Rigid-plastic boundary element method based on the incremental theory

The boundary integral equations and boundary element formulation for rigid-plastic problems are derived based on the Levy-von Mises plastic stress-strain relation and on the fundamental solution obtained by using the linear quick-dropping function. A plastic compression problem in plane strain state is calculated. The results show that the calculated results are in agreement with the experimental results.     

A cubic element program for the solution of Laplace-type equations based on the boundary element method

This paper presents a program written in C language for the solution of Laplace's equations in two dimensions employing cubic boundary elements. The program imposes no restriction on the number of elements to be used in the analysis. Since it makes efficient use of memory it can be used to solve fairly large-sized problems even on a personal computer. Numerical examples are presented to illustrate the accuracy of the results obtained.     

Partitioning technique for boundary element method

The partitioning technique and its Fortran subroutines for the solution of a non-symmetrical fully populated matrix system encountered in the boundary element method are presented. The technique is such that the computer backing store is fully utilized and therefore a large-scale problem can be solved with a small computer. The derivation of formulae for this technique is given in detail. A corresponding computer program is developed and verified through two two-dimensional elastostatic problems. The influence of submatrix size on cost of computation time is discussed.     

Improvement of the accuracy in boundary element method based on high-order discretization

The boundary element method (BEM) is a popular method to solve various problems in engineering and physics and has been used widely in the last two decades. In high-order discretization the boundary elements are interpolated with some polynomial functions. These polynomials are employed to provide higher degrees of continuity for the geometry of boundary elements, and also they are used as interpolation functions for the variables located on the boundary elements. The main aim of this paper is to improve the accuracy of the high-order discretization in the two-dimensional BEM. In the high-order discretization, both the geometry and the variables of the boundary elements are interpolated with the polynomial function P_m, where m denotes the degree of the polynomial. In the current paper we will prove that if the geometry of the boundary elements is interpolated with the polynomial function P_m+1 instead of P_m, the accuracy of the results increases significantly. The analytical results presented in this work show that employing the new approach, the order of convergence increases from O(L₀)^m to O(L₀)^m+1 without using more CPU time where L₀ is the length of the longest boundary element. The theoretical results are also confirmed by some numerical experiments.     

基于结构元的H模糊自适应边界元

针对实际工程系统初始设计阶段经常出现材料的物理特性、结构的几何尺寸以及承受的外来作用等不确定性的问题,研究具有模糊不确定性的边界条件,提出基于模糊结构元（Fuzzy Structure Element,FSE）理论的模糊边界元法.该方法能简便、高效地处理边界条件具有模糊不确定性的系统.数值方法本身具有误差且系统自身具有模糊不确定性,故进一步研究模糊边界元法的H自适应算法,给出实用的误差估计公式;对角点处进行H自适应分析,得到较高精度的解.数值算例验证该方法的有效性和优越性.     

Adaptive finite element heterogeneous multiscale method for homogenization problems

In this paper we present an a posteriori error analysis for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. Unlike standard finite element methods, our discretization scheme relies on macro- and microfinite elements. The desired macroscopic solution is obtained by a suitable averaging procedure based on microscopic data. As the macroscopic data (such as the macroscopic diffusion tensor) are not available beforehand, appropriate error indicators have to be defined for designing adaptive methods. We show that such indicators based only on the available macro- and microsolutions (used to compute the actual macrosolution) can be defined, allowing for a macroscopic mesh refinement strategy which is both reliable and efficient. The corresponding a posteriori estimates for the upper and lower bound are derived in the energy norm. In the case of a uniformly oscillating tensor, we recover the standard residual-based a posteriori error estimate for the finite element method applied to the homogenized problem. Numerical experiments confirm the efficiency and reliability of the adaptive multiscale method.     

Approach of heterogeneous bio-modeling based on material features

To capture the heterogeneity of biomaterials, a material feature based approach of heterogeneous bio-modelling is presented in this paper. The concept of material feature is defined as the specified material distribution of a certain sub-region within a solid, which is a high level abstraction of design intent. These material features are finally laid down on the function representations, which consist of material composition functions. The definition, formation and domain of material composition functions are formally presented. In order to facilitate the evaluation of material distribution, these functions are classified into component function and constraint function. Meanwhile, to capture the distinct material composition partition existing in medical objects, the material interface is introduced. The problem of overlapping and/or ambiguous of the feature domains is addressed. Finally, the feature tree for storing, evaluating of material features and tracing of design intents is proposed and the feature solving algorithm is presented. A prototype heterogeneous bio-modeling system is implemented based on open source graphics kernel VTK, with the help of translation layer to improve the system's efficiency and compatibility.     

