Biaxial crushing of honeycombs: —Part 1: Experiments

The in-plane compression and crushing of honeycombs is known to be closely related to the crushing behavior of the broader class of space filling cellular solids. Previously, the authors conducted an extensive study of uniaxial crushing of a polycarbonate honeycomb with circular cells. In this paper the same honeycomb is crushed biaxially. The crushing was performed in a custom testing facility between rigid platens which can be moved independently in two orthogonal directions. The facility allows testing at various biaxiality ratios and volume reductions as high as 95%. The facility was used to conduct several series of biaxial crushing experiments on nearly square honeycomb specimens (18×21 cells) . In each experiment we recorded the true stress–displacement responses in the x- and y-directions as well as full field views of the deformation using a video camera. Biaxial crushing is quite complex and the prevalent mechanisms of collapse depend on the biaxiality ratio (γ) . As is the case in uniaxial crushing, the onset of collapse involves localized instabilities, however, the extent of localized deformation varies with γ. The energy absorption capacity of the material depends on γ. The highest energy is required when the specimen is crushed at the same rates in the two directions.     

In-plane biaxial crushing of honeycombs—: Part II: Analysis

The in-plane biaxial crushing experiments on polycarbonate honeycomb presented in Part I are simulated using large scale finite element models. The models account for nonlinearities in geometry and due to contact while the polycarbonate is modeled as an elastic-powerlaw viscoplastic solid. Full-scale simulations of the uniaxial crushing of this honeycomb were shown in the past to reproduce experiments with accuracy. In biaxial crushing, it was not practical to model specimens the same size as those in the experiments due to computational limitations; instead, a smaller model with 10×11 cells was adopted. Results from simulations of seven of the crushing experiments in Part I with various biaxiality ratios are presented. Through parametric studies it is demonstrated that the size of the specimen and friction between the specimen and the loading surfaces affect the initial elastic parts of the stress–displacement responses and the onset of instability. By contrast, for average crushing strains higher than approximately 10%, their effect was relatively small and the calculated responses were in good agreement with the experimental ones. As a consequence, the energy absorption capacity was predicted to good accuracy for all biaxiality ratios. In addition, many of the modes of cell collapse seen in the experiment are reproduced in the simulations.     

蜘蛛丝Ⅰ:超级力学性能

介绍蜘蛛丝既有优异的强度、也有优异的延伸率、韧性和适中的刚度,这使得蜘蛛网承受静载和昆虫冲击的能力均超过其他人造和天然材料,无愧超级生物材料的称号.蜘蛛丝的力学性能随应变率的增加而增加,进一步提高了蜘蛛网的抗昆虫冲击能力.蜘蛛丝的黏弹性性质和捕捉丝的黏性能有效防止捕获的猎物被弹出.本文第II部分介绍赋予蜘蛛丝的超级力学性能的自组装分级微结构,第III部分介绍蜘蛛网超级抗损伤和超级带缺陷工作能力的力学奥秘.     

FD-PINN:频域物理信息神经网络

物理信息神经网络(physics-informed neural network, PINN)是将模型方程编码到神经网络中,使网络在逼近定解条件或观测数据的同时最小化方程残差,实现偏微分方程求解.该方法虽然具有无需网格划分、易于融合观测数据等优势,但目前仍存在训练成本高、求解精度低等局限性.文章提出频域物理信息神经网络(frequency domain physics-informed neural network, FD-PINN),通过从周期性空间维度对偏微分方程进行离散傅里叶变换,偏微分方程被退化为用于约束FD-PINN的频域中维度更低的微分方程组,该方程组内各方程不仅具有更少的自变量,并且求解难度更低.因此,与使用原始偏微分方程作为约束的经典PINN相比, FD-PINN实现了输入样本数目和优化难度的降低,能够在降低训练成本的同时提升求解精度.热传导方程、速度势方程和Burgers方程的求解结果表明, FD-PINN普遍将求解误差降低1～2个数量级,同时也将训练效率提升6～20倍.     

