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1.
IntroductionItiswell_knownthatthenonlinearKlein_Gordonequationplaysaveryimportantroleinnonlinearphysicsbecauseofitswidespreadapplicationinmanyfieldsofphysics[1,2 ].ItsgeneralformisUTT-UXX+m2 U+λU3=0 ,( 1 )wherethesubscriptsstandforpartialdifferentiationwithresp… 相似文献
2.
莫嘉琪 《应用数学和力学(英文版)》2010,31(12):1577-1584
A generalized nonlinear disturbed Klein-Gordon equation is studied. Using the homotopic mapping method, the corresponding homotopic mapping is constructed. A suitable initial approximation is selected, and an arbitrary-order approximate solution to the soliton is calculated: A weakly disturbed equation is also studied. 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.
戴天民 《应用数学和力学(英文版)》1982,3(5):633-645
In the present paper functionals for the various possible main variational principles in the nonlinear theory of e-lasticity are derived from the "full energy principle" and several of them are not found yet in the literatures available. Through the derivation of this paper we suggest a conjecture on the nonexistence of the eleventh and the sixth classes for the variational principles in Table 6.1 of H.C. Hu’s monograph [1]. 相似文献
5.
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
6.
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
7.
张汝清 《应用数学和力学(英文版)》1992,13(1):1-10
Based on paper, the variational principle and generalized variational principle of elastic dynamics for elastic body with nonlinear stress-strain relations are introduced in this paper. The generalized instantaneous variational principle is also raised for the mixed harmonious displacement element and the mixed harmonious stress element. 相似文献
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袁镒吾 《应用数学和力学(英文版)》1987,8(9):875-881
In this paper, we obtain a third-order approximate solution for the laminar boundary layer between two planes perpendicular to each other.In boundary layer equations, the viscous and the inertial terms have the same quantity step. In this paper, at first, supposing that the inertial terms are bigger than the viscous terms, we solve the boundary layer equations, and then we suppose that the viscous terms are bigger than the inertial terms. At last, we take the mean value as the valid solution of the boundary layer equations.The first- and the second-order approximate solutions obtained in this paper coincide with the results in ref. [1], while the third-order solution obtained in this paper is better than that in ref. [1]. 相似文献
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In this paper, we introduced the random materials, geometrical shapes, force and displacement boundary condition directly into the functional variational formulations and developed a unified random variational principle and finite element method with the small parameter perturbation method. Numerical examples showed that the methods have the advantages of the simple and convenient program implementation, and are effective for the random mechanics problems. 相似文献
13.
刘成群 《应用数学和力学(英文版)》1984,5(6):1875-1881
Recently Prof. Chien Wei-zang pointed out that in certain cases, by means of ordinary Lagrange multiplier method, some of undetermined Lagrange multipliers may turn out to be zero during variation. This is a critical state of variation. In this critical state, the corresponding variational constraint can not be eliminated by means of simple Lagrange multiplier method. This is indeed the case when one tries to eliminate the constraint condition of strain-stress relation in variational principle of minimum complementary energy by the method of Lagrange multiplier.By means of Lagrange multiplier method, one can only derive, from minimum complementary energy principle, the Hellinger-Reissner Principle, in which only two type of in-dependent variables, stresses and displacements, exist in the new functional. Hence Prof. Chien introduced the high-order Lagrang multiplier method bu adding the quadratic terms.to original functions. The purpose of this paper is to show that by adding to original functionals one 相似文献
14.
The parametric variational principle for elastoplasticity 总被引:4,自引:0,他引:4
A parametric variational principle, the parametric minimum potential energy principle (abbreviated to PMPEP), is presented
for the elastoplastic problems. The principle proposed is free from the restraint of Drucker's postulate and consequently
suitable for solving the nonassociated plastic flow problems in rock, soil, concrete and other geomaterials. 相似文献
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V. D. Bondar' 《Journal of Applied Mechanics and Technical Physics》2000,41(1):120-130
For materials characterized by a linear relation between Almansi strains and Cauchy stresses, relations between stresses and
complex potentials are obtained and the plane static problem of the theory of elasticity is thus reduced to a boundary-value
problem for the potentials. The resulting relations are nonlinear in the potentials; they generalize well-known Kolosov's
formulas of linear elasticity. A condition under which the results of the linear theory of elasticity follow from the nonlinear
theory considered is established. An approximate solution of the nonlinear problem for the potentials is obtained by the small-parameter
method, which reduces the problem to a sequence of linear problems of the same type, in which the zeroth approximation corresponds
to the problem of linear elasticity. The method is used to obtain both exact and approximate solutions for the problem of
the extension of a plate with an elliptic hole. In these solutions, the behavior of stresses on the hole contour is illustrated
by graphs.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41,
No. 1, pp. 133–143, January–February, 2000. 相似文献
18.
E. I. Romenskii 《Journal of Applied Mechanics and Technical Physics》1974,15(2):255-259
It is shown that the complete system of equations of elasticity theory for an isotropic medium admits a unique representation in the hypoelastic form (the tensor of the rate of change of stresses is a linear function of the tensor of strain rates with coefficients depending on the invariants of the stress tensor). It is necessary to this end that the hypothesis be satisfied on the determination of strains by stresses which are unknown. Any arbitrariness in the choice of the coefficients of the hypoelastic relation may result in the thermodynamic identity being infringed. 相似文献
19.
THERANDOMVARIATIONALPRINCIPLEINFINITEDEFORMATIONOFELASTICITYANDFINITEELEMENTMETHODGaoHang-shan(高行山)(NorthwestenPolytechnicalU... 相似文献
20.
A homogeneous, isotropic cylinder in an equilibrium state of plane strain, whose cross-section is a rectangle R : [0 < y
1 < 2L; 0 < y
2 < h] with h/L 1, is considered. There are no body forces and the long sides are stress free. At y
1 = 0 and y
1 = 2L, there are arbitrary loadings, each statically equivalent to a uniformly distributed tensile or compressive stress c. Within the theory of nonlinear elasticity and with the strains and strain gradients assumed to be sufficiently small (but with no such assumptions on the displacement gradients), it is proved that if (,=1,2) represents the Cauchy stress tensor and the Kronecker delta, then |–c11| decays exponentially to zero in R with distance from the nearer end, and the decay constant depends only upon the material but is independent of L. 相似文献