Application Of BEM Research Articles

Evaluation and characterization of Melo Bentonite clay for cosmetic applications

Clays are used in cosmetology with different applications, which are conditioned to the chemical and mineralogical composition and physical-chemical characteristics of these materials. Therefore, the aim of this work was to evaluate the potential application of Melo Bentonite (BEM), clay from Uruguay through different tests. Initially, it was performed the characterization of BEM by X-ray Diffraction (XRD), X-ray fluorescence spectroscopy (XRF), thermal analysis (TGA/DTG), particle size distribution and surface area. The microbial content of natural Melo Bentonite clay was also verified. Two calamine suspensions were formulated with bentonite clay, one containing BEM and the other containing bentonite clay (BE), both at concentration of 5% w/w in glycerin. Bentonite clay was used in accordance to standard. The suspensions were characterized through tests of sedimentation rate, viscosity and pH determination. The physical-chemical characterization of BEM indicated compatible characteristics with those of clay; it was observed only smectite and quartz reflections as crystalline phases and in terms of chemical composition the major presence of silicon, aluminum and magnesium was verified. The microbiological evaluation showed that microbial content of Melo Bentonite presents acceptable limits, according to the Brazilian legislation for cosmetic products. BE was tested by a suspending agent. The sedimentation amount obtained for the suspention that was prepared with BEM was (0.73 mL/min) and with BE (0.63 mL/min). BEM is a better agent suspensor than BE. The viscosity presented by the sample containing BEM was lower than that containing BE; both of them showed non-Newtonian behavior and pseudoplastic flow. The pH of the sample containing BEM was close to neutral (7.72 ± 0.005), while the pH of the sample containing BE was 8.17 ± 0.026. The results showed a possible application of BEM in cosmetic products.

Application of Energetic BEM to 2D Elastodynamic Soft Scattering Problems

Abstract Starting from a recently developed energetic space-time weak formulation of the Boundary Integral Equations related to scalar wave propagation problems, in this paper we focus for the first time on the 2D elastodynamic extension of the above wave propagation analysis. In particular, we consider elastodynamic scattering problems by open arcs, with vanishing initial and Dirichlet boundary conditions and we assess the efficiency and accuracy of the proposed method, on the basis of numerical results obtained for benchmark problems having available analytical solution.

FEM and BEM simulations with the Gypsilab framework

Gypsilab is a Matlab framework which aims at simplifying the development of numerical methods that apply to the resolution of problems in multiphysics, in particular, those involving FEM or BEM simulations. The peculiarities of the framework, with a focus on its ease of use, are shown together with the methodology that have been followed for its development. Example codes that are short though representative enough are given both for FEM and BEM applications. A performance comparison with FreeFem++ is provided, and a particular emphasis is made on problems in acoustics and electromagnetics solved using the BEM and for which compressed H-matrices are used.

Construction of special shape functions for triangular elements with one edge lying in the crack front

This paper presents a new and general construction method of special triangular elements with one edge lying in the crack front. In our method, principal items which represent the asymptotic properties around the crack front in local coordinate system are constructed. Based on the principal items, two groups of basis functions for crack front elements are introduced. Combining undetermined coefficients and basis functions, two types of crack front elements, which are denoted by low order crack front elements and high order ones, are constructed. Secondly, a displacement extrapolation technique with these newly developed elements is proposed. Applying this technique in the BEM applications for crack problems, numerical difficulties, which arise when two vertexes of the assisted line both locate inside the element, can be circumvented conveniently. Finally, two types of elements are employed in the dual boundary element codes for crack problems. Numerical examples are presented to verify the three types of elements. Results show that the stress intensity factors computed by employing these three developed elements are all very accurate compared with the existing results.