工程力学中的互补问题:模型

对互补问题在非线性力学中的一些应用情况给出了较概括的介绍，重点放在了静态接触问题、弹塑性问题以及结构优化问题的互补模型上。将力学问题写成互补模型的好处主要有两点：一是使力学问题有更自然、更精确的数学描述；二是可以考虑用互补问题的有效和强健的数值算法来求解。     

资金项目:国家自然科学基金资助项目

采用能计及非线性结构刚度的颤振方程为控制方程,和非定常N-S方程耦合求解,运用龙格-库塔方法在时域内求解结构响应的时间历程,从而确定颤振临界条件.计算了带结构刚度非线性的跨音速颤振特性.计算结果表明,结构刚度非线性对颤振特性有明显的影响.由于同时具有结构和气动力非线性,导致了具有复杂振荡极限环的特性.     

工程力学中的互补问题:算法

工程力学里很多问题存在互补关系,文献[1]介绍了有关的数学模型。本文介绍了近年来求解互补问题的几种主要方法,包括投影方法、内点方法、方程组方法、延拓方法以及无约束优化方法。与此同时,也介绍了作者近期在互补问题算法方面的一些研究工作。     

充液挠性航天器俯仰运动 1:1:1 内共振动力学分析

采用已推导的俯仰运动矩形贮箱受控刚-液-弹耦合系统在外力矩作用下的耦合动力 学模型，在刚体上加入控制项，详细分析了系统固有频率的精确解与近似解. 应用多尺 度法对耦合系统1:1:1内共振进行解析分析，与数值解比较验证解析解的正确性. 通过近 似解析分析得到刚-液-弹之间的耦合作用机理：1) 液深影响整个系统的软硬特性，当液体发 生软硬特性转化时，处于液体原多值频率区域的刚体和弹性体幅频曲线分支峰值会减弱，且 具有相同的特性转化趋势；处于液体新多值频率区域的刚体和弹性体幅频曲线分支峰值会增 强，且具有相反的特性转化趋势. 2) 刚体和弹性体幅频曲线的峰值均在以受控刚体和弹性体 为主的耦合系统固有频率处，以液体为主固有频率激励，刚体和弹性体振幅较小.     

Tsallis entropy: how unique?

It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability, and the axiomatic foundations.Received: 6 May 2003, Accepted: 7 July 2003, Published online: 9 December 2003PACS: 05.20.-y, 05.70.-a, 05.90. + m, 65.40.Gr     

贝壳Ⅳ:冰模仿生

从古战场的用"冰"如神,到文学艺术中的冰花雪韵,再到科学家手中的冰棱魔模,冰雪赋予各行各业的人以创造灵感.科学家利用水结冰时的杂质偏析现象,让冰棱在三氧化二铝陶瓷悬浮液中定向生长,形成复杂奇妙的冰棱模,析出层状多孔陶瓷,蒸发去水并注入聚合物,再压实,烧结,获得具有矿物桥的层合仿生陶瓷,韧性比组分材料高300多倍,模拟了贝壳珍珠母层的增韧机制.     

Periodic Klein–Gordon Chains with Three Particles in 1:2:2 Resonance

Journal of Dynamics and Differential Equations - In this paper, we deal with the three degrees of freedom Hamiltonian systems describing the Klein–Gordon chains with three particles of equal...     

Addendum to: Symmetry classification of quasi-linear PDE’s. II: an exceptional case

This short note completes the symmetry analysis of a class of quasi-linear partial differential equations considered in the previous paper (Nonlinear Dynamics 51: 309–316, 2008): it deals with an “exceptional” Lie point symmetry which is admitted only if the involved parameters are fixed by precise relationships. The peculiarity of this symmetry is enhanced by the fact that, combined with the presence of a conditional symmetry of “weak” type, it leads to a family of solutions which include, as a particular case, a relevant solution of the Grad–Schlüter–Shafranov equation, well known in plasma physics.     

桩基的稳定性:理论和最新进展

本文对桩基的稳定性分析的数学模型、分析计算方法以及离心机模拟试验的近期文献进行了一定的回顾.主要侧重于桩基的失稳模式和机理分析,包括基于Euler屈曲理论的桩基不稳定性、桩基的定向不稳定性、地震液化中桩基的不稳定性、桩基的动力不稳定性、桩基的后屈曲分析等.最后简单地提出了进一步需要开展的工作.     

