共查询到20条相似文献,搜索用时 46 毫秒
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近些年弹性力学中出现一种新型的变分原理,称为广义混合变分原理.特点是其泛函中包含某些可以任意选择的附加函数,称为分裂因子.新原理将弹性理论中现有的各主要变分原理都统一在一个框架中,并揭示出它们之间更深一层的相互关系.在应用方面,它提供了一个新的数学手段以建立有限元分析中的新模式.这些新模式已经显示出它们的优点:适当调节分裂因子,它们给出更好的数值解答,特别是,可用它们来处理有限元方法中棘手的病态问题.本文综述了线性及非线性弹性理论中的这种新型变分原理并就其在有限元中的应用作了讨论. 相似文献
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固体—气幕—液体耦合系统广义变分原理 总被引:2,自引:1,他引:2
基于驻值势能原理,本文建立了固体-气幕-液体耦合系统的广义变分原理。本文进一步根据薄气幕层的特性,将广义变分原理的相关项适当组合,得出结论:在薄气幕层情况下,固体-气幕-液体三介质耦合问题可以化为在气泡振动方程、速度与压力连续条件限制下的流-固两介质耦合问题来进行数值计算。 相似文献
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耦合热弹性接触问题的变分原理 总被引:1,自引:0,他引:1
本文给出了考虑库伦摩擦力的热弹性接触问题的一个变分原理,该变分原理在约束条件Pn≥0和-μPn≤Pt≤μPn下,在接触边界上自动给出导热条件及剩余互补条件等。从它出发将接触弹性体离散后可直接进行二次规划求解。文中特地引进了因子β,它计及了接触问题中的热量散失和功率损耗 相似文献
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基于驻值势能原理,本文建立了固体-气幕-液体耦合系统的广义变分原理.本文进一步根据薄气幕层的特性,将广义变分原理的相关项适当组合,得出结论,在薄气幕层情况下,固体-气幕-液体三介质耦合问题可以化为在气泡振动方程、速度与压力连续条件限制下的流-固两介质耦合问题来进行数值计算. 相似文献
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From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids. 相似文献
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薛大为 《应用数学和力学(英文版)》1991,12(3):227-236
Two generalized variational principles on nonlinear theory of elasticity with finitedisplacements in which the σ_(ij),e_(i j)and u_i are all three kinds of independent functionsare suggested in this paper.It isproved that these two generalized variational principles areequivalent to each other if the stress-strain relation is satisfied as constraint.Some specialcases,i.e.generalized variational principles on nonlinear theory of elasticity with smalldeformation,on linear theory with finite deformation and on linear theory with smalldeformation together with the corresponding equivalent theorems are also obtained.All ofthem are related to the three kinds of independent variables. 相似文献
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Introduction Thedeformationofsaturatedsoftclayisoneofimportantquestionsingeotechnical engineering.Thenotablecharacteristicisthatthedegreeofitsstrainisgenerallylargerthan10percent.Oneofthecauses[1],Whichleadtoaquantitativedifferencebetweenthe numericalsimu… 相似文献
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黄泊 《应用数学和力学(英文版)》2003,24(5):576-584
IntroductionThemethodofconvolution[1- 3]canbeusedinthestudyofpiezoelectricmaterial.Piezoelectricmaterialisoneoftheimportantsmartmaterials,usedinnovelsmartstructure .ThedynamictheoryforthermopiezoelectricelastomediawassearchedbyNowacki[4 ,5 ],Chandrasekharaiah[6 ]andIesan[7].However,region_wisevariationalprinciplesinlinearthermopiezoelectricelastodynamicshavebeennotestablishedsystematically .AlthoughLuoenandKuangJun_shang[8]havedevelopedsimplifiedGurtin_typevariationalprinciplesinlinearther… 相似文献
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On the variational principles in linear elastodynamics 总被引:14,自引:0,他引:14
A new approach is proposed for the systematic derivation of varïous variational principles in linear elastodynamics. Based on an important integral relation in terms of convolutions given by the authors, the new approach can be used to derive the complementary functionals for the five-field, four-field, three-field, two-field and one-field variational principles more simply and directly. Furthermore, with this approach, it is possible not only to derive the variational principles given by Herrera and Bielak, Oden and Reddy, but also to develop new more general variational principles. And the intrinsic relationship among various principles can be explained clearly. 相似文献
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付宝连 《应用数学和力学(英文版)》1996,17(1):38-44
FuBaolian(付宝连)(ReceivedNov.22,1993;CommunicatedbyChienWeizang)COUPLEDVARIATIONALPRINCIPLESANDGENERALIZEDCOUPLEDVARIATIONALPRI... 相似文献
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An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien's method, a pair of generalized variational principles (GVPs) are established, which directly leads to all four Maxwell's equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem. 相似文献
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In this paper, the Hu-Washizu generalized variational principle isextended to nonlinear elastodynamics with five independent fields. The twokinds of framework of functional, the potential energy and complementaryenergy expressions containing the subsidiary conditions with Lagrangemultipliers are suggested. According to the principle of stationaryfunctional, we have the governing equations and Lagrange multipliersdetermened by the results of variation. The generalized sub-region mixed andhybrid variational principle in nonlinear elastodynamics is presented.Supported by National Natural ScienceFoundation of China. 相似文献
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何吉欢 《应用数学和力学(英文版)》2000,21(7):797-808
IntroductionIn 1 954,Hu[1,2 ]deducedHu_Washizuprinciplebyso_calledtrial_and_errormethod ,andin1 964 ,Chien[3]systematicallydiscussedtheLagrangemultipliermethod ,bywhichhesuccessfullydeducedHu_Washizuprinciple.Afterthatgeneralizedvariationalprinciplescanbearrivedat… 相似文献
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付宝连 《应用数学和力学(英文版)》1994,15(1):37-48
THEVARIATIONALPRINCIPLESOFCOUPLEDSYSTEMSINPHOTOELASTICITYFuBao-lian(付宝连)(YanshanUniversity,Qinhuangdao)(ReceivedNov.8,1989,Co... 相似文献