Renewal of basic laws and principles for polar continuum theories （XI）——consistency problems

Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.     

Study on Deformation of Polycrystalline Aluminum Alloy Using Moiré Interferometry

Polycrystalline aluminum alloy is manufactured by annealing, compared to the width of the specimen, the size of the grains can not be omitted, which makes the specimen anisotropic. Under uniaxial tension, the deformation field is inhomogeneous. In this study, moiré interferometry is successfully applied to measure the deformation of the polycrystalline specimen. The experimental results presented the stress versus strain responses of the marked grains in different orientations and different shapes. By using fringe centering method, the strain distributions under certain load in the centers and on the boundaries of the grains are analyzed.     

旋转倒立双摆摆起控制量的动态设计变量优化

倒立摆的摆起过程是复杂的非线性力学与控制的综合问题,当力学模型和参数确定时,寻求有效方法计算控制律函数是实现摆起的关键。本文以倒立双摆模型为研究对象,将动态设计变量优化方法引入对摆起开环控制律的分析,编制计算机程序进行数值仿真,确定了控制律函数与状态量随时间变化的状态,为复杂强非线性系统的控制提出了一种有效方法。     

板的非线性热弹耦合振动（Ⅰ）：近似解析解

本文以文[2,3,4]为基础,导出了板的热弹耦合非线性振动控制方程,在采用Galerkin法离散化以后,按各个变量性质分别用多尺度法或正则摄动法求得近似解析解。籍此可揭示系统各参数对非线性热弹耦合振动影响的机理和作出必要的近似计算,对工程实际具有较大的参考价值。     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅲ) —NOETHER’S THEOREM

The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether’s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics. The new concrete forms of various conservation laws of couple stress elasticity are derived. The precise nature of these conservation laws which result from the given invariance requirements are established. Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper.     

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT （Ⅰ）—— VERIFICATION OF MATHEMATICAL MODEL AND NUMERICAL METHOD

Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation were substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant vertical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross-sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.     

ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ     

Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods

In this paper, we study an integrable nonlinear evolution equation which arises in the context of nonlinear dispersive waves in hyperelastic rods. To consider bounded travelling-wave solutions, we conduct a phase plane analysis. A new feature is that there is a vertical singular line in the phase plane. By considering equilibrium points and the relative position of the singular line, we find that there are in total three types of phase planes. The trajectories which represent bounded travelling-wave solutions are studied one by one. In total, we find there are 12 types of bounded travelling waves, both supersonic and subsonic. While in literature solutions for only two types of travelling waves are known, here we provide explicit solution expressions for all 12 types of travelling waves. Also, it is noted for the first time that peakons can have applications in a real physical problem.     

陶瓷阻力曲线测定的新方法——断裂栅法

将零厚度单向试件栅刻蚀工艺应用于晶须增韧氮化硅陶瓷基复合材料表面，通过记录试件所在桥路的输出电压值，可得到随载荷不断增大裂纹逐渐向前扩展过程中每一时刻的裂尖位置和裂纹长度，从而得到该种材料的阻力曲线。     

MEASUREMENT OF NON-UNIFORM RESIDUAL STRESSES BY COMBINED MOIRE INTERFEROMETRY AND HOLE-DRILLING METHOD： THEORY, EXPERIMENTAL METHOD AND APPLICATIONS

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moiré interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moiré interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements. The project supported by the FRAMATOME ANP