In this paper, we revisit the point-in-polyhedron problem. After reviewing previous work, we develop further insight into the problem. We then claim that, for a given testing point and a three-dimensional polyhedron, a single determining triangle can be found which suffices to determine whether the point is inside or outside the polyhedron.This work can be considered to be an extension and implementation of Horn's work, which inspired us to propose a theorem for obtaining determining triangles. Building upon this theorem, algorithms are then presented, implemented, and tested. The results show that although our code has the same asymptotic time efficiency as commonly used octree-based ray crossing methods, in practice it is usually several times and sometimes more than ten times faster, while other costs such as preprocessing time and memory requirements remain the same.The ideas proposed in this paper are simple and general. They thus extend naturally to multi-material models, i.e., polyhedrons subdivided into smaller regions by internal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

In this paper, we revisit the point-in-polyhedron problem. After reviewing previous work, we develop further insight into the problem. We then claim that, for a given testing point and a three-dimensional polyhedron, a single determining triangle can be found which suffices to determine whether the point is inside or outside the polyhedron.This work can be considered to be an extension and implementation of Horn's work, which inspired us to propose a theorem for obtaining determining triangles. Building upon this theorem, algorithms are then presented, implemented, and tested. The results show that although our code has the same asymptotic time efficiency as commonly used octree-based ray crossing methods, in practice it is usually several times and sometimes more than ten times faster, while other costs such as preprocessing time and memory requirements remain the same.The ideas proposed in this paper are simple and general. They thus extend naturally to multi-material models, i.e., polyhedrons subdivided into smaller regions by internal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

本文研究了球形颗粒填充复合材料的有效比热问题,考虑了基体和夹杂之间非完好黏结界面的影响,给出了有效比热的近似解析表达式。分别针对界面应力模型(ISM)和线弹簧模型(LSM)两种界面本构关系,对代表性体积单元(RVE)施加特定的位移或应力与温度的边界条件组合,并基于所构造的均匀变形场,以及多相多组分复合材料的Helmholtz自由能表达式,导出了包含界面影响的球形粒子填充的有效比热近似解析表达式。

本文研究考虑温度情况下基体和夹杂之间表/界面效应对复合材料有效性质的影响。由于表/界面效应的存在,即使在没有外力作用和温度改变的自然状态下,材料内部也会诱导产生一个弹性场,对复合材料有效性质的计算应该以此自然状态为参考构形算起。本文在相关文献基础上把表面能密度的表达式扩展到包含温度项的情形,由此推导出的表/界面本构关系以及界面的Young-Laplace方程中也引入了温度项。本文把界面和夹杂的整体作为一种"等效夹杂",通过计算其Helmholtz自由能,进而求出其体积模量、热膨胀系数和比热。把该"等效夹杂"的性质替换单一夹杂的性质应用到一般的细观力学方法中,就可以得到计及表/界面效应的热弹性复...

<正>各类颗粒或纤维填充复合材料中,通常采用线弹簧模型模拟复合位移在界面两侧的不连续,并通过放松罚函数模拟弹簧变形直至达到临界值断裂来模拟界面的逐渐脱胶的过程。但是当界面两侧的材料性质相差较大时,上述方法容易由于物理参数差异大造

作为一个研究小组,北京大学力学与空天技术系的SAP84小组在袁明武教授的领导下,近三十年来一直从事工程结构分析软件的研究,并在结构计算中独立发展了若干高效的算法。本文试图初步总结本小组近几年发展的几个算法——施工模拟、偶然偏心、振型积分、多点线性约束等在工程软件中的实现方案。

Simplicity of mesh generation and robustness against mesh entanglement during large deformations are key attractive features of particle based methods. These features can be exploited in number of engineering problems where traditional techniques suffer due to aforementioned limitations. Numerical modelling of particulate composites is one of such ideal engineering applications where particle based methods can be effectively used due to their simplicity and robustness. Complicated geometrical configurations of particulate composites obtained from techniques such as scanning electron microscopy (SEM) can be easily converted to particle based mesh without loosing much information. This enables more accurate analysis of the chosen composite materials. Therefore, a smooth particle hydrodynamics (SPH) based numerical technique is developed here to investigate the mechanical properties and evolution of debonding process in particulate composites. To perform the numerical study, a Lagrangian corrected SPH (CSPH) method is presented together with an appropriate numerical model for treating material interface discontinuity within the particulate composites. The material interface discontinuity is enforced using an innovative method which combines penalty formulation with a bilinear interface cohesive model for SPH method. The proposed SPH methodology is used in a number of numerical examples involving composite materials and related interface problems. The effect of penalty value on the interface model and of the smoothing length of the SPH method are also analysed during these simulations. The results illustrate the effectiveness, robustness and potential of the developed methodology. It is concluded that the proposed numerical techniques can be easily and effectively applied to simulate multi-phase composites with various interface conditions and, can provide useful information regarding the inherent mechanism of damage evolution and fracture of particulate or fibre reinforced composites. (C) 2009 Elsevier B.V. All rights reserved.

