A Virtual Boundary Element Method for Three-Dimensional Inverse Heat Conduction Problems in Orthotropic Media

This paper aims to apply a virtual boundary element method(VBEM)to solve the inverse problems of three-dimensional heat conduction in orthotropic media.This method avoids the singular integrations in the conventional boundary element method,and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm.When the VBEM is applied to the inverse problems,the numerical instability may occur if a virtual boundary is not properly chosen.The method encounters a highly illconditioned matrix for the larger distance between the physical boundary and the virtual boundary,and otherwise is hard to avoid the singularity of the source point.Thus,it must adopt an appropriate regularization method to deal with the ill-posed systems of inverse problems.In this study,the VBEM and different regularization techniques are combined to model the inverse problem of three-dimensional heat conduction in orthotropic media.The proper regularization techniques not only make the virtual boundary to be allocated freer,but also solve the ill-conditioned equation of the inverse problem.Numerical examples demonstrate that the proposed method is efficient,accurate and numerically stable for solving the inverse problems of three-dimensional heat conduction in orthotropic media.

ELECTRO-MECHANICAL COUPLING ANALYSIS OF MEMS STRUCTURES BY BOUNDARY ELEMENT METHOD

In this paper,we present the applications of Boundary Element Method(BEM) to simulate the electro-mechanical coupling responses of Micro-Electro-Mechanical systems(MEMS). The algorithm is programmed in our research group based on BEM modeling for electrostatics and elastostatics.Good agreement is shown while the simulation results of the pull-in voltages are compared with the theoretical/experimental ones for some examples.

Pile-clayey soil interaction analysis by boundary element method

This paper is an attempt to solve the soil-pile interaction problems using the boundary element method（BEM）.A computer package called PGroupN,which deals mainly with the analysis of the pile group problem,is employed in this study.Parametric studies are carried out to assess the impacts of the pile diameter,pile length,ratio of spacing to diameter and the thickness of soil stratum.The external load is applied incrementally and,at each increment,a check is made that the stress state at the pile-soil interfaces does not violate the yield criteria.This is achieved by specifying the limited stresses of the soil for the axial pile shaft capacity and end-bearing resistance.The elements of the pile-soil interface yielded can take no additional load,and any increase in load is therefore redistributed between the remaining elements until all elements have failed.Thus,by successive application of loading increments,the entire load-displacement relationship for the pile group is determined.It is found that as the applied load reaches the ultimate bearing capacity of the pile group,all the piles will share the same amount of load.An exception to this case is for the center pile in a group of 9 piles embedded in clay,which is not consistent with the behaviors of the other piles in the group even if the load reaches the ultimate state.For the 4 piles group embedded in clay,the maximum load carried by the base does not exceed 8% of the load carried by each pile with different diameters.This low percentage ascertains that the piles embedded in cohesive soils carry most of the load throughout their shafts.

CALCULATION FOR PATH-DOMAIN INDEPENDENT J INTEGRAL WITH ELASTO-VISCOPLASTIC CONSISTENT TANGENT OPERATOR CONCEPT-BASED BOUNDARY ELEMENT METHODS

This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals.

KIN SP:A boundary element method based code for single pile kinematic bending in layered soil

In high seismicity areas, it is important to consider kinematic effects to properly design pile foundations.Kinematic effects are due to the interaction between pile and soil deformations induced by seismic waves. One of the effect is the arise of significant strains in weak soils that induce bending moments on piles. These moments can be significant in presence of a high stiffness contrast in a soil deposit. The single pile kinematic interaction problem is generally solved with beam on dynamic Winkler foundation approaches(BDWF) or using continuous models. In this work, a new boundary element method(BEM)based computer code(KIN SP) is presented where the kinematic analysis is preceded by a free-field response analysis. The analysis results of this method, in terms of bending moments at the pile-head and at the interface of a two-layered soil, are influenced by many factors including the soil-pile interface discretization. A parametric study is presented with the aim to suggest the minimum number of boundary elements to guarantee the accuracy of a BEM solution, for typical pile-soil relative stiffness values as a function of the pile diameter, the location of the interface of a two-layered soil and of the stiffness contrast. KIN SP results have been compared with simplified solutions in literature and with those obtained using a quasi-three-dimensional(3D) finite element code.

REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS

A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results.

Radial integral boundary element method for simulating phase change problem with mushy zone

A radial integral boundary element method(BEM)is used to simulate the phase change problem with a mushy zone in this paper.Three phases,including the solid phase,the liquid phase,and the mushy zone,are considered in the phase change problem.First,according to the continuity conditions of temperature and its gradient on the liquid-mushy interface,the mushy zone and the liquid phase in the simulation can be considered as a whole part,namely,the non-solid phase,and the change of latent heat is approximated by heat source which is dependent on temperature.Then,the precise integration BEM is used to obtain the differential equations in the solid phase zone and the non-solid phase zone,respectively.Moreover,an iterative predictor-corrector precise integration method(PIM)is needed to solve the differential equations and obtain the temperature field and the heat flux on the boundary.According to an energy balance equation and the velocity of the interface between the solid phase and the mushy zone,the front-tracking method is used to track the move of the interface.The interface between the liquid phase and the mushy zone is obtained by interpolation of the temperature field.Finally,four numerical examples are provided to assess the performance of the proposed numerical method.

