共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
THEVARIATIONALPRINCIPLEOFTHINSHELLINSTABILITYHuangyan黄炎,HuangReifang黄瑞芳(ReceiedNov.18.1994CommunicatedbyChienWeizang)Abstract... 相似文献
3.
郑泉水 《应用数学和力学(英文版)》1984,5(2):1185-1196
From the extended energy functional, a unified variational principle and an extended variational principle are given and proved in this paper. It is about the non-conservative, abrupt and divided domains static (or kinetic) system and by using the undetermined energy functional, we can immediately deduce various variational principles. 相似文献
4.
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
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 55–62, May 2007. 相似文献
5.
钱伟长 《应用数学和力学(英文版)》1985,6(1):25-39
In this paper, the generalizd variational principles of plate bending, froblems are established from their minimum potential energy principle and minimum complementary energy principle through the elimination of their constraints by means of the method of Lagrange multipliers. The involutory transformations are also introduced in order to reduce the order of differentiations for the variables in the variation. Funhermore, these involutory transformations become infacl the additional constraints in the varialion. and additional Lagrange multipliers may be used in order to remove these additional constraints. Thus, various multi-variable variational principles are obtained for the plate bending problems. However, it is observed that. nol all the constrainls ofva’iaticn can be removed simply by the ordinary method of linear Lagrange multipliers. In such cases, the method of high-order Lagrange multipliers are usedto remove iliose constrainls left over by ordinary linear multiplier method. And consequently. some funct ionals of more general forms are oblained for the generaleed variational principles of plate bending problems. 相似文献
6.
M. AOUADI 《应用数学和力学(英文版)》2015,36(5):619-632
The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C0-semigroup theory, the well-posedness of the proposed equations is shown. 相似文献
7.
The principle of complementary energy in nonlinear plate theory 总被引:1,自引:0,他引:1
H. Stumpf 《Journal of Elasticity》1976,6(1):95-104
In this paper, the priciple of complementary energy is given for the von Kármán nonlinear plate theory. Thenecessary conditions are three linear and static equilibrium equations in the interior and static boundary conditions on that part of the boundary surface, where forces are prescribed. The stationary value of the complementary energy functional leads to the stress-displacement relations and the geometric boundary conditions.
Zusammenfassung In dieser Arbeit wird das komplementäre Variationsprinzip für die nichtlineare Plattentheorie nach von Kármán untersucht. Als notwendige Bedingungen ergeben sich drei lineare statische Gleichgewichtsbedingungen sowie lineare statische Randbedingungen auf dem Teil des Randes, auf dem die Kräfte vorgegeben sind. Für den stationären Wert des Funktionals erhält man die Schnittgrößen-Verformungsbeziehungen sowie die geometrischen Randbedingungen.相似文献
8.
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
9.
10.
L. F. Yang Q. S. Li A. Y. T. Leung Y. L. Zhao G. Q. Li 《European Journal of Mechanics - A/Solids》2002,21(6):104
Linear and non-linear peaky fuzzy numbers and their arithmetic operations are constructed for the analysis of engineering structures with fuzzy characteristic quantities. Fuzziness of the corresponding quantities is consistently incorporated into the functional of the total potential energy. A set of deterministic recursive equations is obtained as the alternative expressions of the fuzzy variational principle by means of the second-order perturbation technique. The fuzzy Ritz method and the fuzzy finite element method are presented as the applications of the fuzzy variational principle. Accordingly, the roundabout procedures frequently used in the formulations of the fuzzy finite element method are avoided. A benchmark problem of a bending beam with fuzzy Young's modulus under fuzzy external loading is solved by the developed fuzzy numerical methods. Numerical examples show that results determined by these two fuzzy methods are both little conservative, and are in good agreement with those obtained by the analytical method. Moreover, the fuzzy Ritz method or the fuzzy finite element method can provide more valuable information than the conventional deterministic methods. 相似文献
11.
The dynamic principle is proposed that a thermodynamic system evolves in time so that the total energy balance including the energy drawn from the environment becomes stationary for all admissible variations of thermodynamic states. It is shown that this principle allows to obtain variational characterizations of contact Hamiltonian equations (even in presence of ports), reaction equations and doubly nonlinear reaction–diffusion equations. Further, examples are discussed which support this principle. 相似文献
12.
IntroductionIndefinitenesincludesfuzinesandrandomneswhicharethegeneralnatureofengineringstructures.Inthenumericalanalysisofst... 相似文献
13.
马景槐 《应用数学和力学(英文版)》1997,18(1):61-68
This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation
of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem. The
FEM form of this problem and its implementation have also been discussed in the paper. 相似文献
14.
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
15.
Recently Nappa obtains a Gurtin-type variational principle for micromorphic thermoelasticity. However, the use of convolutions is of course restricted to the linear case, which sets a limit to the rang of applicability. This paper establishes a classic variational principles for the discussed problem by the semi-inverse method. 相似文献
16.
This paper builds the general forms of subspace variational principles of rods andshells which are taken as the controlled equations of the constitutive theories developedfrom the three-dimensional (non-polar) continuum mechanics. And the constitutiveequations of rods and shells using the principles are satisfactory. 相似文献
17.
18.
Voronezh University. Translated from Prikladnaya Mekhanika, Vol. 25, No. 1, pp. 106–112, January, 1989. 相似文献
19.
Based on the concept of the effective stress in continuum damage mechanics, this paper studies the damage-coupled problem in elastoplastic creep. By using the parametric variational principle developed from optimal control theory, a numerical principle for the problem discussed has been established, the proof for which is also given. It is found that the principle proposed has a normalized form and can easily be put into application by computer.This project is supported by the National Natural Science Foundation of China 相似文献