Interaction of an Ellipsoidal Inclusion with an Elliptic Crack in an Elastic Material under Triaxial Tension

The interaction of an elastic ellipsoidal inclusion with an elliptic crack in an infinite elastic medium under triaxial loading is analyzed. The stress state in the elastic space is represented as a superposition of the principal state and perturbed states, which are due to the presence and interaction of the inclusion and the crack. The analytical solution of the problem is found using the method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for an elliptic crack. The effect of triaxial loading on the stress intensity factors is analyzed     

深埋椭圆形片状裂纹的偏折扩展

基于无限大弹性基体深埋椭圆形片状裂纹的变形场,推导了椭圆形片状裂纹的能量释放率,采用能量平衡方法建立了椭圆形片状裂纹承受拉应力和剪应力时的复合断裂准则. 考虑裂纹在拉-剪应力作用下的偏折扩展,分析了裂纹的偏折方向,提出了椭圆形片状裂纹发生偏折扩展时的初始偏折位置的确定方法.      

Self-Similar Unsteady Viscous Flow

Four examples of self-similar flows of a viscous fluid are considered: separated flow over an expanding plate immersed in an unbounded unsteady viscous flow, the evolution of the velocity field induced by a vortex-source, the flow near an unsteadily moving permeable flat plate, and the flow near an unsteadily rotating disc. For the first example, a numerical solution is constructed. For the next two examples, an analytical solution is found, while the solution of the last problem is reduced to a system of ordinary differential equations.     

Experimental Investigation of the Interaction between an Electric Arc and a Gas Flow

The results of investigating the shape of an electric arc carrying an electric current of less than 100 A and exposed to an air, nitrogen, or argon stream at a stream velocity of from zero to 20 m/s, when the interelectrode gap is less than 20 mm, are reported. The shape of the arc is qualitatively investigated as a function of the gas type, blowing velocity, and interelectrode gap. It is shown that an arc burning in a channel with insulated walls is much more stable under these conditions than an arc with the same parameters burning in free space.     

一种考虑界面相物性影响的界面单元法

界面是由复杂的界面相简化而成的,界面破坏实际是界面相材料的破坏。数值计算为了方便,如经典模型和内聚力模型等,都把很薄的界面相作无厚度化处理。导致只能考虑界面的面力,而无法考虑界面相内的应力(平行于界面方向的应力)。使界面失效准则先天性地排除了界面相内部应力的影响,从界面相材料失效机理的角度来看这是不够严谨的。本文将界面相材料等效为一种弹性连续体,由界面本构关系推导得到了一种新的界面单元。该单元具有界面参数易确定、对界面相物性可以进行等效描述等优点。通过商用有限元软件ABAQUS和用户子程序UEL实现了数值分析,并与直接物理模型的数值模拟结果进行对比,证明了本方法的简便及准确性。通过对不同界面相厚度结构的进一步分析,探讨了本文方法的可行范围。     

Optimal spacecraft terminal attitude control synthesis by the quaternion method

We consider an optimal control problem of spacecraft retargeting from an arbitrary initial position to a given terminal angular position. The objective is to minimize a path functional. Using the quaternion method, we obtain an analytic solution of this problem and present formalized equations and computational expressions for synthesizing an optimal manoeuvre program. We also present an example and the results of mathematical simulation of the spacecraft motion dynamics under an optimal control, which demonstrate the practical implementability of the control method developed in the present paper.     

A wave-oriented meshless formulation for acoustical and vibro-acoustical applications

Simulating acoustical or vibro-acoustical waves within the medium frequency range is still an open problem today. In this paper, we first demonstrate that it is possible to formulate an improved element-free Galerkin method (I-EFGM) for the uncoupled acoustical problem applied to three-dimensional complex geometries. Then, we develop a partition of unity formulation extended for the elastodynamics (PUM-dyn). Finally, by coupling both formulations with an appropriate formulation for 2D vibro-acoustical coupled problems, we demonstrate that an I-EFGM coupled to the PUM-dyn seems to be an excellent way to reach the medium frequencies accurately and with an acceptable CPU time.     

