A Correction of an Inconsistency in my Paper “Cauchy's Theorem on Manifolds”

The Cauchy postulates are required for the formulation and proof of Cauchy's theorem for the existence of stress. The generalized postulates and theorem in the geometric setting of differentiable manifolds was considered in a previous paper. This note presents an inconsistency in one of the proposed postulates, the boundedness postulate, and corrects it by specifying a weaker requirement.     

基于轨迹约束的地磁场测量误差修正方法

根据磁强计综合误差的数学模型,提出了一种基于轨迹约束的地磁场测量误差修正的方法,同时也对该方法的有效性进行了分析.该方法首先由磁强计的测量数据,根据椭球轨迹的约束,采用最小均方估计作为判断准则,估计12个误差参数,然后利用此参数获得准确的地磁矢量信息.理论分析和仿真验证表明,在某些情况下,轨迹约束修正算法是不可观测的,也给出了检验不可观测存在的方法.由软磁干扰引起的误差不同于磁强计本身误差和安装误差.在出现由软磁干扰引起的误差时,轨迹约束修正算法仅仅能提供12个误差参数中的9个,其余的3个参数需要借助外在的信息来估计.     

Universal scaling law of an origami paper spring

This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E2019). By using both dimensional analysis and data fitting, an universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis.     

Data completion via an energy error functional

We propose, in this Note, a new procedure for data completion based on the minimization of an energy like error functional. The efficiency of the proposed method is illustrated by a thermostatic application. To cite this article: S. Andrieux et al., C. R. Mecanique 333 (2005).     

Sources of error and other difficulties in extensional rheometry revisited: commenting and complementing a recent paper by T. Schweizer

In a recent paper by T. Schweizer (Schweizer 2000) a large collection of experimental difficulties associated with the measurement of uniaxial extensional properties of polymer melts in the Rheometrics RME extensional rheometer is described. The work covers topics such as sample preparation for different types of polymers (sensitive or not to moisture) supplied in different shapes (pellets or powder), the necessary corrections to the tensile force, and the ever-present problem of determining the true strain rates of the experiments. The aim of the present paper is to complement and expand the work of Schweizer by pointing out other experimental problems that are the cause of errors in extensional rheometry of polymer melts. The present analysis, however, is not exclusively dedicated to the RME, unlike that of Schweizer, being directed instead to a general class of apparatus that work according to the principle of stretching a constant length sample between pairs of counter-rotating rollers; for example, all the data shown was obtained with our own extensional rheometer (Maia et al. 1999). This work will focus on the importance of the correct choice of the supporting media used for sample heating and support, the importance of end-effects, and the influence that the griping surfaces can have in such measurements. Received: 23 February 2001 Accepted: 15 May 2001     

环形激光陀螺随机误差测试中的计数误差

详细讨论了环形激光陀螺（RLG）误差测试中的计数误差。首先提出了在角度随机游走为主要误差源的情况下，RLG的离散输出模型。在假设累积角度量化误差为白噪声的前提下推导了方差（或AIlan方差）分析中的量化误差模型。接着指出白噪声假设并不总能成立，特别是对于由计数器只能计整数引致的量化误差（特称为“计数误差”），由于量化间隔很大，这一假设通常不能成立。最后，给出了一种白噪声假设不能成立时的处理方法及仿真数据分析结果。     

Analyses of wrinkled and slack membranes through an error reproducing mesh-free method

