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1.
Thelineartheoryofnonlocalelasticityhasbeenappliedtosomeproblemssuchasfracture,dislocationandwavepropagation[1].Itisusedtosolvemanyproblemswhicharenotexplainedbytheclassicalmechanics.Itispointedoutearlier[2],however,someimportantnonlocalpropertiesinth…  相似文献   

2.
IntroductionThispaperisconcernedwiththenumericalsolution ,byfinitedifferencemethod ,ofthefollowingsingularlyperturbednonlocalboundaryvalueproblem :Lu≡-εu″ +a(x)u=f(x)   ( 0 <x<l) ,( 1 )L0 u≡-εu′( 0 ) +γu( 0 ) =μ0 , ( 2 )L1u≡u(l) -δu(d) =μl   ( 0 <d<l) ,( 3 )whereεisasmallpositiveparameter,…  相似文献   

3.
IntroductionThereexistmanyimperfectionsthatareimpossibletoavoidinanengineeringstructure.Someimportantexperiments[1,2]haveshownthatimperfectionsinastructuremaymakethecriticalloaddecreaseevidently.Sotheinfluenceofimperfectionsuponthecriticalloadofthest…  相似文献   

4.
IntroductionTheone_dimensionalMHDequationsunderLagrangecoordinateare τ t- u x=0 , u t P x 18π x(H2 y H2 z) =0 , Hy t Hyτ u x =0 , Hz t Hzτ u x=0 , S t=0 ,( 1 )whereu ,τ,Hy,HzandSthevelocity ,specificvolume,thecomponentsofmagneticfieldiny_andz_diectionsandtheentropyrespectively .T…  相似文献   

5.
IntroductionUptonow ,thetechnicalliteratureonseparatecracks,voids,inclusionsandtheinteractionsbetweencracksandinclusionshavebeenquiteextensive.However,thecontactproblemsofcrack_inclusiondonotseemtobeaswidelystudied .Thispapercanberegardedasthefurtherrese…  相似文献   

6.
IntroductionByadoptingtheenergymethod,anewmethodtocalculatethestabilityofthecompositeshellofrevolutionispresented.Thismethodtakestheinfluenceofnonlinearprebucklingdeformationsandstressesonthebucklingoftheshellintoaccount.Therelationshipsbetweenthepreb…  相似文献   

7.
IntroductionIn 1 975,B .Mandelbrotadvancedtheconception“fractal”andestablishedhisfractalgeometrytheory .Nowadays,thefractalgeometryisregardedasoneofthebesttoolstodescribethenonlinearproblems.Italsoimprovedthedevelopmentofmanyrelatedfields,suchasdynamicssyst…  相似文献   

8.
Therearemanydocumentsthatdiscussblow_upofthesolutionsfortheinitial_boundaryvlueproblemsofthenonlinearSchr dingerequations,suchaspaper [1 ] .Butthepaper [1 ]hasoneweakpoint,thatis,itcannotunitediscussionforblow_upofthesolutionsfortheinitial_boundaryvalueprobl…  相似文献   

9.
IntroductionAnunevendistributionoftheclearanceofvane_tipalongthecircumferenceorientationcausedbytherelativeeccentricitybetweenimpellerandcylinderofsteamturbinewillresultunequalpneumaticforceofthevanesatthesamestage .Asaresult,inadditiontoatorque,thetra…  相似文献   

10.
IntroductionWhilewestudythestrengthandthecrackofpractisingcomponents,thematerialdefectionshouldbeconsidered .IntheopinionsofCrackMechanics,thematerialdefectioncanbereducedtoplanarcracksandinclusions.Besides,theproblemofshort_fibercompositematerialsuchas…  相似文献   

11.
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   

12.
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   

13.
In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal residual of energy much simpler. The linear nonlocal consitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given. Foundation item: the Natural Science Foundation of Jiangsu Province, China (BK97063)  相似文献   

