Symmetric coupling of multi‐zone curved Galerkin boundary elements with finite elements in elasticity

The coupling of Finite Element Method (FEM) with a Boundary Element Method (BEM) is a desirable result that exploits the advantages of each. This paper examines the efficient symmetric coupling of a Symmetric Galerkin Multi‐zone Curved Boundary Element Analysis method with a Finite Element Method for 2‐D elastic problems. Existing collocation based multi‐zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very difficult to achieve symmetry, increasing the computational work to solve the problem. This paper uses a fully Symmetric curved Multi‐zone Galerkin Boundary Element Approach that is coupled to an FEM in a completely symmetric fashion. The symmetry is achieved by symmetrically converting the boundary zones into equivalent ‘macro finite elements’, that are symmetric, so that symmetry in the coupling is retained. This computationally efficient and fast approach can be used to solve a wide range of problems, although only 2‐D elastic problems are shown. Three elasticity problems, including one from the FEM‐BEM literature that explore the efficacy of the approach are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Nodal sensitivities as error estimates in computational mechanics

Summary This paper proposes the use of special sensitivities, called nodal sensitivities, as error indicators and estimators for numerical analysis in mechanics. Nodal sensitivities are defined as rates of change of response quantities with respect to nodal positions. Direct analytical differentiation is used to obtain the sensitivities, and the infinitesimal perturbations of the nodes are forced to lie along the elements. The idea proposed here can be used in conjunction with general purpose computational methods such as the Finite Element Method (FEM), the Boundary Element Method (BEM) or the Finite Difference Method (FDM); however, the BEM is the method of choice in this paper. The performance of the error indicators is evaluated through two numerical examples in linear elasticity.     

Viscoplastic plane‐strain analysis of infinite solids using elastic supports

A highly efficient novel Finite Element Boundary Element Method (FEBEM) is proposed for the elasto‐viscoplastic plane‐strain analysis of displacements and stresses in infinite solids. The proposed method takes advantage of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) to achieve higher efficiency and accuracy by using the concept of elastic supports to simulate the effects of unbounded solid mass surrounding the region of interest. The BEM is used to compute the stiffnesses of elastic supports and to estimate the location of the truncation boundary for the finite element model. As compared to the conventional coupled FEBEM, the proposed method has three main computational advantages. Firstly, the symmetrical and highly banded form of the standard finite element stiffness matrix is not disturbed. Secondly, the proposed technique may be implemented simply by using standard codes for elasto‐viscoplastic finite element analysis and elastic boundary element analysis. Thirdly, the yielded zone is approximately located in advance by using the BEM and hence, an unnecessarily large extent of the domain does not have to be discretized for the finite element modelling. The efficiency and accuracy of the proposed method are demonstrated by computing elastic and elasto‐plastic displacements and stresses around ‘deep’ underground openings in rock mass subject to hydrostatic and non‐hydrostatic in situ stresses. Results obtained by the proposed method are compared with ‘exact’ solutions and with those obtained by using a BEM and a coupled FEBEM. Copyright © 1999 John Wiley & Sons, Ltd.     

An isogeometric extension of Trefftz method for elastostatics in two dimensions

In this paper, an approach to blend the Hybrid‐Trefftz Finite Element Method (HTFEM) and the Isogeometric Analysis (IGA) called the Isogeometric Trefftz (IGAT) method is presented. The structure of the isogeometric extension of the Trefftz method is formally the same as for its conventional counterpart, except the approximation of the boundary displacements and geometry that are carried out using the Non‐Uniform Rational B‐Splines (NURBS) instead of polynomials. In other words, only the element boundaries are approximated using NURBS basis while the Trefftz approximation is used in the interior of the elements. For that reason, IGAT can be ranked alongside recently developed Isogeometric Boundary Element Method (IGABEM), the NURBS‐Enhanced Finite Element Method (NEFEM), the Isogeometric Local Maximum Entropy (IGA‐LME) method, and the Isogeometrically enhanced Scaled‐Boundary element method (SBFEM), which all use NURBS approximation at the domain boundary only. Theoretical conjectures made in this paper are accompanied by three examples that show that IGAT leads to excellent results using only a few elements.     

OVERHAUSER TRIANGULAR ELEMENTS FOR THREE-DIMENSIONAL POTENTIAL PROBLEMS USING BOUNDARY ELEMENT METHODS

Interpolation to boundary data and one-dimensional Overhauser parabola blending methods are used to derive Overhauser triangular elements. The elements are C¹-continuous at inter-element nodes and no functional derivatives are required as nodal parameters. These efficient parametric representation elements are used to solve three-dimensional potential problems using the Boundary Element Method (BEM). Results obtained are generally as accurate as those obtained using Overhauser quadrilateral elements.     

