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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Further Developments of BEM for Micro and Macromechanical Analyses of Composites: Boundary Element Software Technology-Composite User's Manual

BEST-CMS (Boundary Element Solution Technology - Composite Modeling System) is an advanced engineering system for the micro-analysis of fiber composite structures. BEST-CMS is based upon the boundary element program BEST3D which was developed for NASA by Pratt and Whitney Aircraft and the State University of New York at Buffalo under contract NAS3-23697. BEST-CMS presently has the capabilities for elastostatic analysis, steady-state and transient heat transfer analysis, steady-state and transient concurrent thermoelastic analysis and elastoplastic and creep analysis. The fibers are assumed to be perfectly bonded to the composite matrix, or in the case of static or steady-state analysis, the fibers may be assumed to have spring connections, thermal resistance, and/or frictional sliding between the fibers and the composite matrix. The primary objective of this User's Manual is to provide an overview of all BEST-CMS capabilities, along with detailed descriptions of the input data requirements. A brief review of the theoretical background is presented for each analysis category. Then, Chapter 3 discusses the key aspects of the numerical implementation, while Chapter 4 provides a tutorial for the beginning BEST-CMS user. The heart of the manual, however, is in Chapter 5, where a complete description of all data input items is provided. Within this chapter, the individual entries are grouped on a functional basis for a more coherent presentation. Chapter 6 includes sample problems and should be of considerable assistance to the novice. Chapter 7 includes capsules of a number of fiber-composite analysis problems that have been solved using BEST-CMS. This chapter is primarily descriptive in nature and is intended merely to illustrate the level of analysis that is possible within the present BEST-CMS system. Chapter 8 contains a detailed description of the BEST-CMS Neutral File which is helpful in writing an interface between BEST- CMS and any graphic post-processor program. Finally, all pertinent references are listed in Chapter 9.

Banerjee, P. K.↗
NASA NTRS1989

Comparison of boundary element and finite element methods in spur gear root stress analysis

The boundary element method (BEM) is used to compute fillet stress concentration in spur gear teeth. The results are shown to compare favorably with analogous results obtained using the finite element method (FEM). A partially supported thin rim gear is studied. The loading is applied at the pitch point. A three-dimensional analysis is conducted using both the BEM and FEM (NASTRAN). The results are also compared with those of a two-dimensional finite element model. An advantage of the BEM over the FEM is that fewer elements are needed with the BEM. Indeed, in the current study the BEM used 92 elements and 270 nodes whereas the FEM used 320 elements and 2037 nodes. Moreover, since the BEM is especially useful in problems with high stress gradients it is potentially a very useful tool for fillet stress analyses.

Sun, H.↗
NASA NTRS1994

Experimental validation of finite element and boundary element methods for predicting structural vibration and radiated noise

This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.

Seybert, A. F.↗
NASA NTRS1992

Validation of finite element and boundary element methods for predicting structural vibration and radiated noise

Analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise radiated from the box. The FEM was used to predict the vibration, and the surface vibration was used as input to the BEM to predict the sound intensity and sound power. Vibration predicted by the FEM model was validated by experimental modal analysis. Noise predicted by the BEM was validated by sound intensity measurements. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM modeling using vibration data measured on the surface of the box; (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by a sound intensity scan. The sound power predicted from the BEM model using measured vibration data yields an excellent prediction of radiated noise. The sound power predicted by the combined FEM/BEM model also gives a good prediction of radiated noise except for a shift of the natural frequencies that are due to limitations in the FEM model.

Seybert, A. F.↗
NASA NTRS1991

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid↗
NASA NTRS2005

Computation of Sound Propagation by Boundary Element Method

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Guo, Yueping↗
NASA NTRS1984

Interactive computer graphic surface modeling of three-dimensional solid domains for boundary element analysis

The establishment of the boundary element method (BEM) as a valid tool for solving problems in structural mechanics and in other fields of applied physics is discussed. The development of an integrated interactive computer graphic system for the application of the BEM to three dimensional problems in elastostatics is described. The integration of interactive computer graphic techniques and the BEM takes place at the preprocessing and postprocessing stages of the analysis process, when, respectively, the data base is generated and the results are interpreted. The interactive computer graphic modeling techniques used for generating and discretizing the boundary surfaces of a solid domain are outlined.

Perucchio, R.↗
NASA NTRS1986

Comparative efficiency of finite, boundary and hybrid element methods in elastostatics

The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HBFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.

Schwartz, C. W.↗
NASA NTRS1986

Research related to improved computer aided design software package

The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HVFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.

Walston, W. H., Jr.↗
NASA NTRS1989

Advanced development of the boundary element method for steady-state heat conduction

Considerable progress has been made in recent years toward advancing the state-of-the-art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general-purpose boundary element method (BEM) for steady-state heat conduction. In particular, the BEM implementation involves the use of higher-order conforming elements, self-adaptive integration and multi-region capability. Two- and three-dimensional, as well as axisymmetric analysis, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three-dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady-state heat conduction.

Dargush, G. F.↗
NASA NTRS1989

Probabilistic boundary element method

The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required.

Cruse, T. A.↗
NASA NTRS1991

Application of the boundary element method to transient heat conduction

An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM. Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.