Conformal distance-sigmoidal transformation for evaluating 3D nearly singular integrals over triangular elements

Nearly singular boundary integrals are involved in many applications of BEM, such as thin structures and contact problems. Therefore, the accurate evaluation of such integrals is an important aspect during the successful implementation of BEM. Recently, a conformal mapping for triangular elements has been constructed to eliminate the distorted shape influence and applied to deal with singular integrals. In this paper, the conformal mapping is extended to deal with the nearly singular integrals over triangular elements by combination of the distance transformation proposed by Ma and Kamiya. An improved sigmoidal transformation is employed to rearrange Gaussian points in angular direction more judiciously, and the conformal mapping is introduced to eliminate the distorted shape influence for elements with large aspect ratio or peak/obtuse angles. Extensive numerical tests and comparisons for both planar and curved triangular elements are given to demonstrate the high efficiency and competitiveness of the method presented in this paper.

BIM2BEM integrated approach: Examining status of the adoption of building information modelling and building energy models in Egyptian architectural firms

Abstract Egyptian architectural firms are moving from the use of CAD towards the adoption of BIM. Meanwhile, these firms are challenged with the use of BEM in order to cope with the call for energy conservation. To achieve better collaboration, the approach of BIM2BEM has emerged, aiming to integrate between BEM and BIM, which leads to the production of buildings that cope with updates in environmental policies. Nevertheless, these changes facing Egyptian architectural firms haven’t been examined in an integrated manner in published research work. Thus, the main objective of this paper is to examine the status of the application of both BIM and BEM, in Egypt. The research methodology involved using a semi-structured questionnaire and analysing two office buildings as case studies. Results showed that the application of BIM2BEM approach in Egypt is currently spreading and developing. It also showed that there are several barriers to adoption of this approach.

Application of BEM for Improving Corrosion Assessment of Public Building Stricken by Tsunami Aceh 2004

The earthquake and tsunami that struck Aceh region on December 2004 caused many public buildings submerged by seawater. In long periods, it will promote the premature failure of the existing buildings constructed by reinforced concrete structure due to corrosion. Early detection of the corrosion is urgent. The corrosion assessment using haft-cell potential mapping has been conducted to understand the current status of public buildings after five years tsunami Aceh 2004. The results for four existing public buildings in the region show that the corrosion level of steel in concrete of the buildings was already at intermediate risk. However, these results show only the corrosion risk instead of the actual corrosion of the steel. To improve the corrosion assessment, BEM was employed by simulating some factors that might affect the measured potential on the concrete surface. Laplace equation is used to model the potential in concrete structure. The steel surfaces were represented by using polarization curves. BEM is employed to solve the Laplace equation; hence the potential and current density in the whole domain can be obtained. The simulation results show that the potential corrosion on concrete surface was significantly affected by corrosion of steel, concrete conductivity and concrete cover. Accordingly, by employing BEM, more precise corrosion of steel in concrete can be identified from the measured potential on the concrete surface. Moreover, further study is needed to apply the proposed method in the field.

An hpr-mesh refinement algorithm for BEM

This paper describes a mesh refinement scheme for boundary element method in which the number of elements, the size of elements, element end locations and the element polynomial order are determined to meet the user specified accuracy. The use of grading function in conjunction with the L 1 norm makes the mesh refinement scheme applicable to a variety of boundary element formulation and applications. The algorithm is stable for smooth, discontinuous, as well as singular density functions. Numerical results for mathematical test functions as well as for elastostatic problems demonstrate the viability and versatility of the algorithm for BEM applications.

Application of BEM to generalized plane problems for anisotropic elastic materials in presence of contact

It is in many cases very instructive and useful to have the possibility of treating three-dimensional problems by means of two-dimensional models. It always implies a reduction in computing cost which is particularly significant in presence of non-linearities, derived for instance from the presence of contact between the solids involved in the problem. The term generalized plane problem is adopted for a three-dimensional problem in a homogeneous linear elastic cylindrical body where strains and stresses are the same in all transversal sections. This concept covers many practical cases (for instance in the field of composites), a particular situation called generalized plane strain (strains, stresses and displacements are the same in all transversal sections) being the most frequently analyzed. In this paper, a new formulation is developed in a systematic way to solve generalized plane problems for anisotropic materials, with possible friction contact zones, as two-dimensional problems. The numerical solution of these problems is formulated by means of the boundary element method. An explicit expression of a new particular solution of the problem associated to constant body forces is introduced and applied to avoid domain integrations. Some numerical results are presented to show the performance and advantages of the formulation developed.

