关于用变分法求平面问题的双三角级数解

文[1]给出过设位移为双三角级数用虚位移原理求解平面问题的两个例题。文[2]指出了[1]的错误,给出了一种正确解答。文[3]也对[1]作了讨论,找到若干种(见其表1、2)能使[1]的解答成立的特例。但[2]的解答带有"l+ ...     

极性材料的热弹性力学

本文在文献[1]、[2]、[3]、[5]、[7]的基础上,讨论了线性耦合下,极性材料三维热弹性力学的能量方程、熵生成定律、耗散函数、Fourier热传导方程和它的变分原理。     

Equations of motion for nonholonomic mechanical systems with unilateral constraints

IntroductionThemotionofamechanicalsystemwithunilateralconstraintsismoregeneralthanwithbilateralconstraints1andyetitsinvestigationismoredifficult[1,2].Thesystemswithunilateralconstraintsinvolvetheholonomicmechanicalsystemswithunilateralholonomicconstraints[3～6]andthenonholonondcmeChanicalsystemswithunilateralholonondcconstraintS[7]andthenonholonondcmechanicalsystemswithunilateralnonholonondcconstraintS[2]andsoon.ThispaperstUdiesatypeofmoregeneralsystemswithunilateralconstfaints:nonholonondcs…     

VISCO-ELASTIC SYSTEMS UNDER BOTH DETERMINISTIC AND BOUND RANDOM PARAMETRIC EXCITATION

IntroductionThestudyofrandomparametricexcitedsystemsisimportantintheengineeringsystems,andistheoreticallymoredifficultespeciallywhentheexcitationsarenarrow_bandrandomprocessesandparametricexcitedsystems.Inthecasewhenthesystemsareexcitedbycombineddeterministicharmonicandwide_bandprocesses,StratonovitchandRomanovskii[1] ,Dimentbergetal.[2 ] ,andNamachchivaya[3 ] usingthemethodofrandomaveragingandthemethodofKhasminskiiinvestigatedthealmostcertainstabilityofthesystems.AriaratnamandTam[4]discusse…     

HAMILTON OPERATORS AND HOMOTHETIC MOTIONS IN R3

IntroductionPfaff[1]hasbeendefinedaquaternionproductonleaf (theplanecontainingtheOx_axis) .Byaidoftheproduct,anewproductisdefinedonplaneswhichpassesthroughtheorigindonotcontaintheOx_axisandsomeofthepropertiesofthisproducthavebeeninvestigated .Agrawal[2 ]gavesomealgebricpropertiesofHamiltonoperators.Also ,quaternionswereexpressedintermsof 4× 4matricesbymeansoftheseoperators.Yayli[3]gavehomotheticmotionswithaidoftheHamiltonoperatorsatE4 .Hacisalihoglu[4 ]showedthatallHomotheticmotionsinn_di…     

GURTIN-TYPE REGION-WISE VARIATIONAL PRINCIPLES FOR THERMOPIEZOELECTRIC ELASTODYNAMICS

IntroductionThemethodofconvolution[1- 3]canbeusedinthestudyofpiezoelectricmaterial.Piezoelectricmaterialisoneoftheimportantsmartmaterials,usedinnovelsmartstructure .ThedynamictheoryforthermopiezoelectricelastomediawassearchedbyNowacki[4 ,5 ],Chandrasekharaiah[6 ]andIesan[7].However,region_wisevariationalprinciplesinlinearthermopiezoelectricelastodynamicshavebeennotestablishedsystematically .AlthoughLuoenandKuangJun_shang[8]havedevelopedsimplifiedGurtin_typevariationalprinciplesinlinearther…     

"关于刚体平面运动中动量矩定理的综合讨论"一文中的某些错误——与朱晨同志商榷

文[1]中有一些错误的推导和结论,现指出如下:1.错误及其来源文[1]在"对任意动点和任意相对定点的相对动量矩定理式"讨论中引用了文[2]中的(3)式,由于文[1]的某些符号规定不符合习惯,故把文[2]中正确的(3)式引用成文[1]中错误的(18)...     