Dargush, G. F.↗
NASA NTRS1992

Comparison of analysis and experiment for gearbox noise

Low contact ratio spur gears were tested in the NASA gear-noise rig to study the noise radiated from the top of the gearbox. Experimental results were compared with a NASA acoustics code to validate the code for predicting transmission noise. The analytical code is based on the boundary element method (BEM) which models the gearbox top as a plate in an infinite baffle. Narrow band vibration spectra measured at 63 nodes on the gearbox top were used to produce input data for the BEM model. The BEM code predicted the total sound power based on the measured vibration. The measured sound power was obtained from an acoustic intensity scan taken near the surface of the gearbox at the same 63 nodes used for vibration measurement. Analytical and experimental results were compared at four different speeds for sound power at each of the narrow band frequencies over the range of 400 to 3200 Hz. Results are also compared for the sound power level at meshing frequency plus three sideband pairs and at selected gearbox resonant frequencies. The difference between predicted and measure sound power is typically less than 3 dB with the predicted value generally less than the measured value.

Oswald, Fred B.↗
NASA NTRS1992

Prediction of two-dimensional sound propagation over an arbitrarily-shaped barrier using the boundary element method

2D sound propagation over an arbitrarily-shaped barrier situated on a locally reacting infinite plane in a homogeneous medium is treated utilizing the BEM. The BIE is formulated so that the integral along an infinite homogeneous plane disappears if the half space Green's function is selected to satisfy the boundary condition of this plane. Comparison of the BEM results with test results by Habault and by Kearns shows good agreement of the sound field utilizing the BEM.

Park, Jong M.↗
NASA NTRS1993

A direct approach to finding unknown boundary conditions in steady heat conduction

The capability of the boundary element method (BEM) in determining thermal boundary conditions on surfaces of a conducting solid where such quantities are unknown was demonstrated. The method uses a non-iterative direct approach in solving what is usually called the inverse heat conduction problem (IHCP). Given any over-specified thermal boundary conditions such as a combination of temperature and heat flux on a surface where such data is readily available, the algorithm computes the temperature field within the object and any unknown thermal boundary conditions on surfaces where thermal boundary values are unavailable. A two-dimensional, steady-state BEM program was developed and was tested on several simple geometries where the analytic solution was known. Results obtained with the BEM were in excellent agreement with the analytic values. The algorithm is highly flexible in treating complex geometries, mixed thermal boundary conditions, and temperature-dependent material properties and is presently being extended to three-dimensional and unsteady heat conduction problems. The accuracy and reliability of this technique was very good but tended to deteriorate when the known surface conditions were only slightly over-specified and far from the inaccessible surface.

Martin, Thomas J.↗
NASA NTRS2001

Investigation of Conjugate Heat Transfer in Turbine Blades and Vanes

We report on work carried out to develop a 3-D coupled Finite Volume/BEM-based temperature forward/flux back (TFFB) coupling algorithm to solve the conjugate heat transfer (CHT) which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid which is convecting heat into or out of the solid structure. There are two basic approaches to solving coupled fluid structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid-solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the NASA Glenn compressible Navier-Stokes finite volume code Glenn-HT. The BEM code features constant and bi-linear discontinuous elements and an ILU-preconditioned GMRES iterative solver for the resulting non-symmetric algebraic set arising in the conduction solution. Interface of flux and temperature is enforced at the solid/fluid interface, and a radial-basis function scheme is used to interpolated information between the CFD and BEM surface grids. Additionally, relaxation is implemented in passing the fluxes from the conduction solution to the fluid solution. Results from a simple test example are reported.

Kassab, A. J.↗
NASA NTRS2003

Glenn-ht/bem Conjugate Heat Transfer Solver for Large-scale Turbomachinery Models

A coupled Boundary Element/Finite Volume Method temperature-forward/flux-hack algorithm is developed for conjugate heat transfer (CHT) applications. A loosely coupled strategy is adopted with each field solution providing boundary conditions for the other in an iteration seeking continuity of temperature and heat flux at the fluid-solid interface. The NASA Glenn Navier-Stokes code Glenn-HT is coupled to a 3-D BEM steady state heat conduction code developed at the University of Central Florida. Results from CHT simulation of a 3-D film-cooled blade section are presented and compared with those computed by a two-temperature approach. Also presented are current developments of an iterative domain decomposition strategy accommodating large numbers of unknowns in the BEM. The blade is artificially sub-sectioned in the span-wise direction, 3-D BEM solutions are obtained in the subdomains, and interface temperatures are averaged symmetrically when the flux is updated while the fluxes are averaged anti-symmetrically to maintain continuity of heat flux when the temperatures are updated. An initial guess for interface temperatures uses a physically-based 1-D conduction argument to provide an effective starting point and significantly reduce iteration. 2-D and 3-D results show the process converges efficiently and offers substantial computational and storage savings. Future developments include a parallel multi-grid implementation of the approach under MPI for computation on PC clusters.

Divo, E.↗
NASA NTRS2002

Software Assists in Extensive Environmental Auditing

The Base Enivronmental Management System (BEMS) is a Web-based application program for managing and tracking audits by the Environmental Office of Stennis Space Center in conformity with standard 14001 of the International Organization for Standardization (ISO 14001). (This standard specifies requirements for an environmental-management system.) BEMS saves time by partly automating what were previously manual processes for creating audit checklists; recording and tracking audit results; issuing, tracking, and implementing corrective-action requests (CARs); tracking continuous improvements (CIs); and tracking audit results and statistics. BEMS consists on an administration module and an auditor module. As its name suggests, the administration module is used to administer the audit. It helps administrators to edit the list of audit questions; edit the list of audit locations; assign manditory questions to locations; track, approve, and edit CARs; and edit completed audits. The auditor module is used by auditors to perform audits and record audit results: It helps the auditors to create audit checklists, complete audits, view completed audits, create CARs, record and acknowledge CIs, and generate reports from audit results.

Callac, Christopher↗