14.
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   

15.
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   

16.
陈玲  沈纪苹  李成  刘鑫培 《力学学报》2016,48(1):127-134
针对文献中关于纳米结构刚度受非局部效应影响趋势的不一致预测,基于梯度型的非局部微分本构模型,利用迭代法及泰勒展开法求得了非局部高阶应力的无穷级数表达,非局部应力相当于经典弯曲应力与非局部挠度的逐阶梯度之和.然后推导了梯度型非局部高阶梁弯曲的挠曲轴微分方程,并结合正则摄动思想,求解了非局部挠度的表达式.最后给出数值算例,具体量化挠度受非局部尺度因子的影响大小.研究表明:相比于其经典值,纳米结构的非局部弯曲挠度可呈现出或增大或减小或不变的趋势,考虑梯度型非局部高阶应力降低或提高或不影响纳米结构的刚度,具体结果依赖于外载和边界约束的类型.算例显示外载形式和边界约束条件均各自独立地影响着纳米结构的非局部弯曲挠度,同时首次观察到非局部最大弯曲挠度的位置可能受非局部尺度因子的影响.研究结论解决了非局部弹性力学应用于纳米结构的若干疑点,并为理论的发展和优化提供支持.  相似文献   

17.
I.Intr0ductionNonlocallinearelasticitytheoryisp0ssible0fbuildingthebridgebetweenmicrostructuresofmaterialsandtheirmacrosc0picmechanicsbehaviorsduet0consideringthelong-rangeforcesamongmicroscopicparticles.SincenonIocalfieldtheorywasadvanced,aseriesresultsl…  相似文献   

18.
由于超短激光脉冲具有功率密度高、持续时间短、加工精度高等优势, 近年来被广泛应用于超精细加工、光学储存和微电子器件制造等领域. 本文基于L-S型广义热弹扩散理论, 建立了考虑材料记忆依赖效应和空间非局部效应的记忆依赖型非局部广义热弹扩散耦合理论, 它能够准确预测几何尺寸与内部特征尺寸相近结构的热弹扩散瞬态响应. 推导了所建理论的控制方程, 并基于拉普拉斯积分变换获得了控制方程的解. 作为算例, 利用所建理论和求解方法研究了半无限大薄板受非高斯激光脉冲加热和化学冲击联合作用下的热弹扩散瞬态响应问题, 得到了薄板的温度、化学势、位移、应力和浓度等随非局部参数、热时间迟滞因子和扩散时间迟滞因子等参数变化的分布规律. 结果表明: 传热对传质影响显著, 传质对传热影响甚微; 非局部参数对位移、应力影响显著, 对温度、化学势和浓度几乎没有影响. 该理论及求解方法的建立, 旨在实现材料在机械、热、化学势等冲击作用下传热传质瞬态响应的准确预测.  相似文献   

19.
张培  何天虎 《力学学报》2018,50(3):508-516
现有的广义热弹理论主要适用于求解时间尺度极短但空间尺度仍属宏观尺度的广义热弹问题的动态响应,而当所研究的弹性体的特征几何尺寸也属微尺度时,弹性体的力学响应将呈现出强烈的尺寸相关性,现有的广义热弹理论不再适用. 本文基于通过非局部效应和记记依赖微分修正的广义热弹性理论,研究了两端固定、受移动热源作用的有限长热弹杆的动态响应. 建立了问题的控制方程,给出了问题的初始条件及边界条件,运用拉普拉斯变换及其数值反变换,对方程进行了求解. 数值计算中,首先考察了时间延迟因子对模型所预测各物理量分布的影响;然后对比了模型中的时间延迟因子在两种不同类别核函数下(通过归一化条件修正和未修正形式)对各物理量分布的影响效应;最后考察了考虑新的可以描述尺寸效应的非局部因子对无量纲温度、位移及应力的影响,并用图形进行了示例. 结果表明, 时间延迟因子增大,各物理量的峰值变大,传播距离变小,且时间延迟因子在归一化条件修正过的核函数下影响更加显著;非局部参数几乎不影响无量纲温度的分布,轻微影响无量纲位移的分布,但对无量纲应力的峰值的影响显著.   相似文献   

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