Shift of shock position for a class of nonlinear singularly perturbed problems

Thenonlinearsingularlyperturbedproblemisaveryattentiveobjectofstudyintheinternationalacademiccircles[1].Recently ,manyscholarsstudiedagreatdealofwork .Forexample,Boh啨[2 ],ButuzovandSmurov[3],O’Malley ,Jr.[4 ],Butuzov ,NefedovandSchneider[5 ]andKelley[6 ]andsoon .TheauthorconsideredaclassofsingularlyperturbednonlinearboundaryvalueproblemsfortheordinarydifferentialequationinRefs .[7～ 1 0 ] ,reactiondiffusionequationsinRefs.[1 1～ 1 3 ] ,singularlyperturbedproblemswithnonlocalboundarycond…     

NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

IntroductionRobertMerton[1] startedcontinuous_timefinancialmodelingwithhisexplicitdynamicprogrammingsolutionforoptimalportfolioandconsumptionpolices.Thissetsthestageforhis1973generalequilibriummodelofsecurityprices,anothermilestone .Hismajorcontributionwashisarbitrage_basedproofoftheoptionpricingformulaintroducedbyFisherBlackandMyronScholesin 1973[2 ] ,andhiscontinualdevelopmentofthatapproachtoderivativepricing .Darrelluffie[3 ] derivedtheBlack_ScholesFormulaintraditionaloptionpricingmetho…     

Transversely isotropic hyper-elastic material rectangular plate with voids under a uniaxial extension

IntroductionHyper_elasticmaterials ,suchasrubberandpolyurethane ,havemanyexcellentpropertiesandhavebeenusedwidelyinalmostallregionsofevery_daylifeandindustrialmanufacturing .Thevoidformationandgrowthinhyper_elasticmaterialsduetotheinstabilityofmaterialsplayafundamentalroleinthemechanismsofmaterialfractureandfailure.SotheproblemhasgotacertaindevelopmentinthepasttwentyyearsandtherecentreviewisthatofHorgan[1] .Chou_WangandHorgan[2 ] ,RenandCheng[3 ,4] studiedthegrowthofacentervoidinthecylindero…     

胆碱杂环二酸离子液体水润滑添加剂的制备及结构-性能关系研究

以胆碱和杂环二酸为原料,在去离子水中原位制备了添加剂[Ch]₂[Hdc],并研究了它们的摩擦学性能、腐蚀性、水生生物毒性与分子结构之间的构效关系. 研究发现,水溶液的运动黏度随着水中生成的[Ch]₂[Hdc]浓度的增加而增大,并且当[Ch]₂[Hdc]的分子结构对称性较低、极性较大时,水的黏度增加值相对较大. 这是由于添加剂分子极性较大时,分子间相互作用力较大,导致溶液的黏度增幅更大. 摩擦学性能测试发现,当[Ch]₂[Hdc]的浓度相对较低时,水溶液的减摩抗磨性能与[Ch]₂[Hdc]分子在摩擦副表面的吸附能力有关,分子极性较大,吸附能力较强的[Ch]₂[Hdc]可在摩擦副表面形成更为牢固的润滑保护膜,因而能有效改善水的减摩抗磨性能,反之则不能. 当[Ch]₂[Hdc]的浓度相对较高时,水溶液的减摩性能与其黏度呈反相关关系,抗磨性能则与其黏度呈正相关关系. 这是由于润滑剂黏度相对较大时,其内摩擦力较大,因而表现出较高的摩擦系数,即较差的减摩性能;然而,黏度相对较大的润滑剂则可以在摩擦副表面形成更为牢固的润滑保护膜,因而表现出较低的磨损体积,即较好的抗磨性能. 腐蚀试验结果表明,[Ch]₂[Hdc]可显著降低水对金属基底材料的腐蚀性. 毒性试验显示[Ch]₂[Hdc]对绿藻和海虾毒性远远小于传统离子液体L-B104.      

Cublic spline solutions of axisymmetrical nonlinear bending and buckling of circular sandwich plates

IntroductionBruun[1],Huang[2 ]andWang[3]publishedtheirpapersrelatedtolinearlystaticanalysisofcircularsandwichplates .Liuetal.setupnonlinearbendingequationsofacircularsandwichplate[4 ],andsolvedaseriesofnonlinearproblems[5～ 10 ].Sofartheothersneverdiscuss…     

Analysis of transient thermal stress in cylindrically orthotropic tubes

IntroductionCylindricallyorthotropictubesarenowwidelyappliedinengineering ,theresearchofthestressesfieldhasattractedalotofattentionfromscientistsandengineers .ConsiderableworksonstressfieldduetomechanicalloadinghavebeendonebyLehknitskii[1],Sherrer[2 ]andPagano[3].KalamandTauchert[4 ],HyerandCooper[5 ]studiedthethermalstressesinorthotropiccylindersduetosteaky_statetemperaturegradient.TheproblemoftransientthermalstressesinaholloworthotropiccircularcylinderwasfirstlyproposedandtreatedbyKardoma…     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)

