共查询到20条相似文献，搜索用时 15 毫秒
1.
正今年是钱令希院士诞辰100周年,带着崇敬的心情我们缅怀先生的一生。作为一名杰出的科学家,除了在很多研究工作中取得优秀的成果,钱令希先生的战略眼光更值得我们学习。1950年钱令希先生在中国科学杂志发表《余能理论》[1]。论文中钱令希先生引用了Westergaard 1941年关于余能原理的论文,特别引用了Westergaard的观点,认为余能方法没有受到与其价 相似文献
2.
综述了近场动力学与有限元混合建模方法的研究进展,阐明了各种混合建模方法的基本原理与特点,并重点介绍本课题组在近场动力学与有限元方法混合建模方面的研究工作。现有近场动力学与有限元混合建模方法包括位移协调约束、力耦合、混合函数方法以及子模型方法等,除子模型方法外,都可归结为并行式多尺度分析方法,其基本思想是将计算结构划分为近场动力学子域、有限元子域以及两者的交界区域(或重叠区域、或界面单元、或过渡区域)。子模型方法可归结为显-显分析方法,先采用显式有限元进行整体分析,后采用近场动力学方法对重点区域进行分析。混合建模方法需要着重提高交界区域的计算精度,并且消除虚假力和虚假应力波问题。提出了通过力耦合的近场动力学与有限元混合建模的隐式分析方法,该方法不再设置重叠区,通过杆单元连接近场动力学子域与有限元子域,其中界面上的有限元结点不仅与其所在单元的其他结点发生作用,还通过杆单元与以其为圆心、一定半径的圆域内的其他物质点相互作用。研究表明,本文提出的混合模型和求解方法既能有效解决裂纹扩展等不连续问题,又可提高计算效率,为工程结构破坏问题的计算分析提供一种有效方法。 相似文献
3.
Huang Zaixing 《Acta Mechanica Solida Sinica》1996,9(4):350-356
In this paper, two fundamental problems completely unsolved in nonlocal field theory are studied. The first is the dependence of nonlocal residuals. By studying this problem, a theorem concerning the relationship between the residuals of nonlocal body force and nonlocal moment of momentum is given and proven. The other problem is how to give the stress boundary conditions in the linear theory of nonlocal elasticity. The stress boundary conditions obtained in this paper can not only answer why the nonlocal stress solution satisfying the boundary conditionst
ji
(s)
n
j
¦O
2 =p
i
(p
i
is a constant) on the surface of crack does not exist but also give a model of the molecular cohesive stress on the crack tip. 相似文献
4.
关于非局部场论的两点注记 总被引：1，自引：1，他引：1
研究了非局部场论中尚未完全解决的两个基本问题：其一为局部化体力，力矩残余之间的相关性，由此得到了一个描述两者关系的定理；其二为线性非局部弹性理论的应力边界条件的提法；文中所得到的应力边界条件不仅解释了在裂纹混合边界值问题中线性非局部弹性理论方程的解在常应力边界条件下不存在的问题，而且可以给出裂纹尖端的分子内聚力模型。 相似文献
5.
近场动力学方法及其应用 总被引：4，自引：0，他引：4
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. 相似文献
6.
黄再兴 《应用数学和力学(英文版)》1999,20(7):764-772
In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived. Foundation item: the Natural Science Foundation of Province Jiangshu (BK97063) 相似文献
7.
黄再兴 《应用数学和力学(英文版)》1999,(7)
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8.
提出一种基于非局部思想求解物理学问题的近场动力学算子方法(peridynamic operator method, PDOM). 运用PDOM可将任意阶局部微分及其乘积转化为相应的非局部积分形式, 且无需额外地特殊处理间断点与奇异点等问题. 近年来研究较多的两种非局部算子: 近场动力学微分算子(peridynamic differential operator, PDDO)和非局部算子方法(nonlocal operator method, NOM), 均可视为PDOM的一种特例. 以弹性力学问题为例, 采用变分原理和拉格朗日方程, 建立了适用于分析静/动态弹性力学问题的PDOM模型. 理论分析表明, 当分别限定相互作用域为与位置无关或位置相关的圆形域时, 该PDOM弹性模型即可退化为近年来文献中常见的近场动力学(peridynamics, PD)模型或对偶域近场动力学(dual-horizon peridynamics, DH-PD)模型. 通过3个典型实例: 杆的拉伸与波动、亥姆霍兹方程和含孔板的拉伸, 说明本方法的计算精度、收敛性与数值稳定性. PDOM方法适用于任意均匀或非均匀离散, 且能有效避免零能模式以及由其引起的数值振荡, 可望为各种物理学问题特别是不连续问题的非局部建模求解提供一种新选择. 相似文献
9.
