A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients

A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.

BEM FOR MODAL ANALYSIS OF 3-D ANISOTROPIC STRUCTURES

The boundary element method for the modal analysis of freevibration for 3-D anisotropic structures using particular solutionshas been developed. The complete polynomials of order two are used toconstruct the particular solutions for general anisotropic materials.The numerical results for 3-D free vibra- tion analysis of anisotropic cantilever beam by the method presented is in goodagreement with the results us- ing the Ritz technique. Foranisotropic materials, the numerical results calculated form theproposed method are in good agreement with the results from MSC.NASTRAN.

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.

A Novel BEM for Modeling and Simulation of 3T Nonlinear Generalized Anisotropic Micropolar-Thermoelasticity Theory with Memory Dependent Derivative

The main aim of this paper is to propose a new memory dependent derivative(MDD)theory which called threetemperature nonlinear generalized anisotropic micropolar-thermoelasticity.The system of governing equations of the problems associated with the proposed theory is extremely difficult or impossible to solve analytically due to nonlinearity,MDD diffusion,multi-variable nature,multi-stage processing and anisotropic properties of the considered material.Therefore,we propose a novel boundary element method(BEM)formulation for modeling and simulation of such system.The computational performance of the proposed technique has been investigated.The numerical results illustrate the effects of time delays and kernel functions on the nonlinear three-temperature and nonlinear displacement components.The numerical results also demonstrate the validity,efficiency and accuracy of the proposed methodology.The findings and solutions of this study contribute to the further development of industrial applications and devices typically include micropolar-thermoelastic materials.

Efficient 2D Analysis of Interfacial Thermoelastic Stresses in Multiply Bonded Anisotropic Composites with Thin Adhesives

In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.

Influence of Inhomogeneity and Initial Stress on the Transient Magneto-Thermo-Visco-Elastic Stress Waves in an Anisotropic Solid

The object of the present paper is to study the transient magneto-thermo-visco-elastic stresses in a non-ho- mogeneous anisotropic solid under initial stress. The system of fundamental equations is solved by means of a dual reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are presented graphically to show the effects of initial stress and inhomogeneity on the displacement components and thermal stress components.

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.

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 .

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.

FEM/BEM混合法计算各向异性不均匀介质柱电磁散射

应用有限元-边界元(FEM/BEM)混合法计算二维各向异性不均匀介质柱电磁散射,对介质柱内、外区域分别采用有限元和边界元法进行分析,然后应用边界条件建立部分稀疏部分满填充的矩阵方程。应用内观法结合多波前法求解该矩阵方程,分别计算了均匀分布和不均匀分布的各向异性介质柱的雷达散射截面。数值计算表明,有限元-边界元混合法在分析和计算不均匀开放域电磁问题时有一定的优势。

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。

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。

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.

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 。

各向异性介质覆盖导体柱电磁散射特性的FEM/BEM分析

应用有限元-边界元耦合法计算任意截面形状二维各向异性介质覆盖导体柱的雷达散射截面,对介质柱内、外区域分别应用有限元和边界元法进行分析,然后通过场的连续性进行耦合,形成待求矩阵方程,最后应用内观法结合多波前法求解该方程.作为算例,分别计算了无限长各向同性介质覆盖导体方柱和圆柱在平面电磁波照射下的雷达散射截面,结果与有关文献一致,在此基础上计算了各向异性介质覆盖导体方柱和圆柱的雷达散射截面.