基于非线性梁理论的有限质点法

有限质点法是以向量式力学为基础,用有限数量的质点来模拟结构的变形行为,质点的运动由牛顿运动定律来计算。在有限质点法中,质点通过构件相连,构件约束着质点的运动,并且其内力由质点的运动变量来描述。基于向量式力学的基本思想和非线性梁理论,提出了一种新的有限质点法,该方法在共旋单元坐标系中描述梁的非线性变形。以空间梁系结构为例,推导了计算构件内力的非线性公式,并考虑了弯扭耦合变形。通过两个连续欧拉角的变换公式得到共旋坐标系的旋转矩阵。与传统的有限质点法相比,本文提出的方法避免了刚体虚转动分析。通过四个结构的数值求解,验证了本文方法在计算结构大变形响应时具有较高的精度。     

没有复杂几何概念的单方向场壳体有限变形模型综述

基于Simo和Fox的工作, 介绍一种没有复杂几何概念的现代壳体有限变形理论. 在推导上, 使用三维连续介质理论, 运用现代力学的表示方法. 这个模型提供了非线性几何精确壳体理论的力学分析基础. 这种模型的一个优点是虽然将壳体仍然看作二维结构, 但是它没有复杂的微分几何概念, 如没有协变导数、Riemannian-Christoffel记号等. 另外,还介绍了壳体局部平衡的弱形式或变分表示, 这种表示特别适用于数值计算.      

基础力学课程之教材及教学体系分析(三)——国外材料力学教材及其教学体系分析

本文对力学基础教材,着重对《理论力学》与《材料力学》教材与教学体系等方面进行了分析研究。从国内力学课程与教材建设历史概况,国内力学课程教材建设的成绩与问题,国内力学教材使用情况,引进的国外基础力学原版教材情况,国外理论力学教材体系分析,国外材料力学教材体系分析,国外力学相关课程网络资源调研与分析,及教学技术应用与质量评价等多方面进行了阐述。最后,通过对国外教材的研究,因其所具有的综多特点与特色,为国内力学基础课程教材和课程改革提供了思路和方向。本文为之三,主要阐述国外材料力学教材及其教学体系的比较分析及结尾。     

TEACHING SYSTEM AND TEXTBOOKS OF ELEMENTARY MECHANICS (III)——FOREIGN TEACHING RESOURSES OF MECHANICS OF MATERIALS AND THE TEACHING SYSTEM ANALYSIS 1)

本文对力学基础教材,着重对《理论力学》与《材料力学》教材与教学体系等方面进行了分析研究。从国内力学课程与教材建设历史概况,国内力学课程教材建设的成绩与问题,国内力学教材使用情况,引进的国外基础力学原版教材情况,国外理论力学教材体系分析,国外材料力学教材体系分析,国外力学相关课程网络资源调研与分析,及教学技术应用与质量评价等多方面进行了阐述。最后,通过对国外教材的研究,因其所具有的综多特点与特色,为国内力学基础课程教材和课程改革提供了思路和方向。 本文为之三,主要阐述国外材料力学教材及其教学体系的比较分析及结尾。     

近场动力学方法及其应用

近场动力学(peridynamics,PD)是一种新兴的基于非局部作用思想建立模型并通过求解空间积分方程描述物质力学行为的方法.它兼有分子动力学方法和无网格方法的优点,避免了基于连续性假设建模和求解空间微分方程的传统宏观方法在面临不连续问题时的奇异性,又突破了经典分子动力学方法在计算尺度上的局限,在宏/微观不连续力学问题分析中均表现出很高的求解精度和效率.首先概述了PD方法的理论基础、建模思路和计算体系;进而介绍了PD方法在不同尺度不连续力学问题中的应用,包括均匀与非均匀材料和结构的大变形、损伤、断裂、冲击、穿透和失稳问题,结晶相变动力学问题以及纳米材料和结构的破坏问题;最后讨论了PD方法在理论、计算和应用等方面值得进一步研究的问题.     

关于计算爆炸力学的进展与现状

爆炸问题由于其强烈的非线性,绝大多数情况下不可能给出精确解,并且爆炸在极短的时间内完成强烈的物理过程,能通过实验获得的数据也有限.爆炸力学数值模拟及相关研究领域的工作极大地推动了爆炸力学学科以及武器装备的发展,本文主要对爆炸力学数值方法、材料动态本构模型以及相关工程应用进行评述.     

