Cheng Xiang-sheng. The Generalized Variational Principles in Applications for Nonlinear Structural Analysis[J]. Applied Mathematics and Mechanics, 1993, 14(5): 397-406.
Citation: Cheng Xiang-sheng. The Generalized Variational Principles in Applications for Nonlinear Structural Analysis[J]. Applied Mathematics and Mechanics, 1993, 14(5): 397-406.

The Generalized Variational Principles in Applications for Nonlinear Structural Analysis

  • Received Date: 1990-01-04
  • Publish Date: 1993-05-15
  • This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of σ=βε1/m or τ=Cγ1/m, namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.
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  • [1]
    钱伟长,《关于弹性力学的广义变分原理及其在板壳问题上的应用》,科学出版社(1964).
    [2]
    钱伟长,弹性理论中广义变分原理的研究及其在有限元计算中的应用,力学与实践,1 (1)(1979), 16-24及1(2) (1979), 18-27.
    [3]
    钱伟长,《变分法及有限元》(上册),科学出版社(1980).
    [4]
    钱伟长,拉氏乘子法.高阶拉氏乘子法和弹性理论中更一般的广义变分原理,应用数学和力学,4(2) (1983).
    [5]
    钱伟长,《广义变分原理》,知识出版社(1985).
    [6]
    成祥生,待定乘数法在解超静定杆系结构问题中的应用,江苏省力学会论文91964).
    [7]
    成祥生,材料力,乒中某些超静定结构的一种解法,力学与实践.1(1) (1979), 46-47.
    [8]
    成祥生,结构分析中的广义变分原理及其应用,应用数学和力学,6(7) (1985), 639-648.
    [9]
    W ashizu, K.,(鹜津久一郎),Trariationad Method in Elasticity and Plasticity,Perga-man, London (1968).
    [10]
    鸳津久一郎,《コネルヂ原理入门》.培风馆(1970).
    [11]
    Pian, T,H,(卞学璜),Tong Pin(董平),Finite element methods in continuum mechanics, Adv, in App.Mec,,12(1972),1-53.
    [12]
    薛大为.建议一组关于极限分析的定理.科学通报,20(4) (1975), 81.
    [13]
    Фихтенголъц Г.М.,Курс Дuфференчцалзнозо ц Иumeipaлънoio Исччсленця,Т.I.Гостехиздат.М.Л.(1949)
    [14]
    Timoshenko,S.and J.Gere,Mechanics of Materials,Van Nostrand Reinhold Company,(1972)
    [15]
    Engesser,F.,On statically indeterminate frame with any low of deformation and on theorem of minimum complementary energy,Jour.of Arch and Engin.Union,Hannover,35(1889) 733-744.(in German)
    [16]
    Westergaard,H.M.,On the method of complementary energy and its applications to structures stressed beyond the proportional limit,to buckling and vibrations to suspension bridges,Proc.of ASCE,67,2(1941) 199.
    [17]
    Westergaard,H.M.,On the method of complementary energy,Trans.of ASCE,107,(1942) 765-793.
    [18]
    钱令希,余能原理,中国科学,1(1950)449.
    [19]
    Charlton,T.M.,Analysis of statically-indeterminate structures by the complementary energy method,Engineering,174(1952) 389-391.
    [20]
    Brown,E.H.,The energy theorems of structural analysis,Engineering,179(1955) 305-308,339-342,400-403.
    [21]
    Hoff,N.J.,The Analysis of Structures,John Wiley and Sons,Inc.,New York,(1956) 493.
    [22]
    Argyris,J.H.and S.Kelsey,Energy Theorems and Structural Analysis,Butterworth and Co.,Ltd.,London,(1960) 85.
    [23]
    Langhaar,H.L.,Energy Methods in Applied Mechancis,John Wiley and Sons,Inc.,New York,(1962) 350.
    [24]
    Au,T.,Elementary Structural Mechancis,(1963) 521.
    [25]
    Libove,C.,Complementary energy method for finite deformations,Pro.of ASCE,Jour.of Engi.Mech.Divi.90,EM6(1964) 49-71.
    [26]
    Oran,C.,Complementary energy method for buckling,Pro.of ASCE,Jour.of EMD.,93,EM1(1967) 57-75.
    [27]
    Oden,J.T.Mechanics of Elastic Structures,(1967) 381.
    [28]
    Oran,C.,Complementary energy concept for large deformations,Proc.of ASCE,Jour.of Struc.Divi.93,ST1(1967) 57-75.
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