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modem structural engineering. This paper introduces the boundary element method （BEM） into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic me- dia with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.

海洋结构物波浪砰击的数值研究综述

波浪砰击是发生在波浪与结构物之间的一种强非线性相互作用,其载荷通常具有峰值大、作用时间短的特点.近年来,海上极端环境导致海洋结构物经常遭受严重的波浪砰击,造成生命和财产损失,从而使得波浪砰击问题备受重视.对于复杂的砰击过程,理论分析和模型实验仅能给出砰击载荷的简化解析解及有限的砰击流场信息,数值模拟逐渐成为研究波浪砰击问题的有效手段.目前,国内外学者已经对海洋结构物的波浪砰击载荷特性、砰击作用过程及其影响因素等问题开展了大量的数值研究,并获得了许多重要的研究结论.针对海洋结构物波浪砰击的数值研究进展、现有方法及重要结论进行综述,为波浪砰击数值模拟的进一步研究提供有益参考.

保形(Conformal)结构互连电容的BEM模拟

介绍了一种基于扫描线的复杂保形介质结构快速生成算法 .该算法应用多边形的扩展运算和集合运算形成保形介质 ,同时处理保形介质中的凹槽 ,并已实现于边界元素法三维互连寄生电容提取软件 B3D中 .数值结果表明 ,该算法可靠 ,并有很高效率 .

基于快速多极间接边界元法的地震超材料隔震效应

中国是世界上遭受地震灾害较严重的国家之一。近年来,灾害性地震给人们的生命财产带来了极大的损失,对重大工程结构开展减震隔震设计成为结构设计中重要的一环。本文将快速多极间接边界元法(FMIBEM)应用到2维地震超材料对地震波的散射模拟,并求解一种周期性隔震材料——岩土复合地震超材料(RSCSM)的隔震效应;在精度验证基础上,对RSCSM的带隙结构及不同单晶胞结构下的隔震效果与带隙范围进行详细的数值分析。结果表明:采用FMIBEM能够有效地处理大型地震超材料对地震波的宽频散射问题;RSCSM能够隔离地震波超低频段隙,方形晶胞结构产生的带隙宽度(0.5~17.0 Hz与54.0~72.0 Hz)涵盖了地震波产生危害的主要频段(0.5~2.0 Hz),隔震效果可达35%以上;改变RSCSM的单晶胞结构会对地震超材料带隙结构产生重要影响。方形晶胞结构产生的带隙约为0.5~17.0 Hz和54.0~72.0 Hz;菱形晶胞结构产生的带隙约为0.5~20.0 Hz;菱形单点晶胞结构产生的带隙约为0.5~16.0 Hz和40.0~57.0 Hz;菱形双点晶胞结构产生的带隙约为0.5~14.0 Hz。硬散射体填充率也会对带隙产生重要影响,相同填充率情况下,四边形晶胞能够产生更宽的带隙,并且能够在更低的填充率情况下产生更好的带隙效果。菱形单点与菱形双点晶胞结构只能在非常高的填充率情况下产生较好的带隙效果。本文研究为地震超材料对地震波散射的模拟提供一种高效方法,研究结论可为地基隔震设计提供科学依据。

有限水深环境中声辐射预测的快速边界元法

由于水底和水面的影响,结构在有限水深环境中的辐射声场与在自由空间中的辐射声场有很大区别。为了更高效准确地分析有限水深环境中大规模结构的辐射声场,文章构建一种快速边界元法(boundary element method,BEM)。采用宽频快速多极算法对计算过程进行加速处理,针对算法中最为耗时的M2L/F2H变换过程,通过建立判定准则将均匀层格林函数中的多阶虚源分为近场和远场,从而设计不同求解方案,极大减少M2L/F2H的变换次数,显著提高求解效率。数值算例验证了文章方法的准确性和高效性,并体现出该方法在浅海声学分析中的工程潜力。

弹性空间结构系统的BEM-FEM耦合分析

提出一种供弹性空问结构系统进行数值计算的BEM—FEM耦合分析方法,适用于对称的和非对称的结构,可以承受分布的或集中的荷载作用。结合大直径圆筒结构算例的计算分析,证实这一方法在求解无限域或半无限域介质中弹性空间结构系统时,是一种很有效的方法。

