理想塑性晶体裂纹顶端渐近场

本文从晶体三维塑性流动理论出发,导出了双滑移理想塑性晶体平面应变问题曲基本方程。利用这些方程求得了静止裂纹顶端应力变形场。该场包含有弹性角形区并且整个应力变形场是连续的。进而导出了定常扩展裂纹顶端应力变形场。该场由五个角形区组成:裂纹前方有两个塑性区,它们的边界是速度场间断面。裂纹面附近有一个二次塑性区,中间是两个卸载弹性区,它们交界面也是个速度场间断面。该五个角形区不是唯一的。本文得到了一簇解答。最后本文分析了这些解答在面心立方和体心立方晶体中的应用。     

双层柱壳在流场中辐射声场压力的解析解

应用Donnell壳体理论,对加强内外壳体的横向构件,利用交界面的变形协调条件,等价为作用在壳体上的反力和反力矩,把双层柱壳振动辐射声场压力的求解,归结为求解结构动力方程、流场Helmholtz方程、流体和结构交界面上连续性条件组成的声-流体-结构的耦合振动方程.通过复杂的求解方法,可直接求得双层柱壳近场声压.     

对称集值向量拟均衡问题解集的稳定性

本文研究了对称集值向量拟均衡问题解集的稳定性.证明了在约束映射满足一定连续性与目标映射是锥-恰当拟凸的集值映射条件下,对称集值向量拟均衡问题的解集是稳定的,还证明了每个对称集值向量拟均衡问题的解集至少存在一个本质连通区.     

悬臂梁在倾斜载荷作用下的弹塑性大挠度分析

作为Plastica理论[12]的应用,本文分析了理想弹塑性矩形截面梁在自由端承受倾斜集中力作用时塑性区扩展阶段的大挠度变形.着重讨论了集中力的倾角对弯曲形状、载荷—挠度关系及塑性区长度的影响.结果用解析解和数值解同时给出.     

刚塑性材料塑性动力学问题中的一般方程和通解

本文是文[1～2]的继续。本文讨论了塑性流动理论中的理想刚塑性材料的动力学问题。在引入Dirac-Pauli表象的复变函数理论后,我们可以得到用流函数和理论比例系数表示的一组(两个)所谓"一般方程"。本文还证明了塑性动力学问题的时间发展方程既非耗散型的,又非弥散型的,而其本征方程却是以应力增量的偏张量为本征函数,以理论比例系数为本征值的定态Schr?dinger方程。于是,我们使非线性塑性动力学问题成为线性定态Schr?dinger方程的求解,由此可以得到刚塑性材料塑性动力学问题的通解。     

非均质地层中自然电位测井的数学模型和数值方法

针对非均质地层中电阻率非分块常数,提出一个新的自然电位测井模型.自然电位满足具有交界面跳跃的椭圆边值问题.证明了该椭圆边值问题弱解的存在唯一性;提出一种捕捉交界面电位跳跃的有限差分方法求解此类问题,数值例子验证了该方法的可靠性和有效性.     

一类组合硬化金属材料的成型问题

对一类组合金属材料,即不可压缩、刚塑性、与应变率相关、各向同性、运动中硬化的材料,在非局部接触的Coulomb摩擦边界条件下,考虑其准稳定成型问题.导出一组耦合的变分公式,证明(含延迟时间的)变刚度参数法的收敛性,证明了所得结果的存在性和唯一性.     

均匀分布的一个性质及其应用

运用特征函数的连续性定理和数学归纳法,证明了随机变量服从[0,1]上的均匀分布的充要条件是,它可以用二进制形式表示成独立同伯努利分布的随机变量序列的无穷级数.给出了此结论在生成随机数中的运用,以及在证明独立同分布序列存在性定理中的运用.     