Dynamic analysis of Timoshenko beams by the boundary element method

A Boundary Element Method formulation is developed for the dynamic analysis of Timoshenko beams. Based on the use of not time dependent fundamental solutions a formulation of the type called as Domain Boundary Element Method arises. Beside the typical domain integrals containing the second order time derivatives of the transverse displacement and of the rotation of the cross-section due to bending, additional domain integrals appear: one due to the loading and the other two due to the coupled differential equations that govern the problem. The time-marching employs the Houbolt method. The four usual kinds of beams that are pinned–pinned, fixed–fixed, fixed–pinned and fixed–free, under uniformly distributed, concentrated, harmonic concentrated and impulsive loading, are analyzed. The results are compared with the available analytical solutions and with those furnished by the Finite Difference Method.     

动载荷下应力强度因子的边界元计算

用Ｎａｒｄｉｎｉ－Ｂｒｅｂｂｉａ边界元法计算了动载荷下的应力强度因子，与解析解及有限元解相比较，效果较好。最后对计算结果进行了分析讨论。     

Static boundary element analysis of piles submitted to horizontal and vertical loads

In this paper a numerical model for the analysis of the interaction between soil and piles, with or without rigid caps, subjected to horizontal and vertical loads is presented. The piles are modelled here by the Finite Element Method (FEM) and the soil by the Boundary Element Method (BEM). In this formulation the pile is represented as one finite element and the displacements and tractions along the shaft are approximated by polynomial functions. Some examples are presented and the results obtained with this formulation are very close to those obtained with other formulations and with experimental results.     

表面裂纹应力强度因子计算的边界元法

本文用8节点二次等参元边界元法计算了半椭圆形表面裂纹的应力强度因子。在裂纹尖端附近使用了8节点奇异元,而在除裂尖附近以外的边界使用了4～8节点的变节点单元,以便于网格的疏密过渡。文中采用的等精度积分等处理方法都在一定程度上提高了解法的有效性。通过将本文解与高自由度的Newman有限元解比较表明:本文解的精度是较高的,也说明了用边界元法解这类问题只需很少的自由度就能得到令人满意的结果。     

A general 3D BEM/FEM coupling applied to elastodynamic continua/frame structures interaction analysis

This paper presents a procedure for coupling general finite element models with three‐dimensional bodies modelled by the Boundary Element Method (BEM). Shells, plates and frames are modelled by the Finite Element Method (FEM) and coupled to the BEM domain directly or by means of rigid blocks. The coupling is used for the analysis of buildings connected to half‐space by means of rigid footings, piles or plates in bending and other problems where combinations of different types of sub‐domains are required, composite domains for instance. Several numerical examples are analysed to demonstrate the robustness and accuracy of the proposed scheme. Copyright © 1999 John Wiley & Sons, Ltd.     

随机边界元法在大坝可靠性分析中的应用

本文综合考虑重力坝受自重，水压力及温度场的影响，应用随机边界元法，结合一阶二次矩法，分析了一大坝的强度可靠度的稳定可靠度，所得结果与随机有限元法所得相符。     

Embedded interfaces by polytope FEM

In this paper, the Polytope Finite Element Method is employed to model an embedded interface through the body, independent of the background FEM mesh. The elements that are crossed by the embedded interface are decomposed into new polytope elements which have some nodes on the interface line. The interface introduces discontinuity into the primary variable (strong) or into its derivatives (weak). Both strong and weak discontinuities are studied by the proposed method through different numerical examples including fracture problems with traction‐free and cohesive cracks, and heat conduction problems with Dirichlet and Dirichlet–Neumann types of boundary conditions on the embedded interface. For traction‐free cracks which have tip singularity, the nodes near the crack tip are enriched with the singular functions through the eXtended Finite Element Method. The concept of Natural Element Coordinates (NECs) is invoked to drive shape functions for the produced polytopes. A simple treatment is proposed for concave polytopes produced by a kinked interface and also for locating crack tip inside an element prior to using the singularity enrichment. The proposed method pursues some implementational details of eXtended/Generalized Finite Element Methods for interfaces. But here the additional DOFs are constructed on the interface lines in contrast to X/G‐FEM, which attach enriched DOFs to the previously existed nodes. Copyright © 2011 John Wiley & Sons, Ltd.     

The DRM‐MD integral equation method: an efficient approach for the numerical solution of domain dominant problems

This work presents a multi‐domain decomposition integral equation method for the numerical solution of domain dominant problems, for which it is known that the standard Boundary Element Method (BEM) is in disadvantage in comparison with classical domain schemes, such as Finite Difference (FDM) and Finite Element (FEM) methods. As in the recently developed Green Element Method (GEM), in the present approach the original domain is divided into several subdomains. In each of them the corresponding Green's integral representational formula is applied, and on the interfaces of the adjacent subregions the full matching conditions are imposed. In contrast with the GEM, where in each subregion the domain integrals are computed by the use of cell integration, here those integrals are transformed into surface integrals at the contour of each subregion via the Dual Reciprocity Method (DRM), using some of the most efficient radial basis functions known in the literature on mathematical interpolation. In the numerical examples presented in the paper, the contour elements are defined in terms of isoparametric linear elements, for which the analytical integrations of the kernels of the integral representation formula are known. As in the FEM and GEM the obtained global matrix system possesses a banded structure. However in contrast with these two methods (GEM and non‐Hermitian FEM), here one is able to solve the system for the complete internal nodal variables, i.e. the field variables and their derivatives, without any additional interpolation. Finally, some examples showing the accuracy, the efficiency, and the flexibility of the method for the solution of the linear and non‐linear convection–diffusion equation are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

