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1.
陈惟荣 《应用数学和力学(英文版)》1987,8(10):957-967
An input-output equation of the general spatial 7R mechanism is derived in this paper by using the method in [1] and applying the rotation matrices. The result is the same as [2], but the process of derivation is simpler. Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vectors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation. Moreover, an algorithm, which consists of successive applications of row transformation and expansion based on Laplace’s Theorem, is given to evaluate the 16 × 16 determinant according to its characteristic, so that the evaluation is much simplified. 相似文献
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A variational principle of perturbed motion on viscoelastic thin plates with applications 总被引:1,自引:0,他引:1
In this paper, in the light of the Boltzmann superposition principle in linear viscoelasticity, a mathematical model of perturbed
motion on viscoelastic thin plates is established. The corresponding variational principle is obtained in a convolution bilinear
form. For application the problems of free vibration, forced vibration and stability of a viscoelastic simply-supported rectangular
thin plate are considered. The results show that numerical solutions agree well with analytical solutions.
The project was supported by the National Natural Science Foundation of China (No. 19772027) and the Shanghai Municipal Development
Foundation of Science and Technology (No. 98JC14032). 相似文献
4.
Li-Hua Jin 《Acta Mechanica Solida Sinica》1988,1(3):291-300
In this paper, the idea of variational principles of linear elastic theory is used to establish generalized variational principles for linear elastic materials with voids. The fundamental equations of linear elastic materials with voids used have already been established in Ref. [5]. 相似文献
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In this paper,we have obtained generalized variational principles for linear elasticmaterials with voids from structural function theory.Correspondent relations betweenstructural functions and generalized variational principles are given. 相似文献
6.
电磁弹性固体三维问题的广义变分原理 总被引:10,自引:0,他引:10
提出了以电磁弹性固体所有变量应力、应变、位移、电位移、电场强度、电势、磁感应强度、磁场强度和磁势为自变量的电磁弹性固体三维问题最一般形式的广义变分原理。它们涵盖了电磁弹性固体问题所有的基本方程和边界条件。在此基础上还可以进一步给出部分变量为自变量的其它形式广义变分原理。 相似文献
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Introduction Thedeformationofsaturatedsoftclayisoneofimportantquestionsingeotechnical engineering.Thenotablecharacteristicisthatthedegreeofitsstrainisgenerallylargerthan10percent.Oneofthecauses[1],Whichleadtoaquantitativedifferencebetweenthe numericalsimu… 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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本文从考虑损伤的粘弹性材料的卷积型本构关系出发,建立了在小变形下损伤粘弹性梁-柱的控制方程。提出了以卷积形式表示的梁-柱弯曲问题的泛函,并给出了损伤粘弹性梁-柱的广义变分原理。应用这个广义变分原理,可分别给出梁-柱位移和损伤满足的基本方程,以及相应的初始条件和边界条件。应用Galerkin截断和非线性动力学的数值分析方法,分析了两端简支损伤粘弹性梁柱的动力学行为,给出了不同的材料参数对系统响应的影响。 相似文献
10.
成祥生 《应用数学和力学(英文版)》1993,14(5):417-428
This paper discusses the generalized variational principles founded by thetechnique of Lagrangian multipliers in structural mechanics and analyzes the nonlinearstatically indeterminate structures.It is assumed that the stress-strain relationship ofthe materials of structures has the form ofσ=Bε~(1/m)orτ=Cγ~(1/m),namely,thephysical equations of structures have the shape of exponential functions.Severalexamples are given to illustrate the statically indeterminate structures such as thetrusses,beams,frames and torsional bars. 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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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
13.
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
14.
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
15.
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
16.
Energy principles in theory of elastic materials with voids 总被引:3,自引:0,他引:3
Luo En 《Acta Mechanica Sinica》1992,8(1):44-50
According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author[1], various energy principles in theory of elastic materials with voids can be established systematically. In this paper, an
important integral relation is given, which can be considered essentially as the generalized pr. inciple of virtual work.
Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem of work
in theory of elastic materials with voids, but also to derive systematically the complementary functionals for the eight-field,
six-field, four-field and two-field generalized variational principles, and the principle of minimum potential and complementary
energies. Furthermore, with this appro ach, the intrinsic relationship among various principles can be explained clearly.
The project supported by the National Natural Science Foundation of China 相似文献
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HAMILTONIANSYSTEMSINELASTICITYANDTHEIRVARIATIONALPRINCIPLESWangZhi-guo(王治国)(ResearchInstituteofVibrationEngineering,NanjingUn... 相似文献
19.
The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang. 相似文献
20.
Generalized variational principle on nonlinear theory of naturally curved and twisted closed thin-walled composite beams 总被引:2,自引:0,他引:2
虞爱民 《应用数学和力学(英文版)》2000,21(3):327-334
IntroductionThestaticanddynamicnonlinearanalysisinthenaturallycurvedandtwistedclosedthin_walledslenderbeams(abbrevcurvedandtwistedthin_walledcompositebeams)ofthefibre_reinforcedcompositematerialsiscommonlyandmainlyappliedinchemicalindustryandaeronauti… 相似文献