Molecular dynamics(MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly,we develop a novel coarse-graining method, to automatically handle the material ... 相似文献
10.
Adam Martowicz Jakub Roemer Wieslaw J. Staszewski Massimo Ruzzene Tadeusz Uhl 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2019,99(4)
The work addresses solving partial differential equations (PDE)s for a continuum solid body using a nonlocal formulation. Second order spatial derivatives are of concern as they enable to deal with many dynamic problems in physics. The authors introduce a nonlocal finite difference (FD) scheme to show its applicability to computational mechanics. In the theoretical part of the work exemplary solutions of the second order ordinary derivatives are discussed. The capability of numerical dispersion reduction, which is identified for the proposed approach, is demonstrated for the crude spatial domain discretization. Based on the provided nonlocal FD scheme, discrete forms for the two types of PDEs are derived to indicate potential areas of practical applications for the presented method. Elastic wave equation and thermal diffusion equation are taken into account. Moreover, for the former case, the peridynamics – which is also a nonlocal approach – is also used to derive an alternative discrete formulation. The stability conditions for the provided numerical schemes are determined using von Neumann stability analysis. The limits for the allowed simulation time steps are found. The second part of the paper is devoted to the practical applications of the elaborated nonlocal formulations. There are studied selected thermal and mechanical properties of a gas foil bearing (GFB) component. A rod‐like structural part of GFB made of superalloy Inconel 625 is analyzed. A one‐dimensional model is built to determine temperature and displacement distributions via transient simulations. Again, reduced numerical dispersion is confirmed for the model with a crude mesh. 相似文献
11.
NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS (Ⅰ)──FUNDAMENTAL THEORY 
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下载免费PDF全文 In the linear nonlocal elasticity theory, the solution to the boundary-value problem of the crack with a constant stress boundary condition does not exist. This problem has been studied in this paper. The contents studied contain of examining objectivity of the energy balance, deducing the constitutive equations of nonlocal thermoelastic bodies, and determining nonlocal force and the linear nonlocal elasticity theory. Some new results are obtained. Among them, the stress boundary condition derived from the linear theory not only solves the problem mentioned at the beginning, but also contains the model of molecular cohesive stress on the sharp crack tip advanced by Barenblatt. 相似文献
12.
I.Intr0ductionNonlocallinearelasticitytheoryisp0ssible0fbuildingthebridgebetweenmicrostructuresofmaterialsandtheirmacrosc0picmechanicsbehaviorsduet0consideringthelong-rangeforcesamongmicroscopicparticles.SincenonIocalfieldtheorywasadvanced,aseriesresultsl… 相似文献
13.
非局部—非对称拟连续统理论 总被引：1，自引：0，他引：1
本文基于原子点阵模型,应用广义函数论,建立了非局部一非对称拟连续统理论.并讨论了非对称应力的物理—力学模型,即微观—宏观相结合的模型理论. 相似文献
14.
离心机是惯性导航系统加速度计的标定设备,转盘变形将严重影响标定精度。基于耦合理论研究了离心机流-热-固多场耦合问题的数值计算方法,分析了此类问题的全耦合数学模型,研究了求解数学方程的强、弱耦合算法及其应用。根据耦合方式不同定义了三种分析方法:直接法、顺序迭代法和顺序耦合法,建立了它们与强、弱耦合算法的联系。验证方法正确性后,对比离心机温度场强、弱耦合算法的计算结果发现,强耦合算法计算时间长,但模拟细节好,更接近真实情况,弱耦合算法计算时间短,但精度较低,故采用强耦合算法计算离心机流场和温度场。三种分析方法计算热-结构耦合的结果相近,故选择顺序耦合法计算离心机结构变形。 相似文献
15.