基于快速多极边界元法的沥青混凝土弹性模量预测

由于对沥青混凝土材料的研究无论是试验法还是经验法均建立在宏观层面上,无法与其细观结构建立本质的联系,因此利用快速多极边界元法(Fast Multipole Boundary Element Method,FMBEM),结合数字图像处理技术,实现沥青混凝土二维几何建模及弹性模量预测.通过数字图像处理技术识别拍摄得到的原始...     

H-R自适应边界元的模糊误差估计方法

为克服在利用传统自适应边界元法求解弹性问题时需对不同问题设计不同误差估计公式的缺点,以专家经验为基础,利用模糊逻辑理论,提出一种新的误差分析方法.基于H-R自适应边界元法,用FORTRAN编写求解2个经典平面弹性静力学问题的程序.分析表明该误差分析方法能较好地估计边界元解的误差.     

The boundary element method on the ICL DAP

In this paper we consider the implementation, on the ICL DAP, of a boundary element solution for two-dimensional potential problems. The DAP is shown to be particularly suited to this problem. In particular the numerical quadratures in the contributions to the overall system matrices are calculated in parallel and the rearrangement of the resulting system of equations is conveniently performed using the logical mask facility. A speedup by a factor of 100 is obtained compared with a corresponding sequential code on a DEC 1091.     

Recommendations for tool-handle material choice based on finite element analysis

Huge areas of work are still done manually and require the usages of different powered and non-powered hand tools. In order to increase the user performance, satisfaction, and lower the risk of acute and cumulative trauma disorders, several researchers have investigated the sizes and shapes of tool-handles. However, only a few authors have investigated tool-handles' materials for further optimising them. Therefore, as presented in this paper, we have utilised a finite-element method for simulating human fingertip whilst grasping tool-handles. We modelled and simulated steel and ethylene propylene diene monomer (EPDM) rubber as homogeneous tool-handle materials and two composites consisting of EPDM rubber and EPDM foam, and also EPDM rubber and PU foam. The simulated finger force was set to obtain characteristic contact pressures of 20 kPa, 40 kPa, 80 kPa, and 100 kPa. Numerical tests have shown that EPDM rubber lowers the contact pressure just slightly. On the other hand, both composites showed significant reduction in contact pressure that could lower the risks of acute and cumulative trauma disorders which are pressure-dependent. Based on the results, it is also evident that a composite containing PU foam with a more evident and flat plateau deformed less at lower strain rates and deformed more when the plateau was reached, in comparison to the composite with EPDM foam. It was shown that hyper-elastic foam materials, which take into account the non-linear behaviour of fingertip soft tissue, can lower the contact pressure whilst maintaining low deformation rate of the tool-handle material for maintaining sufficient rate of stability of the hand tool in the hands. Lower contact pressure also lowers the risk of acute and cumulative trauma disorders, and increases comfort whilst maintaining performance.     

A Boundary Element Method for Simulation of Deformable Objects

In this paper,a boundary element method is first applied to real-tim animation of deformable objects and to simplify data preparation.Next,the visibleexternal surface of the object in deforming process is represented by B-spline surface,whose control points are embedded in dynamic equations of BEM.Fi-nally,the above method is applied to anatomical simulation.A pituitary model in human brain,which is reconstructed from a set of anatomical sections, is selected to be the deformable object under action of virtual tool such as scapel or probe.It produces fair graphic realism and high speed performance.The results show that BEM not only has less computational expense than FEM,but also is convenient to combine with the 3D reconstruction and surface modeling as it enables the reduction of the dimensionality of the problem by one.     

A method for reverse engineering of material microstructure for heterogeneous CAD

Integration of material composition, microstructure, and mechanical properties with geometry information enables design and analysis of materials and products in a computer-aided design (CAD) environment. In this paper, we propose a method for the construction of material models from microstructure images, that can be integrated into a heterogeneous CAD representation. The method utilizes Radon and wavelet transforms to compute a surfacelet representation. A novel feature recognition method was developed to identify microstructure features, including embedded fibers and grain boundaries, from the surfacelet representation. The models and methods were demonstrated with examples of synthetic and engineered polymer nanocomposites, a metal alloy, and a medical dataset of human feet.     