Using a Smoothing Averaging Operator to Evaluate Macroscopic Parameters in Structurally Inhomogeneous Materials

A smoothing averaging operator is used in passing from structural to macroscopic modeling of the stress–strained state of an article from a composite material taking into account finite strains. A model is constructed using an integral operator, in which the macroscopic laws of conservation of energy and mass and the equation of motion have the ordinary form used to describe processes in homogeneous materials. As an example, macroscopic parameters are evaluated in a system consisting of an ensemble of inclusions in an infinite matrix.     

SH波对浅埋弹性圆柱及裂纹的散射与地震动

采用Green函数、复变函数和多极坐标等方法研究含圆柱形弹性夹杂的弹性半空间中任意位置、任意方位有限长度裂纹对SH波的散射与地震动. 构造了含圆柱形弹性夹杂的半空间对SH波的散射波,并求解了适合本问题Green函数,即含有圆柱形弹性夹杂的半空间内(表面)任意一点承受时间谐和的出平面线源载荷作用时位移函数的基本解答. 利用裂纹``切割'方法在任意位置构造任意方位的裂纹,可以得到基体中圆柱形弹性夹杂和裂纹同时存在条件下的位移场与应力场. 通过数值算例,讨论各种参数对夹杂上方地表位移的影响.      

Surface tension-induced stress concentration around an elliptical hole in an anisotropic half-plane

We examine the surface tension-induced stress concentration around an elliptical hole inside an anisotropic half-plane with traction-free surface. Using conformal mapping techniques, the corresponding complex potential in the half-plane is expressed in a series whose unknown coefficients are determined numerically. Our results indicate that the maximum hoop stress around the hole (which appears in the vicinity of the point of maximum curvature) increases rapidly with decreasing distance between the hole and the free surface. In particular, for an elliptical or even circular hole in an anisotropic half-plane we find that, with decreasing distance between the hole and the free surface, the hoop stress can switch from compressive to tensile at certain points on the hole's boundary and from tensile to compressive at others. This phenomenon is absent in the case of an elliptical or even circular hole in the corresponding case of an isotropic half-plane.     

Elastic Anisotropic Material with Purely Longitudinal and Transverse Waves

The simplest form of the matrix of elasticity moduli of an anisotropic material conducting purely longitudinal and transverse waves with an arbitrary direction of the wave normal is obtained. A generic solution of equations in displacements is represented in terms of three functions satisfying independent wave equations. In the case of planar deformation, this solution yields a complex representation coinciding with the Kolosov–Muskhelishvili formulas for an isotropic material. The formulas in the present work also determine an anisotropic material with Young's modulus identical for all directions, as in an isotropic medium.     

Analysis of piezoelectric ceramic multilayer actuators based on an electro-mechanical coupled meshless method

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. In this method, an element free Galerkin (EFG) formulation, an enriched basic function and some special shape functions that contain discontinuous derivatives are employed. Based on the moving least squares (MLS) interpolation approach, the EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method can yield an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. In another example studying a ceramic multilayer actuator, the proposed model was found to be accurate in the simulation of stress and electric field concentrations arround the abrupt end of an internal electrode. The project supported by the National Natural Science Foundation of China (10025209, 10132010, and 90208002), and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7203/03E). The English text was polished by Yunming Chen.     

Uniform difference scheme for a singularly perturbed linear 2nd order hyperbolic problem with zeroth order reduced equation

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.     

基于实测挠度、转角和曲率的细长梁分段抗弯刚度识别研究

静载试验是获得结构真卖特性的重要方法和途径，具有直观、可靠的特点。本文基于静载试验实测的挠度、转角和曲率，建立目标函数，通过优化的方法，实现结构分段截面抗弯刚度参数的识别。研究了优化目标函数的建立、优化算法的选取与实现；通过数值算例和一片简支梁静载试验实例分析，对方法的正确性与可行性进行了验证，所得结果可用于结构损伤识别和安全性能评估。     