A mesh-free approximation of large deformations of flexible membrane structures within the tension field theory is considered in this paper. A modification of the wrinkling theory, originally proposed by Roddeman et al. (1987) [Roddeman, D.G., Drukker, J., Oomens, C.W.J., Janssen, J.D., 1987, The wrinkling of thin membranes: Part I—theory; Part II—numerical analysis. ASME J. Appl. Mech. 54, 884–892.], is proposed to study the behaviour of an isotropic membrane under the mixed state of stress (taut, wrinkled and slack). Using the facts that the state of stress is not uniform across an element and that the deformation gradient is a spatially continuous (and possibly non-differentiable) tensor, the proposed model uses a continuously modified deformation gradient to capture the location and orientation of wrinkles more precisely. While the deformation gradient need not be everywhere-differentiable in a wrinkled membrane, it is argued that the fictive non-wrinkled (non-slack) surface may be looked upon as an everywhere-taut surface in the limit as the minor (and major) principal tensile stresses over the wrinkled (slack) portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. The weighted residual from the governing equations are presently solved via a mesh-free method, where the entire domain is discretized only by a set of grid points. A non-uniform-rational-B-spline (NURBS) based error reproducing kernel method (ERKM) has been used to approximate the field variable over the domain. The first step in the method is to approximate a function and its derivatives through NURBS basis functions. However, since NURBS functions neither reproduce any polynomial nor interpolate the grid points (also referred to as control or nodal points), the approximated functions result in uncontrolled errors over the domain including the grid points. Accordingly the error functions in the NURBS approximation and its derivatives are reproduced via a family of non-NURBS basis functions. The non-NURBS basis functions are constructed using a polynomial reproduction condition and added to the NURBS approximation of the function obtained in the first step. Several numerical examples on wrinkled and/or slack membranes are also provided.     

Analysis of the strain field in the vicinity of a crack-tip in an in-plane isotropic paper material

Strains, computed by the finite element method, are evaluated and compared to an experimentally determined strain field. The analyzed low-density paper has been designed to ensure bond–breakage as the dominating damage mechanism and the paper material is approximately in-plane isotropic. An optical non-contact displacement measuring system has been used in fracture tests to determine the strain field in the crack-tip region of a pre-fabricated crack. Additionally, acoustic emission monitored tensile tests have been conducted to determine onset and evolution of damage processes and thereby enabling calibration of required constitutive parameters. The results suggest that the investigated paper material can tolerate significantly higher strains than what is predicted by a classic elastic–plastic J₂-flow theory. Immediately before onset of the final fracture (i.e., localization), the experimental measured normal strain in the near-tip region is around 60% higher than the computed strain when using exclusively an elastic–plastic theory for the corresponding load while the strain computed utilizing a non-local damage theory is of the same order of magnitude as the experimentally measured strain. Hence, it seems essential to include a non-local continuum theory to describe strains in the near-tip region quantitatively correct for paper materials. It is demonstrated that path independence of the well-known J-integral does not prevail for this class of material models. Only for the special situation of a homogenous damage field in the crack-tip region may the stress and strain fields be described by the well-known HRR-solutions.     

亦师亦友情自长——我与《力学与实践》的不解之缘

<正>截止到今天,《力学与实践》即将伴我走过三十七年。三十七年,《力学与实践》在我的学习和工作生涯中,几乎从未缺席。在三十七年的相伴而行中,《力学与实践》之于我,可谓既是良师,又是益友,结下了深厚情谊。我与《力学与实践》相识于1982年。由于所学"力学"专业的关系,便自然走进了《力学与实践》,通过阅读《力学与实践》,我不仅深深地沉浸于"力学"那充满哲理的迷人世界,而且树立了正确的专业思     

Further considerations of the astigmatism error associated with off-axis alignment of an LDA-probe

 Off-axis alignment of an LDA-probe in internal flow measurement is always associated with the appearance of astigmatism and this may have a large effect on the measurement accuracy. In addition to the earlier investigations reported by Zhang and Eisele (1995a, 1996) it is shown that the improper off-axis alignment of the probe leads to separation of laser beams in the formation of the measurement volume. Quantitative calculations made in this paper give a sound basis for estimating this separation and the results imply that the error arising from beam separation is very serious both for LDA- and for PDA-measurements. In addition, the analysis in Sect. 3 reveals that the reduction of the data rate from astigmatism due to off-axis alignment of the probe depends on the focal length of the receiving optics. This relationship has been validated by experiment. Received: 23 December 1996/Accepted: 24 July 1997