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1.
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   

2.
黄再兴  樊蔚勋 《力学季刊》1996,17(2):132-136
本文通过考虑局部化残余力的影响对线性非局部弹性理论进行了修正,由修正后的理论所导出的应力边界条件包含了物体微观结构的长程力的作用,这个结果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,而且可以自然地得到裂纹尖端的Barenblatt分子内聚力模型。  相似文献   

3.
本文采用非局部弹性理论。用Love位移函数导出三维轴对称问题的非局部弹性应力的一般形式解,并求解了圆盘裂纹问题。得到了裂纹尖端区的应力是有界的,再次证实了非局部理论模型求解断裂力学问题的正确性。  相似文献   

4.
脆性断裂的非局部力学理论   总被引:11,自引:0,他引:11  
程品三 《力学学报》1992,24(3):329-338
本文提出一种脆性材料断裂的非局部力学理论,内容包括:Ⅰ、Ⅱ、Ⅲ型Griffith裂纹的非局部弹性应力场,裂纹尖端邻域非局部弹性应力场的渐近形式,脆性开裂的最大拉应力准则。文中给出了这种理论应用于三种基本型裂纹和Ⅰ-Ⅱ、Ⅰ-Ⅲ复合型裂纹临界开裂条件的计算结果,并把它们与一些试验资料和最小应变能密度因子理论进行了对比。  相似文献   

5.
给出非均布表面应力作用下弹性薄板挠曲变形问题的控制方程及边界条件,通过与热应力问题进行物理比拟,对这一问题进行了求解,并采用这一方法对实验中观测到的局部弯曲现象进行了理论解释.  相似文献   

6.
基于裂纹处范德华力效应,采用非局部弹性理论构造纳米板模型,并通过导入哈密顿体系建立含裂纹纳米板振动问题的对偶正则控制方程组。在全状态向量表示的哈密顿体系下,将含裂纹纳米板的固有频率和振型问题归结为广义辛本征值和本征解问题。利用哈密顿体系具有的辛共轭正交关系,得到问题解的级数解析表达式。结合边界条件,得到固有频率与辛本征值的代数方程关系式,进而直接给出固有频率的表达式。数值结果表明,非局部尺寸参数和裂纹长度对纳米板振动的各阶固有频率有直接的影响。对比表明,辛方法是准确且可靠的,可为工程应用提供依据。  相似文献   

7.
以非局部弹性理论为基础,考虑了碳纳米管的小尺度效应,采用欧拉-伯努利梁模型给出了单层碳纳米管的动力学控制方程.研究了小尺度效应对振动简支单层碳纳米管边界条件的影响,并通过具体算例与经典连续介质理论的简支边界条件进行比较.结果表明:简支条件下考虑小尺度效应的非局部弹性理论和经典连续介质理论的边界条件具有同一性.  相似文献   

8.
纤维增强复合材料的轴对称横向裂纹分析   总被引:1,自引:1,他引:0  
从弹性力学解出发,借助积分变换将纤维和基体内的位移场和应力表示成以裂纹面上位错函数为未知量的积分形式。由边界条件纤维增强复合材料三维轴对称裂纹问题化成求解一组奇异积分方程的问题。  相似文献   

9.
赵大华  李华锋 《实验力学》2006,21(4):513-518
工程结构裂纹尖端应力强度因子(SIF)由于形状、荷载的复杂性及边界条件的不确定性,难以用解析法得到,数值计算也有困难,而光弹性法弥补了上述方法的不足。本文用环氧树脂制作圆轴模型,采用机加工的方法制作圆轴模型裂纹,然后将加载模型进行应力冻结,通过光弹性实验研究分析了圆轴裂纹尖端应力分布。由于带环形裂纹的圆轴在弯扭组合变形时,离中性轴最远的裂纹尖端处于复合裂纹状态,而三维光弹性应力冻结法是测定复杂三维问题复合裂纹的有效方法。本文用双参数法测定I型应力强度因子,用切片逐次削去法测定Ⅲ型应力强度因子,实验误差较小。  相似文献   

10.
曹津瑞  鲍四元 《力学季刊》2019,40(2):392-402
基于非局部理论,研究弹性杆在任意边界约束条件下的纵向振动特性.根据Chebyshev 谱级数建立非局部弹性杆的纵向位移形式.在杆的两端引入纵向约束弹簧,通过设置弹簧刚度系数,模拟经典边界及弹性边界.建立非局部杆的能量表达式,由瑞利-里兹法得到齐次线性方程组,求解对应的矩阵特征值与特征向量问题获得非局部杆的固有频率和振型.通过数值仿真计算,研究非局部特征系数与边界约束条件对非局部杆振动频率的影响.结果表明本文方法合理简便,具有良好的精度,且适用于任意弹性边界条件.  相似文献   

11.
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.
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   

14.
This article is concerned with the penny-shaped crack in an infinite body subjected to a uniform pressure on the surface of the carck in nonlocal elasticity. Making use of Love function in classical elasticity, we reduce the stress solution of an axisymmetric problem of the penny-shaped crack. The result of this article shows the stress on the crack tip is finite and demonstrates again the correctness of the nonlocal model for solving problems in fracture mechanics.Project Supported by the Science Foundation of the Chinese Academy  相似文献   

15.
This paper has successfully addressed three critical but overlooked issues in nonlocal elastic stress field theory for nanobeams: (i) why does the presence of increasing nonlocal effects induce reduced nanostructural stiffness in many, but not consistently for all, cases of study, i.e., increasing static deflection, decreasing natural frequency and decreasing buckling load, although physical intuition according to the nonlocal elasticity field theory first established by Eringen tells otherwise? (ii) the intriguing conclusion that nanoscale effects are missing in the solutions in many exemplary cases of study, e.g., bending deflection of a cantilever nanobeam with a point load at its tip; and (iii) the non-existence of additional higher-order boundary conditions for a higher-order governing differential equation. Applying the nonlocal elasticity field theory in nanomechanics and an exact variational principal approach, we derive the new equilibrium conditions, do- main governing differential equation and boundary conditions for bending of nanobeams. These equations and conditions involve essential higher-order differential terms which are opposite in sign with respect to the previously studies in the statics and dynamics of nonlocal nano-structures. The difference in higher-order terms results in reverse trends of nanoscale effects with respect to the conclusion of this paper. Effectively, this paper reports new equilibrium conditions, governing differential equation and boundary condi- tions and the true basic static responses for bending of nanobeams. It is also concluded that the widely accepted equilibrium conditions of nonlocal nanostructures are in fact not in equilibrium, but they can be made perfect should the nonlocal bending moment be replaced by an effective nonlocal bending moment. These conclusions are substantiated, in a general sense, by other approaches in nanostructural models such as strain gradient theory, modified couple stress models and experiments.  相似文献   

16.
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   

17.
A static meshfree implementation of the bond-based peridynamics formulation for linearly elastic solids is applied to the study of the transition from local to nonlocal behavior of the stress and displacement fields in the vicinity of a crack front and other sources of stress concentration. The long-range nature of the interactions between material points that is intrinsic to and can be modulated within peridynamics enables the smooth transition from the square-root singular stress fields predicted by the classical (local) linear theory of elasticity, to the nonsingular fields associated with nonlocal theories. The accuracy of the peridynamics scheme and the transition from local to nonlocal behavior, which are dictated by the lattice spacing and micromodulus function, are assessed by performing an analysis of the boundary layer that surrounds the front of a two dimensional crack subjected to mode-I loading and of a cracked plate subjected to far-field tension.  相似文献   

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