消声器传递损失预测的边界元数值配点混合方法

将边界元法与数值配点法结合形成混合方法用于计算任意截面形状消声器的传递损失。消声器划分为若干子结构,用边界元法计算具有非规则形状的子结构阻抗矩阵,用二维有限元法提取等截面子结构特征值及特征向量,用配点法获得阻抗矩阵;将每个子结构阻抗矩阵连接用于传递损失计算。为减少计算时间提出简化方法计算消声器传递损失。结果表明,混合法在保证计算精度前提下可节省计算时间。     

计及液面晃动和液体可压缩影响时部分潜入水中的截面任意形状柱体的振动分析

本文研究同时计及液面晃动和液体可压缩影响时部分潜入水中的截面任意形状柱体的振动特性,以文[1]的分析为基础,进一步利用三角级数的正交完备性,将水体势函数沿柱体的外壁Fourier级数展开,导出了截面任意形状柱体在水中自由振动时的固有频率和振型函数的解析表达式,结果可借助于计算机数值求得。本文最后还给出了一个算例,分析表明,本文的分析方法对于解决一般柱体与水耦联振动的工程实际问题有着重要的应用价值。     

Kirchhoff型裂纹板的边界元法

本文用的复变函数理论,导出了含裂板弯曲问题的基本解。该基本解满足自由裂纹的边界条件。将其引入直接或间接积分方程中,只要对板的外边界进行离散,就可计算有限尺寸裂纹板的弯曲问题。算例表明,本文所得到的基本解用以求解裂纹板弯曲问题划分的单元较少,精度较高。本文的方法还可用以求解含有形状比较复杂的裂纹或孔洞板弯曲问题的基本解。     

断裂力学的数值方法概述

断裂力学主要研究含有裂缝的结构体的强度以及裂纹扩展规律，以防止结构产生裂纹破坏以及控制裂纹扩展为目的。但是，由于断裂问题以及相关控制方程的复杂性，只有少部分特殊的问题才有解析解，因此，大部分断裂问题需要借助于数值方法才能得到解决。本文就课外阅读的相关文献进行简要介绍和总结，粗略的介绍断裂力学的一些数值方法，例如有限元，边界元以及无网格方法，并对他们的相关的优缺点进行分析。     

求解二维结构-声耦合问题的一种直接方法

本文基于传递矩阵法(TMM)和虚拟边界元法(VBEM)，提出了一种求解在谐激励作用下二维结构-声耦合问题的直接法。文中对任意形状的二维弹性环建立了一阶非齐次运动微分方程组，便于用齐次扩容精细积分法求解，对于含有任意形状孔穴的无穷域流体介质的Helmholtz外问题，采用复数形式的Burton-Miller型组合层势法建立了虚拟边界元方程，保证了声压在全波数域内存在唯一解。根据叠加原理并结合最小二乘法，提出了一种耦合方程的直接解法，由于该方法不存在迭代过程，因而具有较高的计算精度和效率。文中给出了二个典型弹性环在集中谐激励力作用下声辐射算例，计算结果表明本文方法较通常采用的混合FE／BE法更为有效。     

含裂纹的矩形截面压电材料反平面问题的应力场和电场

研究了含裂纹的矩形截面的压电材料在平面内电场和反平面荷载作用下的问题。得到了满足拉普拉斯方程、电渗透裂纹面边界条件的位移函数解和电势函数解,从而得到了电场和弹性场的基本解。最后,用边界配置法计算了应力强度因子和能量释放率。结果表明,这种半解析半数值的方法计算简便,而且具有足够的精确性和广泛的应用性。     

薄壁杆件翘曲剪应力的边界元精确积分解法

用非连续边界元对薄壁杆件的约束扭转进行了分析,推导出了求解边界点二次翘曲函数值的边界积分方程,给出了边界积分方程数值求解时积分计算的精确表达式。数值算例表明:利用边界积分方程方法分析薄壁杆件的约束扭转问题时效率和精度高,同时采用精确积分可以有效的处理"边界层效应"问题。     

基于水平集算法的扩展比例边界有限元法研究

扩展比例边界有限元法在裂纹贯穿单元采用Heaviside阶跃函数描述裂纹面两侧的不连续位移,在裂尖则采用半解析的比例边界有限元描述奇异应力场。该方法具有无需预先知道裂尖渐进场的形式,无需采用特殊的数值积分技术直接生成裂尖刚度阵,对多种应力奇异类型可根据定义直接求解广义应力强度因子的特点。该文将扩展比例边界有限元法与水平集方法相结合,进一步发展了扩展比例边界有限元法,并将其应用于解决裂纹扩展的问题。在数值算例中,通过编写完整的MATLAB分析计算程序,求解了单边缺口的三点弯曲梁和四点剪切梁的裂纹扩展问题,计算结果显示扩展比例边界有限元法能有效地预测裂纹轨迹和荷载-位移曲线。通过参数敏感性分析,还可得出该方法具有较低的网格依赖性,且对裂纹扩展步长不敏感。     