贝壳Ⅰ:科学与艺术珍品

介绍贝壳的艺术美和它带给人类的创造灵感,介绍贝壳在材料强韧化方面所创造的力学奇迹:利用95%左右的原始低强度碳酸钙,加上少量蛋白质和多糖有机胶,建造了精巧的分级嵌套微结构,使韧性比组分材料提高了3个数量级,成为超级生物材料.接下来将继续介绍分级嵌套微结构强韧化的力学机制、连接不同尺度微结构的矿物桥和人类在贝壳仿生方面的进展.     

蜘蛛丝Ⅲ:超级抗损伤网

介绍蜘蛛丝独特的线弹性-软化-强非线性硬化的应力应变曲线对建造超级抗损伤的和超级带缺陷工作能力的蜘蛛网的作用.这种独特力学性质使得蜘蛛网一旦局部靶载荷超载,承载网丝在经历软化大变形后急剧非线性硬化,独自承担过量载荷,直至断裂,而其余网丝的内力继续保持在安全范围内,实现损伤局部化与极小化.仅改变一下应力应变曲线的形状,就使网具有了超级抗损伤能力,体现了蜘蛛应用力学知识的神奇.     

综述:流体力学基础研究的需要

关于流体力学基础研究的长期需要问题。征询了工程界一部分人的意见。其中包括活跃在美国机械工程师协会(ASME)中的传热和流体力学委员会中的大约600人。近200人作了回答,给出了有关需要研究的有用资料。从许多课题中发现有六个领域比较突出:湍流;多相流;流体与结构的相互作用;边界层效应;生物、地球和环境流体的流动;新设备和改进仪器的需要。总结出这六个领域并作为研究重点的初步估计,提交给在1979年2月1—2日在肯塔基大学举行的美国能源部和工程师协会能源委员会召的流体力学和热过程专题讨论会。本文包括了研究重点的阐述和专题讨论会的最终结果。      

力学十年:现状与展望

结合国家自然科学基金数理科学"十三五"规划战略研究报告以及学科发展态势评估系列研究报告《力学十年:中国与世界》,本文简要介绍了国家自然科学基金力学学科的资助情况,通过重点介绍2006—2015年中国力学学科论文数、被引频次和排名前1%论文数、论文引用率、被引频次、论文相对引文影响、排名前1%高被引论文产出率、国际合作与自主研究等情况,对力学学科的发展态势进行了分析,并对力学学科今后发展提出了意见和建议.     

力学十年:现状与展望

结合国家自然科学基金数理科学``十三五'规划战略研究报告以及学科发展态势评估系列研究报告《力学十年:中国与世界》, 本文简要介绍了国家自然科学基金力学学科的资助情况,通过重点介绍2006---2015年中国力学学科论文数、被引频次和排名前1%论文数、论文引用率、被引频次、论文相对引文影响、排名前1%高被引论文产出率、国际合作与自主研究等情况,对力学学科的发展态势进行了分析,并对力学学科今后发展提出了意见和建议.      

Genetic counselling: evolution or involution?

The need for genetic counselling derives from the peculiarities of genetic information, as compared to other biomedical tests, with particular reference to (a) its predictive character; (b) the existing gap between the ability to diagnose and to treat an inherited disorder, and (c) the psychological, social and ethical problems that genetic testing can raise. Counselling is traditionally performed by healthcare professionals, specifically trained to help individuals to develop ways of dealing with genetic information and gain a better understanding of the problems related with it. The growing number of genetic tests (for rare Mendelian as well as for common disorders), the development of easier and cheaper molecular techniques, the increasing tendency of physicians to have recourse to genetic tests, by-passing alternative diagnostic procedures, are all factors that contribute to the vast increase in the demand for genetic tests, a demand which is significantly out of step with the available numbers of trained counsellors. This paper discusses possible solutions, including the institution of committees with regulatory powers on genetic testing, the promotion of studies on models of genetic services, on programmes to monitor the services currently offered by test providers, and the expansion of training programmes and of employment opportunities for genetic counsellors.