Simplicity of mesh generation and robustness against mesh entanglement during large deformations are key attractive features of particle based methods. These features can be exploited in number of engineering problems where traditional techniques suffer due to aforementioned limitations. Numerical modelling of particulate composites is one of such ideal engineering applications where particle based methods can be effectively used due to their simplicity and robustness. Complicated geometrical configurations of particulate composites obtained from techniques such as scanning electron microscopy (SEM) can be easily converted to particle based mesh without loosing much information. This enables more accurate analysis of the chosen composite materials. Therefore, a smooth particle hydrodynamics (SPH) based numerical technique is developed here to investigate the mechanical properties and evolution of debonding process in particulate composites. To perform the numerical study, a Lagrangian corrected SPH (CSPH) method is presented together with an appropriate numerical model for treating material interface discontinuity within the particulate composites. The material interface discontinuity is enforced using an innovative method which combines penalty formulation with a bilinear interface cohesive model for SPH method. The proposed SPH methodology is used in a number of numerical examples involving composite materials and related interface problems. The effect of penalty value on the interface model and of the smoothing length of the SPH method are also analysed during these simulations. The results illustrate the effectiveness, robustness and potential of the developed methodology. It is concluded that the proposed numerical techniques can be easily and effectively applied to simulate multi-phase composites with various interface conditions and, can provide useful information regarding the inherent mechanism of damage evolution and fracture of particulate or fibre reinforced composites. (C) 2009 Elsevier B.V. All rights reserved.

Local transformation, or topological reconnection, is one of the effective procedures for mesh improvement method, especially for three-dimensional tetrahedral mesh. The most frequently used local transformations for tetrahedral mesh are so-called elementary flips, such as 2-3 flip, 3-2 flip. 2-2 flip, and 4-4 flip. Owing to the reason that these basic transformations simply make a selection from several possible configurations within a relatively small region, the improvement of mesh quality is confined. In order to further improve the quality of mesh, the authors recently suggested a new local transformation operation, small polyhedron reconnection (SPR) operation, which seeks for the optimal tetrahedralization of a polyhedron with a certain number of nodes and faces (typically composed of 20-40 tetrahedral elements).This paper is an implementation of the suggested method. The whole process to improve the mesh quality by SPR operation is presented; in addition, some strategies, similar to those used in advancing front technique, are introduced to speed up the operation. The numerical experiment shows that SPR operation is quite effective in mesh improvement and more suitable than elementary flips when combined with smoothing approach. The operation can be applied to practical problems, gaining high mesh quality with acceptable cost for computational time. Copyright (C) 2009 John Wiley & Sons, Ltd.

Local transformation, or topological reconnection, is one of the effective procedures for mesh improvement method, especially for three-dimensional tetrahedral mesh. The most frequently used local transformations for tetrahedral mesh are so-called elementary flips, such as 2-3 flip, 3-2 flip. 2-2 flip, and 4-4 flip. Owing to the reason that these basic transformations simply make a selection from several possible configurations within a relatively small region, the improvement of mesh quality is confined. In order to further improve the quality of mesh, the authors recently suggested a new local transformation operation, small polyhedron reconnection (SPR) operation, which seeks for the optimal tetrahedralization of a polyhedron with a certain number of nodes and faces (typically composed of 20-40 tetrahedral elements).This paper is an implementation of the suggested method. The whole process to improve the mesh quality by SPR operation is presented; in addition, some strategies, similar to those used in advancing front technique, are introduced to speed up the operation. The numerical experiment shows that SPR operation is quite effective in mesh improvement and more suitable than elementary flips when combined with smoothing approach. The operation can be applied to practical problems, gaining high mesh quality with acceptable cost for computational time. Copyright (C) 2009 John Wiley & Sons, Ltd.

本文采用Smooth Particle Hydrodynamics(SPH)方法研究复合材料的等效力学性能和界面脱胶演化过程。应用修正的拉格朗日格式,采用罚数方法表征界面的位移不连续性和本质边界条件,模拟了含圆形和椭圆形夹杂的二维复合材料在平面应变条件下的脱胶破坏过程.

<正>基于粒子的无网格法的最有吸引力的特点是简单的格点生成以及在大变形问题中方法实施的鲁棒性。这些特点在大量工程问题中可以得到体现而传统方法在这些问题中的应用受到一定的限制,例如颗粒或纤维增强的复合材料界面破坏数值模拟。从扫描电镜得到的复杂几何构形可以很容易地转换成无网格法的粒子分布,从而

Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.

In this paper, we investigate boundary recovery, the problem that has troubled researchers ever since Delaunay-based methods were applied to generate mesh. There are a number of algorithms for boundary recovery already and most of them depend heavily on adding extra nodes. In this paper, we make an effort to seek a method to recover boundaries without using extra nodes.It was noted that some previous algorithms imposed artificial boundary constraints on a meshing problem at the recovering stage; we first try to discard these artificial constraints and thus make things easier. Then a new method is proposed by which the boundaries can be recovered by means of two operations: (1) creating a segment in the mesh and (2) removing a segment from the mesh. Both operations are special cases of a general local transformation called small polyhedron reconnection operation. The method works well when coupled with the sphere-packing method proposed by the first author. If the mesh sizing function is suitable, a good configuration of nodes will be created accordingly by the sphere-packing method and the boundary can be recovered by the local transformation presented here without inserting extra nodes. Copyright (c) 2007 John Wiley & Sons, Ltd.