The Generalized Variational Principles in Applications for Nonlinear Structural Analysis

Cheng Xiang-sheng

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1993 > 14(5): 397-406

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.

Citation:

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

PDF( 636 KB)

The Generalized Variational Principles in Applications for Nonlinear Structural Analysis

Cheng Xiang-sheng

Tongji University, Shanghai

Received Date: 1990-01-04
Publish Date: 1993-05-15

Abstract

Abstract

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=βε^1/m or τ=Cγ^1/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.
- generalized variational principle,
- nonlinear structures,
- statically indeterminate structures

FullText(HTML)

References(28)

References

[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．