IntroductionDecentralizedcontroltheoryalreadyexistsforlarge_scalesystems[1,2 ].ThereaftertheH∞robustcontroltheorywasappliedtosolvedisturbanceattenuationandreliablecontrolproblemsofsuchsystems[3～5 ]sothatfindingthecriticaloptimalparameterγ- 2crisanessentialstep ,hereγcristheoptimalH∞normofthesystem .ZhongandZhong[6 ]showedthattheLinear_Quadratic (LQ)optimalcontrolandKalman_Bucyfilteringtheoryareanalogoustostaticsinstructuralmechanics.Zhongetal.alsoshowed[7～ 9]thattheproblemofdetermini…     

对“计入横向剪切变形平板弯曲的边界元素法”一文的讨论

文[1]基于书[2]中介绍的三个广义位移的板弯曲理论,提出了一种边界单元法。虽然文[1]中的两个数字例题与精确解符合较好,但从基本概念上说,文[1]对书[2]有重要的误解。首先是在计及横向剪切变形的梁、板理论中,由切向力形成的力矩m_x,m_y,是否可     

Post-buckling of a cantilever rod with variable cross-sections under combined load

IntroductionSinceEuler[1] ,Lagrange[2 ] ,Love[3 ] etal.investigatedtheslenderrod ,asoneofthebasicstructuralstabilityproblems ,manyattentionshavebeenpaidtothepost_bucklingofelasticrodsforalongtime .Today ,flexiblerodshavebeenwidelyusedasspring ,linkages ,robot’sarms,largeantennasandsoon .Hence ,thestudiesofpost_bucklingofelasticrodshavewideengineeringandapplyingbackgroundsinrecentdays .Basedontheassumptionthattheaxiallineoftherodisinextensible ,Timoshenkoetal.[4] examinedthepost_bucklingofco…     

关于“关于极限分析新上、下限定理中权因子的讨论”一文的讨论

文[1]探讨了极限分析法的一些问题,本文对文[1]提出下述商榷意见. 1.文[1]中所建立的新上限定理和新下限定理是错误的.今举例说明:设选取的σ_ij~*和ε_ij~o处处满足条件σ_ij~*ε_ij~o<0,则不论对于什么结构,也不论该结构承受什么样的外载,只要这些外载与某一参数成比例地增加,那么根据文[1],立即可以得出该结构的真实极限载荷值的上限值和下限值均等于零.这就是说,该任意结构不受外载时就会发生流动,显然这结论是有问题的. 2.根据文[2]的论证方法和所得结果,可以改正文[1]的错误.正如文[3]所述,文[4]存在着原则错误,因此,文[1]以文[4]为基础而建立的有关定理就不可能正     

Research on an orthogonal relationship for orthotropic elasticity

IntroductionAsymplecticsystematicmethodology[1- 3]forelasticitywasestablishedbyZhongWan_xie .Hepresentedcreativelythedualvectorsandthesymplecticorthogonalrelationshipandopenedaworkplatformparalleledtothetraditionalelasticity[4 - 9].AnewdualvectorandanewdualdifferentialmatrixLwerepresentedforasymplecticsystematicmethodologyfortwo_dimensionalelasticityandaneworthogonalrelationshipwasdiscoveredforisotropicplaneproblems[4 ]byLuoJian_hui.Theneworthogonalrelationshipisgeneralizedfororthotropicelas…     

铸铁压缩破坏的宏观分析及其他

文献[1]发表后,我们写了《对〈铸铁单向压缩破坏的最大剪应力理论之否定〉一文的讨论》,于1985年11月投寄《力学与实践》.今又看到文献[2]和[3],想再谈几点看法.1.文献[1]是从宏观分析来否定最大剪应力理论的.虽然结论中有"被现有宏观理论所否定的最大拉应力"一句,但人们只是在文献[3]发表后才知道作者的结论是从细观得出的.鉴于文献[3]亦未给出这个问题的细观分析,所以这里仍限于从宏观来讨论问题.2.对于最大拉应变理论,文献[3]不再象文献[1] ...     

对《关于力的功的定义》一文的答复

<正> 上官飞同志在本刊1987年第3期发表的《关于力的功的定义》[1]一文中,对孟昭礼教授及作者等在文献[2]和[3]中提出的关于功的定义的一些主要观点进行了讨论.所得结论是“通常所表述的功的定义是严格的,完整的,而似乎不须再作补充或修正”.本文作者对此不敢苟同,现将我们的看法进一步阐明,以作为对文[1]的答复.首先,文[2]、[3]中指出,接触力的作用点这一概