滚筒洗衣机机箱动态特性分析

结合实验模态与有限元理论模态分析，对滚筒洗衣机的机箱进行振动特性分析。首先，采用有限元软件ANSYS理论模态分析对机箱进行模态求解，得到计算模态参数;另外，用脉冲激励法对机箱进行模态实验，得到实验模态参数。通过比较理论模态与实验模态参数，结果表明吻合较好。基于对机箱固有特性的分析，提出机箱结构动态特性修改方案，并通过理论验证，说明改进后机箱的振动特性得到了明显的改善。     

Boundary element analysis of thin plates internally bounded by rigid patches

Procedures are described for modelling a structural system consisting of thin Kirchhoff plates with internal patch areas capable of displacing as rigid flat surfaces. The physical prototype for these patches could be interconnection points for one-dimensional frame type elements of various shapes and layout, rigidly connected at these finite size 'joints' in the plate. The numerical procedure for modelling the thin plate is the Direct Boundary Element Method (DBEM) and a simple overview of this procedure is provided. Potential trouble spots, of which the user should be aware, are described. The paper will be of interest to structural engineers for analysis of frames having both plate and simple frame elements, for example, building frames; and also to researchers seeking the greater detail that this refined procedure can provide. As a practical tool, the methods described are computationally competitive with existing procedures, including the more rugged approaches used by building structural engineers for dynamic and torsional analysis.     

MTMDs控制高速铁路简支箱梁桥车致振动噪声的研究

轨道不平顺性激励引起桥梁结构振动,进而向空间辐射噪声。为了探明多重调谐质量阻尼器（MTMDs）对桥梁结构噪声的影响,选取32 m双线混凝土简支箱梁为研究对象,建立了移动集中力-桥梁-MTMDs耦合振动模型,根据桥梁的挠曲频响函数,求取了MTMDs的最优控制参数。在此基础上,采用瞬态有限元法和声学边界元法研究了不同数量调谐质量阻尼器对桥梁的减振、降噪效果。研究结果表明：MTMDs能有效控制桥梁的最大振动响应;由于MTMDs仅对一阶竖弯频率处的结构振动控制有效,使得其对结构噪声的控制效果不甚明显,对近轨侧25 m处声场的平均降噪效果约0.5 dB。     

Four-parameter functionally graded cracked plates of arbitrary shape: A GDQFEM solution for free vibrations

The dynamic behavior of moderately thick FGM plates with geometric discontinuities and arbitrarily curved boundaries is investigated. The Generalized Differential Quadrature Finite Element Method (GDQFEM) is proposed as a numerical approach. The irregular physical domain in Cartesian coordinates is transformed into a regular domain in natural coordinates. Several types of cracked FGM plates are investigated. It appears that GDQFEM is analogous to the well-known Finite Element Method (FEM). With reference to the proposed technique the governing FSDT equations are solved in their strong form and the connections between the elements are imposed with the inter-element compatibility conditions. The results show excellent agreement with other numerical solutions obtained by FEM.     

A numerical algorithm for simulation of the electric corona discharge in the triode system

A numerical algorithm is described to calculate the charge density, electric field and corona current distribution in the corona triode. The algorithm employs a hybrid technique based on the Boundary and Finite Element Methods (FEM). FEM is used to determine the electric field because of free space charge produced by the corona discharge. The Boundary Element Method (BEM) is applied for calculating the other component of electric filed as a result of the voltage applied to the electrodes. The Method of Characteristics (MOC) is used to update the space charge density distribution. The characteristic lines are traced backwards from points of the analysed domain to the corona wire. The current density, electric field and space charge density distributions can be controlled by changing the configuration of the system. Results of calculations in a few different cases show the influence of different parameters on the work of the corona triode.     

高层建筑—地基动力相互作用半解析法的研究

提出一种上部结构有限条法、地基（土）特解边界元法相结合的半解析方法，首次建立了这一力学模型在频域内的运动方程，并编制了求解结构－地基动力相互作用的程序。通过计算有关算例，并与ＳｕｐｅｒＳＡＰ程序计算结果进行比较，证明本文的基本理论和计算程序是正确、可行的。     

Testing complete and compact radial basis functions for solution of eigenvalue problems using the boundary element method with direct integration

This paper analyses the performance of the main radial basis functions in the formulation of the Boundary Element Method (DIBEM). This is an alternative for solving problems modeled by non-adjoint differential operators, since it transforms domain integrals in boundary integrals using radial basis functions. The solution of eigenvalue problem was chosen to performance evaluation. Natural frequencies are calculated numerically using several radial functions and their accuracy is evaluated by comparison with the available analytical solutions and with the Finite Element Method as well. The standard radial basis functions have presented similar performance to compact radial functions, being even slightly superior.