非紧致阻抗圆柱气动噪声数值预测与控制方法

为预测非定常流动与非紧致阻抗固体边界相互作用产生的气动噪声,开发一种基于精确格林函数和声模拟理论的气动噪声数值预测方法。非紧致阻抗边界对声波的散射作用计入精确格林函数,远场噪声采用FW-H方程计算。对具有任意几何外形的非紧致阻抗边界,采用边界元方法计算满足声学硬边界或声学阻抗边界条件的精确格林函数。同时,推导了具有阻抗边界条件的二维非紧致圆柱精确格林函数的解析解用以验证数值计算方法。数值计算结果表明数值解与解析解的结果一致,数值解要取得好的网格收敛效果需要在一个波长内布置至少20个网格点。圆柱绕流气动噪声预测结果表明,非紧致边界的阻抗特性对声传播有显著影响,采用合适的阻抗布置方式可以取得有效的噪声控制效果。     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

An efficient dual boundary element technique for a two-dimensional fracture problem with multiple cracks

An efficient dual boundary element technique for the analysis of a two-dimensional finite body with multiple cracks is established. In addition to the displacement integral equation derived for the outer boundary, since the relative displacement of the crack surfaces is adopted in the formulation, only the traction integral equation is established on one of the crack surfaces. For each crack, a virtual boundary is devised and connected to one of the crack surfaces to construct a closed integral path. The rigid body translation for the domain enclosed by the closed integral path is then employed for evaluating the hypersingular integral. To solve the dual displacement/traction integral equations simultaneously, the constant and quadratic isoparametric elements are taken to discretize the closed integral paths/crack surfaces and the outer boundary, respectively. The present method has distinct computational advantages in solving a fracture problem which has arbitrary numbers, distributions, orientations and shapes of cracks by a few boundary elements. Several examples are analysed and the computed results are in excellent agreement with other analytical or numerical solutions.     

Stress intensity factors for fatigue cracking of round bars

The stress intensity factor for a single edge crack of either straight or circular front in a round bar has been determined using both the degenerated quarter-point isoparametric finite element and experimental fatigue crack growth data, and compared with values found by earlier investigators.The results of this study confirm that the stress intensity factors for straight edged surface cracks are lower in round bars than in square bars and a comparison of finite element and experimental results indicates that the effective stress intensity factor at the centre of the fatigue crack front in a round bar is 17% greater than its theoretical value.A correction function is proposed to account for the effect on the stress intensity factor of the circular boundary of a round bar.     

Torsion of an elastic space with a crack on the surface of revolution

Numerical methods for solving integral equations of an axisymmetric problem of torsion of an elastic space with cracks on the surface of revolution are suggested for the cases of cracks crossing the axis of symmetry and cracks that have no common points with this axis. We also present relations for calculating the stress intensity factors at crack tips. Numerical results are obtained for a conic or paraboloidal simply connected crack and for a doubly connected crack lying on a surface formed by the revolution of an arbitrarily oriented straight segment or a parabolic arc. The crack faces are either subjected to a constant load or free of any forces; the body is subjected to torsion at infinity.Karpenko Physico-Mechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 6, pp. 87–93, November–December, 1993.     

A New Boundary Element for Plane Elastic Problems Involving Cracks and Holes

By applying the new boundary integral formulation proposed recently by Chau and Wang (1997) for two-dimensional elastic bodies containing cracks and holes, a new boundary element method for calculating the interaction between cracks and holes is presented in this paper. Singular interpolation functions of order r^-1/2 (where r is the distance measured from the crack tip) are introduced for the discretization of the crack near the crack tips, such that stress singularity can be modeled appropriately. A nice feature for our implementation is that singular integrands involved at the element level are integrated analytically. For each of the hole boundaries, an additional unknown constant is introduced such that the displacement compatibility condition can be satisfied exactly by the complex boundary function H(t), which is a combination of the traction and displacement density. Another nice feature of the present formulation is that the stress intensity factors (both K_{_I} and K_{_II}) at crack tips are expressed in terms of the nodal unknown of H(t) exactly, and no extrapolation of numerical data is required. To demonstrate the accuracy of the present boundary element method, various crack problems are considered: (i) the Griffith crack problem, (ii) the interaction problem between a circular hole and a straight crack subject to both far field tension and compression, and (iii) the interaction problem between a circular hole and a kinked crack subject to far field uniaxial tension. Excellent agreement with existing results is observed for the first two problems and also for the last problem if the crack-hole interaction is negligible. This revised version was published online in August 2006 with corrections to the Cover Date.     

