共查询到20条相似文献,搜索用时 15 毫秒
1.
HAMILTONIANSYSTEMSINELASTICITYANDTHEIRVARIATIONALPRINCIPLESWangZhi-guo(王治国)(ResearchInstituteofVibrationEngineering,NanjingUn... 相似文献
2.
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
3.
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
4.
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
5.
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.
Hai-Chang Hu 《Acta Mechanica Solida Sinica》1992,5(2):175-182
It is proved in this paper that the functionals of equivalent variational principles are different essentially only in terms of weighted residues. Consequently, the simplest method for constructing equivalent variational principles is to add weighted residues to known functionals as first used by Courant [4]. 相似文献
7.
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
8.
The paper proposes a modification of the mixed variational principle from which stationarity conditions are derived in the
form of a mixed system of equations resolved for the first derivatives of the displacement and stress components acting in
a plane perpendicular to one of the coordinate axes. The variational principle allows decreasing the dimension of the problem
of elasticity thus reducing the system of equations to a canonical form. The modified mixed principle helps immediately obtain
a canonical system of equations for various applied theories. This possibility is demonstrated with the example of the Timoshenko
theory of plates
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 55–62, May 2007. 相似文献
9.
胡成栋 《应用数学和力学(英文版)》1986,7(11):1083-1094
First of all, this paper gives Legendre transformation for the so-called partial corresponding variables of strain energy function Σ(Eij) and complementary strain energy function Σc(Sij) of the elastic materiel, and introduces the corresponding blending complementary strain energy function Σchk! and blending strain energy function Σhk!. Moreover, a series of generalized variational principles of the corresponding blending energy form of non-linear elasticity is given. As a special case, there exist corresponding results[1] in linear elasticity. 相似文献
10.
N. M. Borodachev 《International Applied Mechanics》2004,40(11):1263-1268
A new representation of the stress tensor in the linear theory of elasticity is proposed. The representation satisfies the equilibrium equations and the compatibility conditions for strains. In this representation, the stress tensor is expressed in terms of a harmonic vector. The second boundary-value problem for an elastic half-space and elastic layer is considered as an example.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 85–91, November 2004.This revised version was published online in April 2005 with a corrected cover date. 相似文献
11.
some general theorems and generalized and piecewise generalized variational principles for linear elastodynamics 总被引:1,自引:0,他引:1
From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and the related theorems of time terminal conditions derived from it. The variational principles of potential energy action and complementary energy action, the H-W principles, the H-R principles and the constitutive variational principles for elastodynamics are obtained. Hamilton's principle, Toupin's work and the formulations of Ref. [5], [17]-[24] may be regarded as some special cases of the general principles given in the paper. By considering three cases: piecewise space-time domain, piecewise space domain, piecewise time domain, the piecewise variational principles including the potential, the complementary and the mixed energy action fashions are given. Finally, the general formulation of piecewise variati 相似文献
12.
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
13.
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
14.
戴天民 《应用数学和力学(英文版)》2000,21(1):27-32
IntroductionItiswell_knownthatthereexiststheargumentbetweenAtkinson(see[1~4])andEringenandco_workers(see[5~7])overthenon_loca... 相似文献
15.
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
16.
By taking infinite periodic beams as examples, the mutual variational principle for analyzing the free wave propagation in
periodic structures is established and demonstrated through the use of the propagation constant in the present paper, and
the corresponding hierarchical finite element formulation is then derived. Thus, it provides the numerical analysis of that
problem with a firm theoretical basis of variational principles, with which one may conveniently illustrate the mathematical
and physical mechanisms of the wave propagation in periodic structures and the relationship with the natural vibration. The
solution is discussed and examples are given.
Supported by Doctorate Training Fund of National Education Commission of China 相似文献
17.
The structural theory of short-term damage is used to study the coupled processes of deformation and microdamage of a physically
nonlinear material in a combined stress state. The basis for the analysis is the stochastic elasticity equations for a physically
nonlinear porous medium. Damage in a microvolume of the material is assumed to occur in accordance with the Huber-Mises failure
criterion. The balance equation for damaged microvolumes is derived and added to the macrostress-macrostrain relations to
produce a closed-form system of equations. It describes the coupled processes of nonlinear deformation and microdamage of
the porous material. Algorithms are developed for calculating the dependence of microdamage on macrostresses and macrostrains
and plotting stress-strain curves for a homogeneous material under either biaxial normal loading or combined normal and tangential
loading. The plots are analyzed depending on the type of stress state
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 30–39, November 2006. 相似文献
18.
Luo En 《Acta Mechanica Sinica》1993,9(2):142-148
According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author[1], some basic principles in dynamic theory of elastic materials with voids can be established systematically. In this paper,
an important integral relation in terms of convolutions is given, which can be considered as the generalized principle of
virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the
reciprocal theorem in dynamic 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 simplified Gurtin-type variational principles. Furthermore,
with this approach, the intrinsic relationship among various principles can be explained clearly.
The project supported by the Foundation of Zhongshan University Advanced Research Center 相似文献
19.
正今年是钱令希院士诞辰100周年,带着崇敬的心情我们缅怀先生的一生。作为一名杰出的科学家,除了在很多研究工作中取得优秀的成果,钱令希先生的战略眼光更值得我们学习。1950年钱令希先生在中国科学杂志发表《余能理论》[1]。论文中钱令希先生引用了Westergaard 1941年关于余能原理的论文,特别引用了Westergaard的观点,认为余能方法没有受到与其价 相似文献
20.
Mindlin’s (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown that writing the consistency conditions obtained from the equivalency between the atomistic crystal lattice dynamics of the bulk material and its counterpart in the second strain gradient elasticity is insufficient for the calculations of all the additional constants. As it will be discussed, there are two missing conditions which are then provided by consideration of the free standing film problem that bring the surface effect into account. As a consequence of surface effect consideration, the modulus of cohesion which is one of the important additional constants is calculated. Moreover, an analytical expression for the surface energy in terms of the modulus of cohesion, Lamé constants, materials characteristic lengths, and the film thickness is presented. If the film thickness is much bigger than the magnitude of the characteristic lengths of the material, then the surface energy would no longer depend on the film thickness. 相似文献