Controlling errors in the process of automating boundary element method analysis

In this article, an application of a current sheet as a finite element in the boundary element method (BEM) is described. A detailed procedure for mathematical and software implementation of a current sheet element (CSE) as a finite boundary element (FBE) in BEM analysis is presented. For a simple generic magnetic circuit with a stator and a rotor, the calculated magnetic field and torque values are compared with the values obtained by two different finite-element method (FEM)-based simulation programs showing good agreement; however, elucidating the fact that even by employing professional FEM tools, on fairly simple problems, accurate determination of forces and torques is not necessarily guaranteed. Certain aspects of using the Maxwell stress tensor (MST) for the determination of forces and torques on the rotor domain are discussed. Since the primary magnetic field sources are currents in a set of conductors of the circular cross section, analytical expressions are used for the calculation of the primary field. Due to the selected geometry of the FBEs, i.e., CSEs, after a numerical determination of their currents by BEM, analytical expressions are employed for the calculation of FBE fields as well.

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems.

<div class="htmlview paragraph">Radiated noise from various components is of increasing concern for today's automotive manufacturers. Traditionally, this analysis was usually performed with Boundary Element Method (BEM) software. Unfortunately, there is no sensitivity or optimization capability within any known BEM code. This paper addresses the problem by describing the software developed by CDH, i.e., OPT and VAO, which combine the structural FEM analysis <i>and</i> optimization with BEM analysis such that one can perform analysis and optimization very quickly and efficiently. A sample air cleaner problem is described which illustrates the minimization of radiated noise at a predefined far-field positions.</div>

An efficient numerical scheme for obtaining the two dimensional impurity profile and structural features of the semiconductor devices is proposed. The finite element method (FEM) is used to solve the drift-diffusion equation of impurities in silicon. The thermal oxidation using a model based on steady-state oxidant diffusion is dealt with the boundary element method (BEM). Both methods are employed for calculating the complicated geometry and the boundary conditions in the simulation, where these methods are simultaneously used for the oxidizing condition. For the finite element analysis, mass lumping is introduced to get the stable result. The matrix obtained is asymmetric and irregular sparse, the matrix is solved by the Conjugate Gradient-Squared method (CGS) with preconditioning-conditioning (Incomplete LDU factorization). Thus a more economical calculation method is obtained than the conventional FEM and BEM analysis, using Gaussian elimination method.

Statistics of eigensolutions for systems with random shape parameters using BEM

The boundary element method (BEM) is a numerical technique to solve the boundary integral for the vector analysis of diffraction.1,2 Boundary integral methods model the interaction between an incident field and a diffractive optical element (DOE) using distributions induced on the surface of the DOE by the incident field. For a conductor the surface distribution is a current and, for a dielectric, it is a polarization field. Re-radiation from the surface distribution, in turn, generates a diffracted field. The objective of the BEM is the determination of the surface distribution given the incident field and DOE.

<div class="htmlview paragraph">A reactive type of muffler of a 4-stroke Auto-Rickshaw was modeled using a commercially available Acoustic Finite Element Analysis (FEA) software like Sysnoise. Design sensitivity of different geometry parameters of mufflers to its Insertion Loss over a wide frequency range was studied. The analytical results were validated by the Laboratory Speaker test. But in the presence of a hot gas flow, the Insertion Loss characteristics of the muffler were far different. As the flow speed increased, negative attenuation was found in some frequency bands.</div> <div class="htmlview paragraph">The second part of the paper studies the software prediction of structure borne noise from a transmission cover of a Motorcycle. The sound power level was predicted by uncoupled fluid-structure analysis of Boundary Element Method (BEM). To reduce the sound power radiated from its top surface, a ribbed pattern and increase in thickness were proposed. The software output regarding the sound radiation efficiency of the cover was only partly validated.</div>

A two-dimensional boundary element method for analysis of closed or partially closed cracks under normal and frictional forces is developed. The single domain dual formulation is used. As a contact problem is non-linear due to the friction phenomena at the crack interface and also because of the boundary conditions which may change during the loading, it is formulated in an incremental and iterative fashion. The stress intensity factors are calculated with the J-integral method. Also crack growth is considered. Several benchmark cases have been analysed to verify the results given by the method. The stress intensity factors and crack paths calculated are similar to those given in the literature. © 1997 John Wiley & Sons, Ltd.

