On Large Deformation Unilateral Contact Problem with Friction(Ⅰ)——Incremental Variational Equations

Shang Yong; Chen Zhi-da

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1989 > 10(12): 1049-1058

Shang Yong, Chen Zhi-da. On Large Deformation Unilateral Contact Problem with Friction(Ⅰ)——Incremental Variational Equations[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1049-1058.

Citation:

Shang Yong, Chen Zhi-da. On Large Deformation Unilateral Contact Problem with Friction(Ⅰ)——Incremental Variational Equations[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1049-1058.

Citation:

Shang Yong, Chen Zhi-da. On Large Deformation Unilateral Contact Problem with Friction(Ⅰ)——Incremental Variational Equations[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1049-1058.

PDF( 620 KB)

On Large Deformation Unilateral Contact Problem with Friction(Ⅰ)——Incremental Variational Equations

Beijing Graduate School, China University of Mining, Beijing

Received Date: 1988-11-02
Publish Date: 1989-12-15

Abstract

Abstract

Based on the theory and technique of nonlinear geometric field theory of continuum, a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in this paper. An expression for two and three-ditnensicnal continua is derived, and the incremental variational equation for large deformation of changing boundary contact and the variational inequality in rate form tire obtained, which provides the theoretical basis for the computation of elastic-plastic large deformation contact problem with friction.

FullText(HTML)

References(15)

References

[1]	陈至达,《有理力学》,中国矿业大学出版社(1988).
[2]	钱伟长,《变分法及有限元》,科学出版社(1980).
[3]	尚勇,带有接触摩擦边界弹塑性天变形问题的理论和有限元分析,中国矿业大学博士学位论文(1987).
[4]	秦忠,基于新的大变形理论的非线性有限元及其应用,中国矿矿业大学博士学位论文(1986).
[5]	谢和平,岩石蠕变损伤非线性大变形分析及微观断裂的FRACTAL模型,中国矿业大学博士学位论文(1987).
[6]	Shang Yong and Chen Zhi-da,Analysis of large elastic-plastic deformation by finite clement method using co-moving coordinate,Proc.ICNM,Shanghai,ed.Chien Wei-zang(1985).
[7]	Fichero,G.,Problemi elastostatici con vincali unilaterali problema di Signorini conambigue conditional contorno,Mem.Acc.Naz.Lincei,Ⅷ,7a(1964).
[8]	Duvant,G.and J.L.Lions,Un probleme d'slasticitéavec frottement,J.Mec.,10(1970),409-420,.
[9]	Panagiolopoulos,P.D.,A variational inequality approach to the friction problem of Structures with convex strain energy density and application to the frictional unilateral contact problem,J.Struct.Mech.,6,3(1978),303-318.
[10]	Oden,J.T.and E.B.Pires,Contact problems in elastostatics with nonlocal friction law,TICOM Report,University of Texas,Austin(1981).
[11]	Pires,E.B.and J.T.Oden,Analysis of contact problems with friction under oscillating loads,Comp.Meth.Appl.Mech Eng.,39(1983),337-362.
[12]	Bathe,K.J.,A solution method for plane and axisymmetric contact problems,Int.J.Num.Meths.Eng.,21(1985),65-88.
[13]	Bufler,M.,Derivation of the variational inequalities and extremum principles of the frictionless elastic contact problem,Comp.Meth.Appl.Mech.Eng.,53(1985).,163-182.
[14]	Ekeland,I.and R.Teman,Convex Analysis and Variational Problems,North-Holland(1976).
[15]	Haber,R.B.and B.H.Hariandja,An Eulerian-Lagrangian finite element approach to large deformation frictional contact,Comp.and Structure,20(1985),194-201.