向量拟平衡问题的本质解及解集的本质连通区

本文研究向量拟平衡问题,得到了向量拟平衡问题解的一个存在性结果,证明了在满足一定的连续性和凸性条件的问题构成的空间Y中,大多数(在Baire分类意义下)问题的解集是稳定的,并证明Y的某子集中,每个向量拟平衡问题的解集中至少存在一个本质连通区。作为应用,我们导出了多目标广义对策弱Pareto-Nash平衡点的存在性,证明了在满足一定的连续性和凸性条件的多目标广义对策构成的空间P中,大多数对策的弱Pareto-Nash平衡点是稳定的,并证明了P中的每个对策的弱Pareto-Nash平衡点集中至少有一个本质连通区。     

区传递7-(v,k,λ)设计

具有良好传递性的区组设计是代数组合学研究的一个重要领域.1993年,Cameron和Praeger证明了不存在区传递的8-设计.因此研究区传递的7-设计的存在性是一个很重要的课题.2013年,龚罗中和刘伟俊证明了不存在指数超过5的区传递7-设计.本文在此基础上证明了不存在区长小于100的区传递7-设计.     

Structural Modeling in the Mechanics of Porous Materials

A new method for analyzing the deformation behavior of rigid and elastic foams with a small volume content of solid phase ( < 0.2) is developed. Various structural models for describing the elastic behavior of rigid and elastic plastic foams are used and compared. The results of structural simulation of anisotropic auxetic (i.e., having a negative Poisson ratio) foams with concave cells are presented. For cyclic uniaxial compression of rigid foams and volumetric deformation of elastic foams, the stress-strain curves are obtained. The general shape of the curves agrees well with the nonlinearly elastic behavior of plastic foams observed in experiments.     

The problem of the stability of quasilinear flows with respect to perturbations of the hardening function

A formulation of the linearized boundary-value problem of the stability of a deformation process with respect to small perturbations of the hardening function (of the scalar constitutive relation of the material) is presented. The characteristic vector relations of the medium are assumed to be linear. The occurrence of rigid zones in the domain of the solid and the change in their boundaries in the perturbed motion are taken into account. A perfect rigid plastic deformation and the flow of a Newtonian fluid are considered explicitly as the basic flow. In the latter case, the equation of the asymptotic boundary of the rigid zone, which appears when there is a small variation in the yield stress and a transition to a viscoplastic material, is derived.     

Rigid‐plastic hybrid element analyses of the plane strain upsetting

A rigid‐plastic hybrid element method (HEM) for simulation of metal forming is developed. This method is a mixed approach of the rigid‐plastic domain‐BEM and the rigid‐plastic FEM based on the theory of compressible plasticity. Because the compatibilities of not only velocity but also velocity's derivative between the adjoining boundary elements and finite elements can be met, the velocities and the derivatives of the velocity can be calculated with the same precision for the rigid‐plastic HEM. Then, it is considered that the rigid‐plastic HEM is a more precise method in formulation than the conventional rigid‐plastic FEMs for which the compatibilities of velocity's derivative cannot be met. The plane strain upsetting processes with two friction factors are analyzed by the rigid‐plastic HEM in this article. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 726–737, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10031.     

Concentrators of deformations and fracture of plastic bodies

An approach to the investigation of shape discontinuity regions as strain concentrators is proposed. The near-concentrator strain fields are determined on the basis of the theory of ideal rigid-plastic body; under the condition of plane deformation, their determination is reduced to integration of ordinary differential equations. The deformation as a function of the location of the plastic region and its shape evolution in the process of plastic flow is studied. The plastic flow is demonstrated to be not unique (within the framework of solution completeness). A deformation criterion for the choice of the preferred plastic flow is suggested. The fracture of a V-notched strip is considered. On the basis of the solutions obtained, an approach to the investigation of the fracture processes for more complicated models is formulated.     

Flow of viscoplastic materials through converging channels

Many classical rigid perfectly/plastic solutions cannot be extended to more complicated rigid plastic materials, such as rigid plastic hardening materials and rigid viscoplastic materials. The present paper reveals sources of this difficulty in the case of flow of rigid viscoplastic material through infinite converging rough wedge-shaped and axisymmetric channels. Two types of viscoplastic models without strain hardening are considered, with and with no saturation stress. The maximum friction law is adopted at the friction surface. Qualitative features of the solutions are compared to those occurring in compression of a rigid plastic layer between rough, parallel plates. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Steady-State Frictional Heat Generation on a Periodic Sliding Contact

We investigate the motion of a periodic system of rigid, isolated, parabolic dies along the surface of a half-space. The action of friction forces results in heat generation in the contact region. We assume that the surfaces of the dies are thermally insulated and the half-space is a heat conductor. We reduce the problem under consideration to a set of two integral equations for the contact temperature and pressure. We solve these equations numerically and investigate the influence of thermal deformation on the distributions of temperature and pressure and on the dimensions of the contact region.     