Explicit solutions of magnetoelastic fields in a soft ferromagnetic solid with curvilinear cracks

The problem of curvilinear cracks lying on a soft ferromagnetic solid subjected to a remote uniform magnetic induction is considered. With the complex variable technique, the general solutions of both the magnetic field quantities and the magnetoelastic stresses can be obtained. In order to illustrate the effect of magnetic induction, the solutions for the problem with one arc crack and two arc cracks are presented in a closed form. The stress intensity factors in the vicinity of crack tip and the crack opening condition are also derived. Considering the magnetic stress induced by an oblique magnetic field on the crack surface, one can find that the stress intensity factors of mode-I and mode-II are related to the incident angle of magnetic induction, the crack half angle and the magnetic susceptibility as displayed with figures. It is noticed that the present work is available even for a ferromagnetic material with low susceptibility. For the limiting case of the crack half angle in the one arc crack problem approaching to zero, the stress intensity factors are also provided and analytically compared with the existing ones of the straight crack problem.     

Complex hypersingular integral equation for the piece-wise homogeneous half-plane with cracks

New complex hypersingular integral equation (CHSIE) is derived for the half-plane containing the inclusions (which can have the different elastic properties), holes, notches and cracks of the arbitrary shape. This equation is obtained by superposition of the equations for each homogeneous region in a half-plane. The last equations follow from the use of complex analogs of Somigliana's displacement and stress identities (SDI and SSI) and Melan's fundamental solution (FS) written in a complex form. The universal numerical algorithm suggested before for the analogous problem for a piece-wise homogeneous plane is extended on case of a half plane. The unknown functions are approximated by complex Lagrange polynomials of the arbitrary degree. The asymptotics for the displacement discontinuities (DD) at the crack tips are taken into account. Only two types of the boundary elements (straight segments and circular arcs) are used to approximate the boundaries. All the integrals involved in CHSIE are evaluated in a closed form. A wide range of elasticity problems for a half-plane with cracks, openings and inclusions are solved numerically.     

预应力铝合金筋嵌入式补强钢筋混凝土梁裂缝分析与计算

完成了7根预应力7075铝合金筋嵌入式补强混凝土梁试件的四点弯曲静载试验,应用非接触式数字图像相关法对混凝土加固梁的裂缝形成、分布、裂缝宽度和间距进行分析,研究了铝合金加固量、预应力以及预应力水平对嵌入式补强混凝土梁试件破坏模式和裂缝特性的影响。试验研究表明:铝合金筋嵌入式补强法可以显著提高混凝土梁的承载能力,施加预应力进一步增强加固梁的强度并延缓混凝土开裂和钢筋屈服;端部锚固有效避免了加固梁试件发生剥离破坏,提高高强铝合金强度利用率;施加预应力、增大加固量和提高预应力水平,均可以有效控制裂缝扩展,减小裂缝宽度和间距;根据中国《混凝土结构设计规范》(GB 50010?2010)对嵌入式非预应力/预应力铝合金筋补强混凝土梁的裂缝宽度和分布进行了计算,理论计算值与试验结果吻合良好,结果表明:中国混凝土结构设计规范给出的正常使用状态下最大裂缝宽度计算方法能够较好地考虑预应力、加固筋数量以及预应力水平对最大裂缝宽度的影响,适用于嵌入式补强钢筋混凝土受弯构件的裂缝计算与分析。     

Crack analysis in unidirectionally and bidirectionally functionally graded materials

Mixed-mode crack analysis in unidirectionally and bidirectionally functionally graded materials is performed by using a boundary integral equation method. To make the analysis tractable, the Young's modulus of the functionally graded materials is assumed to be exponentially dependent on spatial variables, while the Poisson's ratio is assumed to be constant. The corresponding boundary value problem is formulated as a set of hypersingular traction boundary integral equations, which are solved numerically by using a Galerkin method. The present method is especially suited for straight cracks in infinite FGMs. Numerical results for the elastostatic stress intensity factors are presented and discussed. Special attention of the analysis is devoted to investigate the effects of the material gradients and the crack orientation on the elastostatic stress intensity factors.     

Numerical solutions for polygonal cracks

An effective numerical scheme capable to deal with polygonal and branching cracks in a plane is proposed. It is suggested to decompose the general singular integral equation, SIE, for curvilinear cracks into a set of SIEs for straight cuts coinciding with straight crack segments. Solutions of SIEs are sought as bounded for all internal ends of the cuts and unbounded for the left end of the left cut and the right end of the right cut. The Gauss-Chebyshev quadrature is applied to each SIE that eventually leads to an over-determined system of linear algebraic equations followed by the application of the least squares method to solve this system. Stress intensity factors are calculated for some crack configurations. This scheme provides satisfactory accuracy although no correct asymptotic behaviour of the solution at internal ends is taken into consideration. The results are verified against the known results for branching cracks.     

An effective method of stress intensity factor calculation for cracks emanating from a triangular or square hole under biaxial loads

This paper is concerned with stress intensity factors for cracks emanating from a triangular or square hole under biaxial loads by means of a new boundary element method. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfied and the crack‐tip displacement discontinuity elements proposed by the author. In the boundary element implementation, the left or the right crack‐tip displacement discontinuity element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called a Hybrid Displacement Discontinuity Method (HDDM). Numerical examples are included to show that the method is very efficient and accurate for calculating stress intensity factors for plane elastic crack problems. In addition, the present numerical results can reveal the effect of the biaxial loads on stress intensity factors.