An Internet-based computing platform for the boundary element method

Computers combined with the Internet are dramatically changing the engineering practices in design and analysis. More and more engineering software applications are moving to the Internet, prompted by the promising advantages, such as easy access for users everywhere with an Internet connection, easy upgrade of the software, easy control of the software. All these advantages will contribute to faster and cost-effective engineering software development and applications. Successful applications of the Internet computing depend largely on the speed of data transfer on the network. The boundary element method (BEM) has the inherent advantages over other domain-based numerical methods, because the size of the BEM model files are always considerably smaller, leading to faster data transfer on the current network. In this paper, a successful investigation in implementing the BEM on the Internet is presented. A BEM code for 2D elastostatic problems is used as the first solver in this work. A graphical-user interface (GUI) for the pre- and post-processing using Java, which provides platform-independent applications, is developed and implemented on the Internet. Demonstration problems using the developed platform clearly show the feasibility of the Internet-based computing and the potentials of this platform for future BEM development with further research.     

A mixed finite element method for boundary flux computation

Most finite element schemes for thermal problems estimate boundary heat flux directly from the derivative of the finite element solution. The boundary flux calculated by this approach is typically inaccurate and does not guarantee a global heat balance.In this paper we present a mixed finite element method for calculating the boundary flux and show the superiority of this method through numerical examples of both diffusion and advection-diffusion problems.     

Multi-scale boundary element modelling of material degradation and fracture

In the present paper a multi-scale boundary element method for modelling damage is proposed. The constitutive behaviour of a polycrystalline macro-continuum is described by micromechanics simulations using averaging theorems. An integral non-local approach is employed to avoid the pathological localization of micro-damage at the macro-scale. At the micro-scale, multiple intergranular crack initiation and propagation under mixed mode failure conditions is considered. Moreover, a non-linear frictional contact analysis is employed for modelling the cohesive-frictional grain boundary interfaces. Both micro- and macro-scales are being modelled with the boundary element method. Additionally, a scheme for coupling the micro-BEM with a macro-FEM is also proposed. To demonstrate the accuracy of the proposed method, the mesh independency is investigated and comparisons with two macro-FEM models are made to validate the different modelling approaches. Finally, microstructural variability of the macro-continuum is considered to investigate possible applications to heterogeneous materials.     

Recent developments in the Trefftz method for finite element and boundary element applications

In 1926 E. Trefftz published a paper about a variational formulation which utilizes boundary integrals. Almost half a century later researchers became interested again in the ideas of Trefftz when the potential advantage of the Trefftz-method for an efficient use in numerical application on a computer was recognized. The concept of Trefftz can be used both for finite element and boundary element applications. A crucial ingredient of the Trefftz- method is a set of linearly independent trial functions which a priori satisfy the governing differential equations under consideration. In this paper an overview of some recent developments to construct trial functions for the Trefftz-method in a systematic manner is given. Using different types of approximation functions (singular or non-singular) we can obtain very accurate finite element and boundary element algorithms.     

An efficient shape optimization technique of a two-dimensional body based on the boundary element method

An efficient approximation method to determine the optimum shape of the minimum weight of a body subjected to stress and displacement constraints is suggested by using the boundary element method. The objective function of weight is approximated to an expansion of a second-order Taylor series and the stress and displacement constraints to expansions of a first-order Taylor series, based on the boundary element sensitivity analysis at the current design point. The approximated subproblem is then solved by a linear complementary pivot method. Design variable reduction techniques of isoparametric interpolation and trigonometric series interpolation for the design boundary shape are also adopted for reducing the degrees of freedom of the design problems.     

Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem

We present the numerical implementation of a boundary element approximation for the plane mixed boundary value problem of the Laplacian. The performed Galerkin procedure is based on the direct boundary integral method. Its accuracy is improved by using appropriate singularity functions as additional test and trial functions besides quadratic splines. We analize the consistency error of the used numerical integrations and present asymptotic error estimates for the fully discretized numerical scheme which are of the same optimal orders as the Galerkin errors.