Parallel -Matrix Arithmetics on Shared Memory Systems

**-matrices, as they were introduced in previous papers, allow the usage of the common matrix arithmetic in an efficient, almost optimal way. This article is concerned with the parallelisation of this arithmetics, in particular matrix building, matrix-vector multiplication, matrix multiplication and matrix inversion.Of special interest is the design of algorithms, which reuse as much as possible of the corresponding sequential methods, thereby keeping the effort to update an existing implementation at a minimum. This could be achieved by making use of the properties of shared memory systems as they are widely available in the form of workstations or compute servers. These systems provide a simple and commonly supported programming interface in the form of POSIX-threads.The theoretical results for the parallel algorithms are confirmed with numerical examples from BEM and FEM applications.

The Eigenvalue Problem for the 2D Laplacian in ?-Matrix Arithmetic and Application to the Heat and Wave Equation

A class of matrices (H-matrices) has recently been introduced by Hackbusch for approximating large and fully populated matrices arising from FEM and BEM applications. These matrices are data-sparse and allow approximate matrix operations of almost linear complexity. In the present paper, we choose a special class of H-matrices that provides a good approximation to the inverse of the discrete 2D Laplacian. For these 2D H-matrices we study the blockwise recursive schemes for block triangular linear systems of equations and the Cholesky and LDLT factorization in an approximate arithmetic of almost linear complexity. Using the LDLT factorization we compute eigenpairs of the discrete 2D Laplacian in H-matrix arithmetic by means of a so-called simultaneous iteration for computing invariant subspaces of non-Hermitian matrices due to Stewart. We apply the H-matrix techniques to approximate the solutions of the high-frequency 2D wave equation for smooth initial data and the 2D heat equation for arbitrary initial data by spectral decomposition of the discrete 2D Laplacian in, up to logarithmic factors, optimal complexity.

536 メモリ節約型時間域BEMの超音波シミュレーションへの適用(OS 非破壊評価とモニタリング(2))

536 メモリ節約型時間域BEMの超音波シミュレーションへの適用(OS 非破壊評価とモニタリング(2))

Application of BEM and sensitivity analysis to the solution of the governing diffusion–convection equation for a continuous casting process

This paper presents a two-dimensional diffusion–convection boundary problem which models a continuous casting process of a pure substance (e.g. copper). The boundary problem is formulated for both liquid and solid subdomains separated by a phase change front. Its location is unknown and has to be updated during the iteration process utilising the so-called front tracking algorithm. The solution procedure is based on the Boundary Element Method and involves the total derivative of the temperature and relevant sensitivity coefficients to find a correct position of the phase change front. In order to considerably reduce the number of degrees of freedom in the front tracking algorithm, the position and shape of the phase change front is interpolated by a small number of Bezier segments. Numerical examples are included to demonstrate the main features of the developed algorithms.

Biot's consolidation theory—application of BEM with time independent fundamental solutions for poro-elastic saturated media

This paper discusses the application of boundary elements, with time independent fundamental solutions, to solve Biot's plane strain consolidation equations for poro-elastic saturated media, assuming incompressible grains and fluid. The time marching scheme divides the analysis in small steps and applies finite differences to integrate the diffusion equations as well as to determine the time derivative of the total volumetric stresses. Each phase of the consolidation phenomenon is solved independently within a time step, and the exchange of common data associated to an iterative procedure provides means of coupling the two analyses. The domain integrals in the elastostatic integral equation, provides simple means of simulating elastic media heterogeneity, without any changes in the existing matrices, using the same procedure adopted to introduce plasticity to the BEM.