壁虎粘附微观力学机制的仿生研究进展

本文针对壁虎粘附系统最小单元的真实形状, 类似于有限尺寸纳米薄膜的铲状纤维, 综述了对其微观粘附力学机制主要影响因素的多个研究, 主要考虑了有限尺寸纳米薄膜长度、厚度、撕脱角等对撕脱力的影响; 物体表面粗糙度以及环境湿度等对粘附的影响因素; 包括实验、理论及数值模拟的研究及结果比较. 最后给出仿生粘附力学方向仍然存在的主要科学问题及进一步的研究展望.     

《计算力学学报》20年

中国力学学会主办的《计算力学学报》连同其前身《计算结构力学及其应用》已经出版20年了。在纪念《计算力学学报》创刊20年之际,回顾20年来中国在计算力学基本理论、方法和应用软件等多方面所取得的成就,展望新世纪的重要研究与应用很有意义。计算力学致力于研究运用现代计算技术求解工程和科学中的力学及与力学相耦合问题的理论、算法和软件。当今,现代计算技术对社会的科技进步和经济发展已经成为不可或缺的基础。计算、实验及理论已经成为科学的三大支柱。计算力学在推动力学学科的发展中也起着越来越重要的作用。钱学森指出[1],“总…     

PROGRESS IN THE BIONIC STUDY ON GECKO＇S MICRO-ADHESION MECHANISM

本文针对壁虎粘附系统最小单元的真实形状, 类似于有限尺寸纳米薄膜的铲状纤维, 综述了对其微观粘附力学机制主要影响因素的多个研究, 主要考虑了有限尺寸纳米薄膜长度、厚度、撕脱角等对撕脱力的影响; 物体表面粗糙度以及环境湿度等对粘附的影响因素; 包括实验、理论及数值模拟的研究及结果比较. 最后给出仿生粘附力学方向仍然存在的主要科学问题及进一步的研究展望.     

征稿简则

1.《力学学报》是力学学科的综合性学术刊物.它遵循理论与实践统一和百花齐放、百家争鸣的方针,主要刊载:在理论上、方法上以及对国民经济建设方面,具有创造性的力学理论、实验和应用研究论文,综述性的专题论文以及研究简报,学术讨论等,以促进力学学科的发展,为社会主义四个现代化服务.读者对象主要为从事力学工作的科研人员、高等院校师生以及工程技术人员.     

分数阶对称金融模型复杂度分析及有限时间同步

分析了一类分数阶对称金融非线性系统的复杂度特性,利用有限时间同步理论设计控制器,实现了有限时间同步。根据分数阶系统定义和Adomain分解法对该系统的非线性项进行Adomain分解,结合分解系数定义系统的表达式,将其离散化。基于谱熵复杂度及C0复杂度的基本算法,利用Matlab仿真其复杂度曲线及复杂度图谱。为进一步探究对称金融非线性系统的动力学特性,利用有限时间同步理论设计误差控制器,实现有限时间同步,仿真结果表明该控制器可使系统在极短的时间内实现同步且鲁棒性好。     

A stabilized finite element formulation for high‐speed inviscid compressible flows using finite calculus

This paper aims at the development of a new stabilization formulation based on the finite calculus (FIC) scheme for solving the Euler equations using the Galerkin FEM on unstructured triangular grids. The FIC method is based on expressing the balance of fluxes in a space–time domain of finite size. It is used to prevent the creation of instabilities typically present in numerical solutions due to the high convective terms and sharp gradients. Two stabilization terms, respectively called streamline term and transverse term, are added via the FIC formulation to the original conservative equations in the space–time domain. An explicit fourth‐order Runge–Kutta scheme is implemented to advance the solution in time. The presented numerical test examples for inviscid flows prove the ability of the proposed stabilization technique for providing appropriate solutions especially near shock waves. Although the derived methodology delivers precise results with a nearly coarse mesh, a mesh refinement technique is coupled to the solution process for obtaining a suitable mesh particularly in the high‐gradient zones. Copyright © 2014 John Wiley & Sons, Ltd.     

