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At least 19 records

Generalized Transition Finite-Boundary Elements for high speed flight structures

A new class of 'Generalized Transition Finite-Boundary Elements' formulation is presented to predict temperature and/or stress distribution of flight structures at high speeds. A tweleve-noded three-dimensional transition element and a variable degree of freedom eight-noded element are formulated. These elements are incorporated into the formulation of the heat transfer and structural analysis problems by utilizing a newly introduced 'material approximation functions' concept. Results obtained from limited examples compared with the solutions from analytical and other finite element analysis solution. Numerical examples presented illustrate the effectiveness of these elements.

Sarigul-Klijn, Nesrin↗

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.↗

A finite element boundary integral formulation for radiation and scattering by cavity antennas using tetrahedral elements

A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.

Gong, J.↗

A finite-element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is used to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require a knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Jin, Jian-Ming↗

Coupling finite and boundary element methods for two-dimensional potential problems

A finite element-boundary element (FE-BE) coupling method based on a weighted residual variational method is presented for potential problems, governed by either the Laplace or the Poisson equations. In this method, a portion of the domain of interest is modeled by finite elements (FE) and the remainder of the region by boundary elements (BE). Because the BE fundamental solutions are valid for infinite domains, a procedure that limits the effects of the BE fundamental solution to a small region adjacent to the FE region, called the transition region (TR), is developed. This procedure involves a judicious choice of functions called the transition (T) functions that have unit values on the BE-TR interface and zero values on the FE-TR interface. The present FE-BE coupling algorithm is shown to be independent of the extent of the transition region and the choice of the transition functions. Therefore, transition regions that extend to only one layer of elements between FE and BE regions and the use of simple linear transition functions work well.

Krishnamurthy, T.↗

Coupling finite and boundary element methods for 2-D elasticity problems

A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.

Krishnamurthy, T.↗

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.↗

Analysis of random structure-acoustic interaction problems using coupled boundary element and finite element methods

A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.

Mei, Chuh↗

A Hybrid Boundary Element-Finite Volume Method for Unsteady Transonic Airfoil Flows

A hybrid boundary element finite volume method for unsteady transonic flow computation has been developed. In this method, the unsteady Euler equations in a moving frame of reference are solved in a small embedded domain (inner domain) around the airfoil using an implicit finite volume scheme. The unsteady full-potential equation, written in the same frame of reference and in the form of the Poisson equation. is solved in the outer domain using the integral equation boundary element method to provide the boundary conditions for the inner Euler domain. The solution procedure is a time-accurate stepping procedure, where the outer boundary conditions for the inner domain are updated using the integral equation -- boundary element solution over the outer domain. The method is applied to unsteady transonic flows around the NACA0012 airfoil undergoing pitching oscillation and ramp motion. The results are compared with those of an implicit Euler equation solver, which is used throughout a large computational domain, and experimental data.

Hu, Hong↗

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto-Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

We present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2-D planar rate-and-state fault with off-fault visco-plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co-evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off-fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off-fault bulk even at higher angles of maximum compression. In conclusion, this produces damage patterns that deviate from the traditional off-fault fan-like distribution observed in dynamic rupture simulations and emphasizes the significance of long-term deformation in interpreting observations.

58 GEOSCIENCES↗

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.

Kempel, Leo C.↗

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.

Kempel, Leo C.↗

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↗

Computational solid mechanics (finite elements and boundary elements) - Present status and future directions

Computational finite-element and boundary-element methods are reviewed, and their application to the mechanics of solids is discussed. Stability conditions for general FEMs are considered in addition to the use of least-order, stable, invariant, or hybrid/mixed isoparametric elements as alternatives to the displacement-based isoparametric elements. The use of symbolic manipulation, adaptive mesh refinement, transient dynamic response, and boundary-element methods for linear elaslticity and finite-strain problems of inelastic materials are also discussed.

Atluri, S. N.↗

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-composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exac, 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.

Jin, Jian-Ming↗

A finite element-boundary integral method for cavities in a circular cylinder

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.

Kempel, Leo C.↗

Finite-element boundary-integral simulation of thin wires and inhomogeneous penetrable bodies in subsurface multilayered anisotropic media

With the prevailing presence of drilling wells near the subsurface in mature oil and gas fields, the application of electromagnetic methods can be particularly challenging where the electromagnetic field is affected by the steel casing. In the past decades, borehole-to-surface and crosswell electromagnetic methods have been utilized for monitoring of reservoir and underground CO 2 storage. This paper presents a unified finite-element boundary-integral (FEBI) method capable of simultaneously modeling the complex electromagnetic interactions between thin metallic wires (representing steel casings) with 3D trajectory and arbitrary 3D inhomogeneous penetrable bodies (such as CO 2 plumes or hydrocarbon reservoirs) within anisotropic multilayered subsurface environments. Unlike existing approaches that treat these components separately or require dense discretization, or are limited to vertical wells, our unified formulation preserves flexible electromagnetic coupling while delivering improved computational efficiency. Assuming the background formation is multilayered anisotropic media, the surface integral equation method is applied to model the thin wires and boundaries of the inhomogeneous bodies. Meanwhile, the finite element method is applied to model the volume of inhomogeneous bodies. Here, the performance of the proposed FEBI method is assessed through comparison with reference numerical results and its practical significance is demonstrated through CO 2 plume monitoring scenarios.

97 MATHEMATICS AND COMPUTING↗

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Jin, Jian-Ming↗