Blended kernel approximation in the ℋ︁‐matrix techniques

AbstractSeveral types of ℋ︁‐matrices were shown to provide a data‐sparse approximation of non‐local (integral) operators in FEM and BEM applications. The general construction is applied to the operators with asymptotically smooth kernel function provided that the Galerkin ansatz space has a hierarchical structure.The new class of ℋ︁‐matrices is based on the so‐called blended FE and polynomial approximations of the kernel function and leads to matrix blocks with a tensor‐product of block‐Toeplitz (block‐circulant) and rank‐k matrices. This requires the translation (rotation) invariance of the kernel combined with the corresponding tensor‐product grids. The approach allows for the fast evaluation of volume/boundary integral operators with possibly non‐smooth kernels defined on canonical domains/manifolds in the FEM/BEM applications. (Here and in the following, we call domains canonical if they are obtained by translation or rotation of one of their parts, e.g. parallelepiped, cylinder, sphere, etc.) In particular, we provide the error and complexity analysis for blended expansions to the Helmholtz kernel. Copyright © 2002 John Wiley & Sons, Ltd.

262 直接ブロック帯行列化BEMの定常音場解析への応用(OS08-3 境界要素法とその周辺技術(3))(OS08 境界要素法とその周辺技術)

262 直接ブロック帯行列化BEMの定常音場解析への応用(OS08-3 境界要素法とその周辺技術(3))(OS08 境界要素法とその周辺技術)

A sparse [formula omitted]-matrix arithmetic: general complexity estimates

In a preceding paper (Hackbusch, Computing 62 (1999) 89–108), a class of matrices ( H -matrices) has been introduced which are data-sparse and allow an approximate matrix arithmetic of almost linear complexity. Several types of H -matrices have been analysed in Hackbusch (Computing 62 (1999) 89–108) and Hackbusch and Khoromskij (Preprint MPI, No. 22, Leipzig, 1999; Computing 64 (2000) 21–47) which are able to approximate integral (nonlocal) operators in FEM and BEM applications in the case of quasi-uniform unstructured meshes. In the present paper, the general construction of H -matrices on rectangular and triangular meshes is proposed and analysed. First, the reliability of H -matrices in BEM is discussed. Then, we prove the optimal complexity of storage and matrix–vector multiplication in the case of rather arbitrary admissibility parameters η<1 and for finite elements up to the order 1 defined on quasi-uniform rectangular/triangular meshes in R d, d=1,2,3 . The almost linear complexity of the matrix addition, multiplication and inversion of H -matrices is also verified.

A Sparse ℋ-Matrix Arithmetic.

The preceding Part I of this paper has introduced a class of matrices (ℋ-matrices) which are data-sparse and allow an approximate matrix arithmetic of almost linear complexity. The matrices discussed in Part I are able to approximate discrete integral operators in the case of one spatial dimension. In the present Part II, the construction of ℋ-matrices is explained for FEM and BEM applications in two and three spatial dimensions. The orders of complexity of the various matrix operations are exactly the same as in Part I. In particular, it is shown that the applicability of ℋ-matrices does not require a regular mesh. We discuss quasi-uniform unstructured meshes and the case of composed surfaces as well.

428 弾性板に作用する衝撃荷重同定逆問題への境界要素法とフィルタ理論の応用

428 弾性板に作用する衝撃荷重同定逆問題への境界要素法とフィルタ理論の応用

Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity

In the direct formulation of the boundary element method, body-force and thermal loads manifest themselves as additional volume integral terms in the boundary integral equation. The exact transformation of the volume integral associated with body-force loading into surface ones for two-dimensional elastostatics in general anisotropy, has only very recently been achieved. This paper extends the work to treat two-dimensional thermoelastic problems which, unlike in isotropic elasticity, pose additional complications in the formulation. The success of the exact volume-to-surface integral transformation and its implementation is illustrated with three examples. The present study restores the application of BEM to two-dimensional anisotropic elastostatics as a truly boundary solution technique even when thermal effects are involved.