Fractional Calculus via Functional Calculus: Theory and Applications

This paper demonstrates the power of the functional-calculus definition oflinear fractional (pseudo-)differential operators via generalised Fouriertransforms.Firstly, we describe in detail how to get global causal solutions of linearfractional differential equations via this calculus. The solutions arerepresented as convolutions of the input functions with the related impulseresponses. The suggested method via residue calculus separates an impulseresponse automatically into an exponentially damped (possibly oscillatory)part and a `slow' relaxation. If an impulse response is stable it becomesautomatically causal, otherwise one has to add a homogeneous solution to getcausality.Secondly, we present examples and, moreover, verify the approach alongexperiments on viscolelastic rods. The quality of the method as an effectivefew-parameter model is impressively demonstrated: the chosen referenceexample PTFE (Teflon) shows that in contrast to standard classical modelsour model describes the behaviour in a wide frequency range within theaccuracy of the measurement. Even dispersion effects are included.Thirdly, we conclude the paper with a survey of the required theory. Therethe attention is directed to the extension from the L ₂-approachon the space of distributions .     

钢桁腹式混凝土组合箱梁翼板纵向应力的计算方法研究

为研究钢桁腹式混凝土组合箱梁翼板纵向应力沿横桥向的分布情况,运用有限元软件ANSYS建立一座35m等截面简支钢桁腹式混凝土组合箱梁的有限元模型,考虑斜向腹杆杆力作用会使翼板产生附加轴力及相应的附加应力,故利用能量变分法原理推导出组合箱梁的翼板纵向弯曲应力和纵向附加应力计算公式,并据此探讨适用于计算组合箱梁的翼板纵向应力的方法。将有限元值和理论值进行比较,吻合程度良好。研究结果表明,组合箱梁的下翼板纵向应力可采用纵向弯曲应力计算公式进行计算;为获得组合箱梁的翼板附加轴力,可将组合箱梁的钢桁腹杆和混凝土纵梁取出,认为两者通过节点构造共同构成平面桁架,翼板附加轴力即为平面桁架的弦杆杆力;组合箱梁的上翼板纵向应力可通过纵向弯曲应力和经修正的纵向附加应力叠加获得。     

KNOWLEDGE AND APPLICATION: FURTHER DISCUSSIONS ON THE COURSE OF CALCULUS IN THEORETICAL AND APPLIED MECHANICS CURRICULUN

讨论了力学专业中微积分教学的目的、方法,是计划在北京大学出版社出版的《微积分导引(下册)》的前言。     

On exact solutions of a class of fractional Euler–Lagrange equations

In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian L(x(t), where _a ^c D _t ^α x(t)) and 0<α<1, such that the following is the corresponding Euler–Lagrange

The theory and applications of generalized H-space

This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces.In this paper,the uniformity and properties far generalized H-space are considered.The conditions of metrization and the form of metric functions for generalized H-spaces,H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented.The results of this paper generalize and unify some recent results of[1-2,8,10].     

Numerical simulation of flocculation and transport of suspended particles: Application to metered-dose inhalers

This study investigates the dynamics of flocculation and transport of solid particles suspended in a liquid propellant. Polydisperse particles with lognormal size distribution are considered. Collision of particles is presumed to be controlled by upward velocity differential and Brownian motion. These mechanisms are enhanced by the van der Waals force. Flocculation of the particles is described using the continuous form of the Smoluchowski equation. Upward transport of the particles is specified via a convection term. The general dynamics of the system is governed by a nonlinear transient partial integro-differential equation which is solved numerically. The technique employed is based on discretizing the size distribution function using orthogonal collocation on finite elements. This is combined with a finite difference discretization of the physical domain, and an explicit Runge–Kutta–Fehlberg time marching scheme. The numerical analysis is validated by comparing with a closed form analytical solution. The simulation results represent the particle size distribution as a function of time and position. The method allows prediction of the effects of the initial conditions and physical properties of the suspension on its dynamic behavior and phase separation.     

Propagation of Transient Acoustic Waves in Layered Porous Media: Fractional Equations for the Scattering Operators

Acoustic waves scattering from a rigid air-saturated porous medium is studied in the time domain. The medium is one dimensional and its physical parameters are depth dependent, i.e., the medium is layered. The loss and dispersion properties of the medium are due to the fluid-structure interaction induced by wave propagation. They are modeled by generalized susceptibility functions which express the memory effects in the propagation process. The wave equation is then a fractional telegraphists equation. The two relevant quantities are the scattering operators—transmission and reflection operators—which give the scattered fields from the incident wave. They are obtained from Volterra equations which are fractional equations for the scattering operators.