基于Eringen非局部弹性理论,直接利用逐次逼近法推导了非局部应力场的精确表达,该精确的非局部应力可具体表示为一个无穷级数的形式.然后以微梁的横向弯曲和纯弯曲变形为例,建立平衡方程并求解及分析了挠度受非局部效应的影响.结果表明:根据所取非局部小尺度参数大小的不同,非局部微梁的弯曲挠度可低于也可以高于经典力学下的挠度,非局部效应的增大可提高亦可降低结构的抗弯刚度.论文结果证明了Wang以及Lim等分别提出的两种相反的非局部模型的各自正确性.同时首次发现,弯曲挠度随着非局部效应的增大而上下波动且存在若干跳跃点,挠度是非局部小尺度参数的非单调函数,研究同时给出了一种确定材料非局部常数的建议途径. 相似文献
16.
Petr Pelech 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2019,99(6)
Motivated by earlier works by S.A. Silling and R.B. Lehoucq, we re‐examine the notion of stress and force flux in peridynamics ‐ a useful connection to measurable quantities and classical view of continuum mechanics. Based on the idea of traction we define two new peridynamic stress tensors and which stand, respectively, for analogues of the Cauchy and 1st Piola‐Kirchhoff stress tensors from classical elasticity. We show that the tensor differs from the earlier defined peridynamic stress tensor ; though their divergence is equal. We address the question of symmetry of the tensor which proves to be symmetric in case of bond‐based peridynamics; as opposed to the inverse Piola transform of (corresponding to the analogue of Cauchy stress tensor) which fails to be symmetric in general. We also derive a general formula of the force‐flux in peridynamics and compute the limit of for vanishing non‐locality, denoted by . For the sake of brevity we stick to bond‐based peridynamic in our calculations. We show that this tensor surprisingly coincides with the collapsed tensor , the limit of the original tensor . At the end, using this flux‐formula, we suggest an explanation why the collapsed tensor (and hence ) can be indeed identified with the 1st Piola‐Kirchhoff stress tensor. Throughout the whole paper we suppose that the deformation is sufficiently regular. 相似文献
17.
近场动力学非普通状态理论在采用节点积分时将引起零能模式,造成位移场、应力应变场的数值不稳定性,影响计算精度甚至会导致完全错误的结果,因此必须对其进行控制.目前国际上还没有十分有效的零能模式控制方法.本文针对零能模式问题,提出了一种通用的、高效的控制方法.根据近场动力学线性键理论,确定非均匀变形对应弹性张量的具体形式,考虑了微模量随不同作用键的变化.通过最小位能原理推导出非均匀变形引起的力状态,结合近场动力学力状态,得到稳定力状态表达式.从而建立起基于线性键理论的稳定关联材料模型,并应用于含圆孔平板、三点弯试件线弹性变形和损伤破坏过程模拟.数值结果表明,本文模型能有效抑制近场动力学非普通状态理论中的零能模式现象.与已有零能模式控制方法相比,其物理意义明确,不包含控制参数,避免了复杂的零能模式参数调节过程,提高了计算效率. 相似文献
18.
In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum fieM theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic fiteld theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation, We show that there is the nonlocal body moment in the nonlocal elastic solids. The noniocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves. 相似文献
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20.
周期性弹性复合结构(声子晶体)中传播的弹性波存在特殊的色散关系:弹性波只能在某段频率范围内无损耗的传播,该频率范围称为通带.一维声子晶体的色散问题可以看作分层介质中弹性波的传播问题,利用二维弹性理论予以分析.为了研究非局部效应对声子晶体带隙特性的影响,将Eringen的二维非局部弹性理论引入到Hamilton体系下,利用精细积分与扩展的Wittrick Williams算法可获取任意频率范围内的本征解.通过对不同算例的数值计算,分析和对比了非局部理论方法与传统局部理论方法的差别.并进一步指出了该套算法的适用性和优势所在. 相似文献