基于LMS Virtual.Lab的油底壳辐射噪声预测分析

随着以仿真计算为主的振动噪声控制技术应用于产品结构设计的日益成熟,仿真技术对发动机油底壳的表面辐射噪声预测分析起到了越来越大的作用。本文根据油底壳实体模型建立了有限元分析模型,通过模态分析确定了主要振动位置,利用ANSYS谱分析得到了表面振动位移,采用直接边界元法利用LMS Virtual.Lab软件分析了油底壳外场辐射噪声,并探讨了油底壳含油量及肋板结构对辐射噪声的影响。

Wave Reflection by Rectangular Breakwaters for Coastal Protection

In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considered.The main objective is an understanding of the effect of the current and various geometrical parameters on the reflection coefficient.The wave used in the study is based on potential theory,and the submerged structures consist of two rectangular breakwaters positioned at a fixed distance from each other and attached to the bottom of a wave flume.The numerical modeling approach employed in this work relies on the Boundary Element Method(BEM).The results are compared with experimental data to validate the approach.The findings of the study demonstrate that the double rectangular breakwater configuration exhibits superior wave attenuation abilities if compared to a single rectangular breakwater,particularly at low wavenumbers.Furthermore,the study reveals that wave mitigation is more pronounced when the current and wave propagation are coplanar,whereas it is less effective in the case of opposing current.

THE CALCULATION OF THE VOLUME INTEGRAL IN BEM OF TWO DIMENSIONAL ELASTICITY

In this paper, a method of transforming volume integrals to boundary integrals is given for complicated loadings such as a i(y)x i and b i(x)y i . In the present method the volume integrals are approximately transformed to boundary integrals.

基于真实细观形貌的固体推进剂力学性能虚单元预示方法

真实的细观形貌是进行固体推进剂细观力学性能预示的基础。通过CT扫描图片处理获得了固体推进剂真实的细观几何形貌及各组分参数,并生成了固体推进剂颗粒填充模型;采用多边形网格剖分方案,减少使用常规单元时各组分颗粒尺度差异带来的低质量网格影响;通过对单元和节点的后处理,设计了应对真实细观形貌的周期边界条件处理方案;引入虚单元法(VEM)开展固体推进剂细观力学性能预示,设计含夹杂算例,验证了VEM以及周期边界条件处理方案的可行性和准确性;利用内聚力单元模拟基体与颗粒间的“脱湿”效应,对真实细观模型以及颗粒填充模型开展了等效松弛模量测试。仿真结果表明,真实细观模型中不规则的颗粒几何形状会抑制“脱湿”现象的发生,其表现出的等效松弛模量较颗粒填充模型大。此外,两类模型预示的松弛模量最大相对误差为13.1%,这表明在固体推进剂配方设计中颗粒填充模型可以替代真实的几何模型进行固体推进剂等效力学性能的预示。结合VEM在应对固体推进剂各组分几何尺度差异以及周期性边界条件设计方面的优势,可进一步利用VEM开展三维固体推进剂力学性能的预示。

基于数据驱动的浅海波导声辐射预测方法

结合计算力学和深度学习理论,提出一种基于数据驱动的浅海波导声辐射预测方法。通过集成有限元法—虚质量法—基于虚源法的边界元法的计算框架,获取浅海波导声辐射响应,为深度学习提供大量声压数据;进而,通过训练ConvNeXt卷积神经网络提取采样点声场特征;最终实现浅海水下结构辐射声压级的快速预测,并通过算例表明预测方法的有效性。

二维多重调和方程的BEM(法)及其应用

对二维多重非齐次调和方程应用BEM求解时将会出现域内积分项 ,在假定非齐次项为m次调和的情况下 ,将域内积分转化为边界积分 ,从而给出了相应的不含域内积分项的边界和积分方程 。

BEM/FEM耦合螺旋桨静强度计算方法

[目的]螺旋桨强度的可靠性与船舶安全航行直接相关。为了快速且准确地计算螺旋桨强度,[方法]将边界元(BEM)和有限元法(FEM)耦合开发螺旋桨强度预报程序。运用低阶边界元法程序对螺旋桨进行水动力性能计算,并使用普朗特—许力汀平板摩擦阻力公式进行粘性修正,然后将计算得到的桨叶表面压力和粘性修正力作为有限元法结构计算的面力输入。针对螺旋桨结构形状的特殊性,发展实体螺旋桨有限元结构单元的自动划分方法,运用有限元结构计算方程计算出螺旋桨在表面压力和体积力作用下的应力与位移分布。以DTRC 4119模型桨为例,对提出的方法进行收敛性和网格无关性分析,并与文献的有限元软件计算结果进行比较,以验证其有效性。[结果]计算结果表明,提出的方法能够准确计算螺旋桨的应力和位移分布。[结论]该方法避免了人工建模及有限元网格划分的过程,具有实施程序简便、计算效率高等优点,可嵌入到螺旋桨的理论设计和优化设计过程中,形成快速计算螺旋桨强度的能力,提高螺旋桨设计的效率。