Hybrid simulation strategy for multiple planar collisions with changing topologies and local deformation

The development of a hybrid strategy for the simulation of multiple plastic-elastic collisions is presented. The strategy attempts to bridge the gap between finite element methods (FEM), which typically require excessively long computation times for multiple impact simulations, and lumped parameter approaches that cannot provide accurate local deformation information. The proposed strategy employs a finite element routine solely to simulate the impact phase, thereby obtaining detailed local deformation information. The simulation of the flight phase between impacts, however, proceeds under rigid body dynamics, resulting in significant reduction in computation time. The transfer of control between FEM and rigid body dynamics is automatic and the points of contact need not be known a priori. The progressive object internal plastic strain, determined from FEM, is retained from one impact to the next, thereby ensuring a certain degree of continuity of the physical properties of the body. An example is presented to demonstrate the efficacy of this approach.     

柱形弹体撞击塑性变形的G.I.泰勒理论的分析解及其改进

柱形弹体对刚性靶体的纵向撞击塑性变形理论是G.I.泰勒[1]首先提出的.这个理论的重要性在于通过这个理论可以从实验数据计算动力屈服强度,而且从实验结果[2]中看到,动力屈服强度和撞击速度无关,动力屈服强度高于静力屈服强度,对某些材料而言,可以超出好几倍.这样就为弹塑性撞击研究提供了一个重要的根据.但是,泰勒理论由于微分方程的复杂性,求解过程都是数值计算,这样对使用其结果时深感不便.本文提供了全部分析解,并对其结果进行了讨论.本文对冲量计算进行了修正,修正理论的分析解指出,其结果比泰勒理论的解更加符合实验[2].     

On a partially debonded rigid line inclusion penetrating a circular inhomogeneity

We derive closed-form solutions to the mixed boundary value problem of a partially debonded rigid line inclusion penetrating a circular elastic inhomogeneity under antiplane shear deformation. The two tips of the rigid line inclusion are just mutual mirror images with respect to the inhomogeneity/matrix interface, and the upper part of the rigid line inclusion is debonded from the surrounding materials. By using conformal mapping and the method of image, closed-form solutions are derived for three loading cases: (i) the matrix is subjected to remote uniform stresses; (ii) the matrix is subjected to a line force and a screw dislocation; and (iii) the inhomogeneity is subjected to a line force and a screw dislocation. In the mapped ξ-plane, the solutions for all the three loading cases are interpreted in terms of image singularities. For the remote loading case, explicit full-field expressions of all the field variables such as displacement, stress function and stresses are obtained. Also derived is the near tip asymptotic elastic field governed by two generalized stress intensity factors. The generalized stress intensity factors for all the three loading cases are derived.     

A semi-analytical solution for shallow tunnels with radius-iterative-approach in semi-infinite space

This study presents a semi-analytical elastic-plastic solution for a shallow tunnel subjected to ground loss in the strain-softening surrounding rock. The most important contribution is the radius-iterative-approach in which the initial plastic radius is first determined by the strain continuity boundary condition on the elastic-plastic interface and then corrected to the precise one. The corrected approach follows three steps: (1) Applying the radius increment technique to semi-infinite space (2) Carrying out the plastic radius correction by using iteration method from the elastic-plastic interface to the tunnel wall. (3) If the calculated convergence value is equal to the convergence value on the tunnel wall, the accurate determination of the plastic region, stresses, and displacements, of the whole half plane, can be derived consequently. All the results compare favorably with numerical simulation results. The study completes the theoretical framework for addressing the fundamental problem of shallow tunnels excavated in the semi-infinite space and also provides a useful theoretical tool for potential application on the tunnel and underground engineering problems.