Prediction of sound fields in cavities using boundary-element methods
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Bernhard, R. J.↗
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Results for “boundary element method”
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Alternative methods for computing sound radiation from vibrating surfaces
The merits of various numerical and experimental methods for computing sound fields radiated from vibrating structures are examined. The finite difference method, the finite element method, direct boundary element method, indirect boundary element near-field acoustic holography, two-microphone methods, and spatial transformation of sound fields are considered. The proper utilization of the methods is discussed.
Bernhard, R. J.↗
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.↗
Nonlinear Structural Analysis
Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.
Source record↗
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.↗
A boundary element alternating method for two-dimensional mixed-mode fracture problems
A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.
Raju, I. S.↗
Applications of FEM and BEM in two-dimensional fracture mechanics problems
A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.
Min, J. B.↗
A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures
The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.
Smeltzer, Stanley S.↗
A finite element: Boundary integral method for electromagnetic scattering
A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.
Collins, J. D.↗
Stress-intensity factor calculations using the boundary force method
The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort.
Tan, P. W.↗
INVESTIGATING THE FEASIBILITY AND STABILITY FOR MODELING ACOUSTIC WAVE SCATTERING USING A TIME-DOMAIN BOUNDARY INTEGRAL EQUATION WITH IMPEDANCE BOUNDARY CONDITION
Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. This work considers using either an impedance or an admittance (inverse of impedance) boundary condition to allow for acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces. Three acoustic liner models are discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and the Broadband Impedance Model. In both the Helmholtz and Three-Parameter models, liner impedance is specified at a given frequency, whereas the Broadband model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for acoustic liners are derived for each model and coupled with a time-domain boundary integral equation. The scattering solution is obtained iteratively using a boundary element method with constant spatial and third-order temporal basis functions. Time-domain boundary integral equations are unfortunately prone to numerical instabilities due to resonant frequencies resulting from non-trivial solutions in the interior domain. When reformulated with the Burton-Miller method, the instabilities are eliminated. Using a Burton-Miller reformulation, the stability of the boundary element method assuming a liner boundary condition is assessed using eigenvalue analysis. The stability of each liner model is discussed, and it is shown that the Three-Parameter and Broadband models are sufficient for modeling an acoustic liner on the surface of scattering bodies. The Helmholtz model demonstrates strict limitations for stability, whereas the Three-Parameter and Broadband models are stable for most cases. Also included in this work is an assessment of the spatial accuracy of the time-domain boundary element method with respect to the surface element basis functions, as well as a performance study of the numerical algorithm.
computational mathematics↗
Modeling of Structural-Acoustic Interaction Using Coupled FE/BE Method and Control of Interior Acoustic Pressure Using Piezoelectric Actuators
A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural-acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the acoustic domain. Results for a system consisting of an isotropic panel and a cubic cavity are in good agreement with exact solutions and experiment data. The response of a composite panel backed cavity is then obtained. The results show that the mass and stiffness of piezoelectric layers have to be considered. The coupled finite element and boundary element equations are transformed into modal coordinates, which is more convenient for transient excitation. Several transient problems are solved based on this formulation. Two control designs, a linear quadratic regulator (LQR) and a feedforward controller, are applied to reduce the acoustic pressure inside the cavity based on the equations in modal coordinates. The results indicate that both controllers can reduce the interior acoustic pressure and the plate deflection.
Mei, Chuh↗
User's Manual for FEM-BEM Method
A user's manual for using FORTRAN code to perform electromagnetic analysis of arbitrarily shaped material cylinders using a hybrid method that combines the finite element method (FEM) and the boundary element method (BEM). In this method, the material cylinder is enclosed by a fictitious boundary and the Maxwell's equations are solved by FEM inside the boundary and by BEM outside the boundary. The electromagnetic scattering on several arbitrarily shaped material cylinders using this FORTRAN code is computed to as examples.
Butler, Theresa↗
Electromagnetic Scattering Analysis of Arbitrarily Shaped Material Cylinder by FEM-BEM Method
A hybrid method that combines the finite element method (FEM) and the boundary element method (BEM) is developed to analyze electromagnetic scattering from arbitrarily shaped material cylinders. By this method, the material cylinder is first enclosed by a fictitious boundary. Maxwell's equations are then solved by FEM inside and by BEM outside the boundary. Electromagnetic scattering from several arbitrarily shaped material cylinders is computed and compared with results obtained by other numerical techniques.
Deshpande, M. D.↗
Parallel computation using boundary elements in solid mechanics
The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.
Chien, L. S.↗
Computing Fiber/Matrix Interfacial Effects In SiC/RBSN
Computational study conducted to demonstrate use of boundary-element method in analyzing effects of fiber/matrix interface on elastic and thermal behaviors of representative laminated composite materials. In study, boundary-element method implemented by Boundary Element Solution Technology - Composite Modeling System (BEST-CMS) computer program.
Goldberg, Robert K.↗
Numerical Strip-Yield Calculation of CTOD and CTOA
A recently developed numerical method based on the strip yield analysis approach was used to calculate the Crack Tip Opening Displacement (CTOD) and Crack Tip Opening Angle (CTOA) for a number of complex crack configurations of practical interest. This method is an adaptation of the dislocation-density based boundary element method. In this Boundary Element approach, crack-face opening displacements are obtained at any point on a crack using a series of definite integrals evaluated exactly in closed form for a variety of crack geometries, including infinite or finite extent, with arbitrarily applied loading conditions.
Beek, Joachim↗
A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures
A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.
Jin, Jian-Ming↗