3-D Aerodynamic Shape Design Using Hessians Based on Incomplete Sensitivities

We investigate the practicability of an optimization algorithm based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for 3D shape design problems, using approximate sensitivities of objective functions, where the contribution of the partial derivatives of the flow state with respect to the control variables is neglected. Therefore, it is worthwhile to investigate how an optimization method based on the Hessian behaves in this context. Indeed, the Hessian should be far from its real value if the gradient approximation is wrong. The optimization methodology is characterized by an unstructured CAD-free framework for shape and mesh deformations, an automatic differentiation of programs for the computation of the gradient of the cost function, and an unstructured flow solver. The redesign of transonic and supersonic wings has been considered and the performance of the BFGS method has been analyzed in comparison with a steepest descent method. Taking into account that a line search is too expensive to be carried out in such problems, a step size proportional to the gradient modulus has been employed for updating the control variables. Numerical results show that the BFGS method does not suffer from the approximation used in the evaluation of sensitivities, and leads to an effective improvement of the efficiency of the optimization methodology. These results can be then considered an a posteriori justification for incomplete sensitivities.     

A tri-material elastodynamic solution for a transversely isotropic full-space

A linear elastic full-space composed of an upper half-space, a lower half-space and a layer of three different transversely isotropic materials under an internal load is considered. The axes of symmetry of the different regions are assumed to be normal to the planar interfaces of the regions and are thus parallel. An arbitrary load in the frequency domain is allowed on a finite patch located at the interface of the upper half-space and the adjacent layer. By means of the complete displacement potentials, the displacements and stresses in the three regions are determined in Fourier–Hankel space in the form of line integrals. The solution can be degenerated to the solution for (i) a full-space under an arbitrary buried load, (ii) a half-space contain a layer bonded to the top of it under an arbitrary surface force, (iii) a half-space under an arbitrary surface load, (iv) a two layer half-space under an arbitrary force applied at the interface of two regions, (v) a half-space under an arbitrary buried force, (vi) a layer of finite thickness fixed at the bottom and under an arbitrary surface load, and (vii) a bi-material full-space under an arbitrary load at the interface of two materials. Examples of the displacements and stresses are obtained numerically and compared to existing solutions.     

Rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor

The paper shows a rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor. It is shown that an eccentric rotor core leads to an electromagnetic force and an angular rotor core to an electromagnetic moment, which both force the rotor to vibrate. For these two kinds of magnetic unbalance, a rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness—radial and angular electromagnetic stiffness—the mass moment of inertia and the gyroscopic effect of the rotor. With this model, the absolute orbits of the shaft centre, the shaft journals and the bearing housings can be calculated, as well as the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be computed. In addition to the mathematical derivation of the model, also a numerical example is shown for clarification. The aim of the paper is, on the one hand, to show the mathematical coherences—based on an analytical model—between rotordynamics and the electromagnetics for an induction motor with an eccentric and angular rotor core and, on the other hand, to derive a calculation method for evaluating the vibration sensitivity regarding these two different kinds of magnetic unbalance.     

A partially implicit method for simulating viscous aerofoil flows

A partially implicit method for the unsteady compressible Navier-Stokes equations is developed. The method is based on an explicit treatment of streamwise fluxes and an implicit treatment of normal fluxes. This leads to a linear system which is generated by an efficient finite difference procedure and which is block pentadiagonal. The method is tested on a shock-induced oscillatory flow over an aerofoil. Parallel implementations of an explicit, fully implicit and partially implicit method are investigated.     

Deformations of an elastic pipe submitted to gravity and internal fluid flow

This paper describes the deformation of an elastic pipe submitted to gravity and to an internal fluid flow. The pipe is clamped horizontally at one end and free at the other end. As the fluid velocity increases, the shape changes from an elastic beam deflected by its own weight towards an horizontal position. The shape of the pipe is characterized experimentally and is compared with a theoretical model based on the Euler–Bernoulli approximation and the conservation of the fluid momentum. We study how the determination of the pipe deformation provides an estimation of the conveyed fluid flow. Finally, the vertical force produced by the conveyed fluid to lift off a mass is deduced.     

On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.