边界元法计算近边界点参量的一个通用算法

针对边界元法存在近力界点参量计算的困难,给出了一个通用性方法,将近边界点到边界单元的距离参数通过分部积分变换到积分式之外,从而计算出二维问题近边界点参量的几乎强奇异和超奇异积分,由此,对任何近边界点参量,提出了整套计算方案,算例证明了本法的有效性。     

Plane Elastic Boundary Value Problem Posed by Displacement and Force Orientations on a Closed Contour

A boundary value problem (BVP) of the plane elasticity posed in terms of the orientations of forces and displacements is considered. The main aim of the present paper is to investigate the solvability of BVPs of this kind. Firstly, analysis of two cases is performed: the case of a circle with special orientations of force and displacement vectors on the circumference and the case of an arbitrary contour with coaxial orientations of these vectors. The solutions obtained indicate that the problem can have a certain number of solutions or be unsolvable. Then the BVP is reduced to a boundary integral equation and its solvability is investigated for the general case of a smooth simple-connected closed contour. As a result, the number of linearly independent solutions is determined. This number only depends upon the angle between the force and displacement vectors. This revised version was published online in July 2006 with corrections to the Cover Date.     

Continuous Dependence on Base Data in an Elastic Prismatic Cylinder

This paper establishes the continuous dependence of the displacement on the base geometry and load of the decay behaviour in a prismatic semi-infinite cylinder occupied by an anisotropic homogeneous linear elastic material. The cylinder is in equilibrium under zero body-force, zero displacement on the lateral boundary and pointwise specified displacement on the base. A differential inequality is derived which on integration leads to an inequality in terms of the perturbation of the base geometry and differences in the base displacement. Continuous dependence is an immediate consequence. This revised version was published online in July 2006 with corrections to the Cover Date.     

边界元法中计算几乎奇异积分的一种无奇异算法

边界元法中存在几乎奇异积分的计算困难。引起边界单元上几乎奇异积分的因素是源点到其邻近单元的最小距离δ。本文拓展文[1]的思想,进一步采用分部积分将δ移出奇异积分式中积分核之外,转换后积分核是δ的正则函数。所以几乎强奇异和超奇异积分被化为无奇异的规则积分与解析积分的和,可由通常的Gauss数值积分解。文中应用此正则化技术求解了弹性力学平面问题的近边界点位移和应力。     

弹性力学问题中一个新的边界积分方程——自然边界积分方程

位移导数边界积分方程一直存在着超奇异积分计算的障碍.该文提出以符号算子δij和εij作用于位移导数边界积分方程,施用一系列变换将边界位移、面力和位移导数转成为新的边界张量,从而得到一个新的边界积分方程——自然边界积分方程.自然边界积分方程的奇异性为强奇性,文中给出了相应的Cauchy主值积分算式.自然边界积分方程与位移边界积分方程联合可直接获取边界应力.几个算例表明了自然边界积分方程的正确性.     

Bi-2223/Ag高温超导带材内部结构损伤演化及力学性能研究

在北京同步辐射实验室X光形貌站,采用X光透射成像技术,对Bi-2223/Ag高温超导带材内部结构以及在载荷作用下的损伤演化过程进行研究,分辨率约为5μm。实验结果表明:在带材的线弹性段,超导芯存在微裂纹损伤,但未形成端面的穿透性裂纹;当带材进入塑性流动区后,损伤明显加剧,贯穿性裂纹阻断了电流通道,材料失去超导性。     

幂率型非线性粘弹性裂纹尖端场

研究幂率型非线性粘弹性裂纹尖端场为了推导的需要,首先列出了幂率型硬化材料的HRR奇异场和高阶渐近场论证了它们实质上是各向同性、不可压缩、幂率型、非线性弹性裂纹尖端场,回顾了求解非线性粘弹性问题的弹性回复对应原理之后,给出了在第一类边界条件下求解幂率型非线性粘弹性材料裂纹问题的对应原理得到了幂率型非线性粘弹性材料,特别是改性聚丙稀的裂纹尖端应力、应变和位移的解答.     

A Constitutive Framework for Tubular Structures that Enables a Semi-inverse Solution to Extension and Inflation

Traditional constitutive frameworks for high-strain materials are ill-suited to solve extension and inflation, one of the simplest problems involving tubes, or more complicated problems. Moreover, it is experimentally necessary to minimize the covariance amongst constitutive response functions. We sought, hence, a constitutive framework that minimizes covariance and simplifies the balance equations for tubes, hoses, and arteries. Central to this theory are six objective scalars or strain attributes that decouple dilatation and distortion and succinctly define the strain. Because there is a one-to-one relationship between them and the components of the Right Cauchy–Green deformation tensor, these six strain attributes can be used to define the strain energy density function for hyperelastic materials. This approach yields mostly orthogonal response terms for high strain deformation (14 of the 15 inner products vanish). For infinitesimal deformation, the response terms are fully orthogonal. Further utility is demonstrated by showing how the governing equations are simplified for tubular structures and how response functions can be determined for the first time from the extension and inflation of thick-walled tubes composed of a homogeneous material with incompressible, hyperelastic behavior. This solution is applicable for materials with orthotropic behavior, and using the chain rule, this solution can be used for materials with isotropic behavior.     

Modeling of planar nonshallow prestressed beams towards asymptotic solutions

Employing the geometrically exact approach, the governing equations of nonlinear planar motions around nonshallow prestressed equilibrium states of slender beams are derived. Internal kinematic constraints and approximations are introduced considering unshearable extensible and inextensible beams. The obtained approximate models, incorporating quadratic and cubic nonlinearities, are amenable to a perturbation treatment in view of asymptotic solutions. The different perturbation schemes for the two mechanical beam models are discussed.     

三维问题边界元法中几乎奇异积分的正则化算法

当源点靠近边界单元时,边界积分方程通常存在几乎奇异积分的计算难题.基于三角形单元,将源点到单元的距离与单元特征长度比值定义为接近度,用于度量边界单元中积分奇异性的程度.将单元上的面积分在局部的极坐标系ρθ下表示,利用一些初等函数的积分公式,获得对变量ρ作单层积分的解析表达式.几乎强奇异和超奇异面积分被转化为沿单元围道上一系列线积分,而Gauss数值积分能够有效计算这些线积分.应用该算法分析三维弹性薄壁结构获得了成功.