMAT). A study is undertaken to compare the predicted effective elastic properties of the wound RUC to a laminate representation of the wound RUC, which neglects the undulations. Additionally, two different sets of periodic boundary conditions (PBCs) have been examined. One approximates the real boundary conditions using a standard approach and the other represents the PBCs exactly through the use of an offset. Lastly, a comparison of the local elastic stress fields is made among the models and approaches. Since wound structures are often approximated as laminated structures, it is important to understand the degree to which this assumption is valid, namely by first comparing the elastic constants and local elastic fields. This will provide, on the one hand, information concerning the bulk mechanical behavior and, on the other hand, insights concerning local load distributions and likely damage initiation sites.

Composites↗

A variationally coupled FE-BE method for elasticity and fracture mechanics

A new method for coupling finite element and boundary element subdomains in elasticity and fracture mechanics problems is described. The essential feature of this new method is that a single variational statement is obtained for the entire domain, and in this process the terms associated with tractions on the interfaces between the subdomains are eliminated. This provides the additional advantage that the ambiguities associated with the matching of discontinuous tractions are circumvented. The method leads to a direct procedure for obtaining the discrete equations for the coupled problem without any intermediate steps. In order to evaluate this method and compare it with previous methods, a patch test for coupled procedures has been devised. Evaluation of this variationally coupled method and other methods, such as stiffness coupling and constraint traction matching coupling, shows that this method is substantially superior. Solutions for a series of fracture mechanics problems are also reported to illustrate the effectiveness of this method.

Lu, Y. Y.↗

Radiation and scattering from printed antennas on cylindrically conformal platforms

The goal was to develop suitable methods and software for the analysis of antennas on cylindrical coated and uncoated platforms. Specifically, the finite element boundary integral and finite element ABC methods were employed successfully and associated software were developed for the analysis and design of wraparound and discrete cavity-backed arrays situated on cylindrical platforms. This work led to the successful implementation of analysis software for such antennas. Developments which played a role in this respect are the efficient implementation of the 3D Green's function for a metallic cylinder, the incorporation of the fast Fourier transform in computing the matrix-vector products executed in the solver of the finite element-boundary integral system, and the development of a new absorbing boundary condition for terminating the finite element mesh on cylindrical surfaces.

Kempel, Leo C.↗

Electromagnetic scattering and radiation from microstrip patch antennas and spirals residing in a cavity

A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy.

Volakis, J. L.↗

Accuracy of the domain method for the material derivative approach to shape design sensitivities

Numerical accuracy for the boundary and domain methods of the material derivative approach to shape design sensitivities is investigated through the use of mesh refinement. The results show that the domain method is generally more accurate than the boundary method, using the finite element technique. It is also shown that the domain method is equivalent, under certain assumptions, to the implicit differentiation approach not only theoretically but also numerically.

Yang, R. J.↗

Thermal viscoplastic buckling during the growth of silicon ribbon

This paper is an analysis of the conditions to be satisfied in order to avoid buckling during the growth of a silicon ribbon that is being slowly pulled from the melt. A viscoplastic constitutive equation with a dislocation density effect is used to model the material behavior. The critical thicknesses and the corresponding deflection shapes are calculated by the finite element method for the cantilever boundary conditions. The value of the parameter which controls the speed of the lateral deflection is computed by using Galerkin's method. It is demonstrated that, due to the effect of viscoplasticity, some deflection shapes increase in magnitude with time and other shapes damp out.

Tsai, C. T.↗

Predicting the Rotor-Stator Interaction Acoustics of a Ducted Fan Engine

A Navier-Stokes computation is performed for a ducted-fan configuration with the goal of predicting rotor-stator noise generation without having to resort to heuristic modeling. The calculated pressure field in the inlet region is decomposed into classical infinite-duct modes, which are then used in either a hybrid finite-element/Kirchhoff surface method or boundary integral equation method to calculate the far field noise. Comparisons with experimental data are presented, including rotor wake surveys and far field sound pressure levels for two blade passage frequency (BPF) tones.

Biedron, Robert T.↗

Predicting the Rotor-Stator Interaction Acoustics of a Ducted Fan Engine

A Navier-Stokes computation is performed for a ducted-fan configuration with the goal of predicting rotor-stator noise generation without having to re- to heuristic modeling. The calculated pressure field in the inlet region is decomposed into classical infinite-duct, modes, which are then used in either a hybrid finite-element /Kirchhoff surface method or boundary integral equation method to calculate the far field noise. Comparisons with experimental data are presented, including rotor wake surveys and far field sound pressure levels for 2 blade passage frequency (BPF) tones.

Biedron, Robert T.↗

Theoretical determination of nozzle admittances using a finite element method

A finite element method (FEM) is used to predict the admittances of axisymmetric nozzles. The flow in the nozzle is assumed to be isentropic and the disturbances are assumed to be small so that linear analyses apply. An approximate two dimensional compressible flow model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear acoustic wave equation. This partial differential wave equation is transformed to an integral equation using Galerkin's method and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. A two dimensional finite element method using linear triangular elements is used to solve the integral acoustic equation. A one dimensional FEM is used to solve the reduced nozzle acoustic equation developed by Crocco and the solution is used to verify the sufficiency of the boundary residual formation. It is shown that agreement between predicted values of the admittance and experimental data is quite good.

Sigman, R. K.↗

A Unified Wall Boundary Treatment for Viscous and Inviscid Flows in the CE/SE Method

In the setting of the conservation element-solution element (CE/SE) method, a new and unified wall boundary treatment for the Navier-Stokes and Euler Equations is proposed. In essence, the shear stress exerted on the fluid by a wall is modeled as a source term as a part of local spacetime flux conservation in the vicinity of a wall boundary. When the fluid is inviscid, the source term vanishes and the boundary condition reduces to the usual 'slip' condition. On the other hand, when the fluid is viscous, the source-term effect is consistent with the traditional no-slip condition. Numerical results show that the new treatment is robust, efficient, and accurate for viscous and inviscid flows.

Chang, Sin-Chung↗