The use of the tension-softening model for analyzing fracture processes of rock is examined with special reference to the effect of confining pressure on the fracture extension. Tension-softening curves are measured by means of the J-based technique from unconfined tests performed on compact tension (CT) specimens of granite. On the basis of the determined tension-softening relation, numerical analyses are executed using a boundary element method (BEM) to simulate fracture of the granite under confining pressures. Numerical results are compared to the experimental results of two series of tests for which CT specimens and thick-walled cylindrical specimens were loaded to failure under confining pressures ranging from 0 to 26.5 MPa. It is shown that the BEM analyses can predict the observed fracture behavior. Based on the results, it is demonstrated that the tension-softening relation provides a suitable model to analyze the fracture process in the rock. The source mechanism for the pressure sensitive fracture is discussed by examining the growth of the fracture process zone.

Scaling integration method for singular integrals and its application to BEM

Dissimilar joint of steel and aluminum alloy was produced by YAG laser welding. Maximum tensile shear strength was about 86 % of tensile strength of aluminum alloy. About 10 μm thickness intermetallic layer was observed at the interface of the joint. Temperature distribution was calculated by BEM (Boundary Element Method) analysis combined with the results of temperature measuring test. According to BEM analysis, maximum temperature at the interface was between melting point of aluminum and steel. Diffusion occurred during laser welding between solid state steel and liquid state aluminum to produce thin intermetallic layer

Following the initiation of corrosion in reinforcement, expansion of corrosion products generates corrosion-induced cracks in concrete. At the meso-scale, accumulation and coalescence of micro-cracks create the fracture process zone. Since nucleation of an individual micro-crack can be detected by acoustic emission (AE) techniques, the moment tensor analysis of AE waves is applied to quantitatively identify cracking kinematics of a location, a crack-type and a crack orientation. At the macro-scale, initiation and extension of the corrosion-induced cracks are analyzed by means of classical fracture mechanics, applying the boundary element method (BEM). The generation of corrosion-induced cracks was simulated in expansion tests on concrete specimens. Kinematical mechanisms of micro-cracks were identified by the SiGMA (Simplified Green's functions for Moment tensor Analysis) analysis. By applying the two-domain BEM analysis, extension of the corrosion-induced crack in an arbitrary direction was analyzed. With respect to the orientations of crack extension, results of the BEM analysis were compared with those of the SiGMA analysis, introducing the normalized stress intensity factors. It is demonstrated that extension of the corrosion-induced crack is governed by the mode-I failure both at the meso-scale and at the macro-scale.

Corrosion of reinforcing steel-bar (rebar) is modelled phenomenologically as corrosion losses of three phases. Corresponding to these phases, high AE activities are characteristically observed twice during the corrosion process. It is shown that the 1st AE activity corresponds to the onset of the corrosion in rebar and at the 2nd period of high activity AE events result from concrete cracking due to the expansion of rebar caused by corrosion products. The expansion caused by corrosion products generates micro-cracks in concrete as corrosion-induced cracks, of which mechanisms can be investigated experimentally by AE. To this end, SiGMA (Simplified Green’s functions for Moment tensor Analysis) is applied to the corrosion process in reinforced concrete. To compare with cracking mechanisms identified by SiGMA, a numerical analysis by the two-dimensional boundary element method (BEM) is performed for stress analysis and applied boundary nodes were determined from a diffusion analysis of chloride contents by the finite element method (FEM). Thus, fracture mechanisms of corrosion-induced cracks are quantitatively evaluated by AE-SiGMA and BEM. For on-site measurement of the corrosion in reinforced concrete, hybrid nondestructive evaluation (NDE) is going to be developed. Here, acoustic emission (AE) measurement is conducted, along with measuring half-cell potentials and polarization resistances at the surface of concrete. In order to identify the corroded area along rebar, the potential inversion by BEM (PiBEM) analysis is applied. Thus, plausible areas of the corrosion in rebar are identified.

A boundary element analysis of the axisymmetric extrusion processes

SUMMARYIn order to study the interaction of sloshing and structural vibrations of baffled tanks, a reduced order model based on modal analysis of structure model and boundary element method for fluids motion is developed. For this purpose, the governing equations of elastic structure and incompressible flow are used to derive simple models to simulate both fields. Using the modal analysis technique, the structural motions are applied to the fluid model and on the other hand by using boundary element method, the fluid loads are applied to the structural model. Based on this formulation, a code is developed which is applicable to an arbitrary elastic tank with arbitrary arrangement of baffles. The obtained results are validated with literature data and then the effects of baffle flexibility on the sloshing frequencies and structural vibration frequencies are investigated. Copyright © 2011 John Wiley & Sons, Ltd.