On an Axially Symmetric Elastic-Plastic Torsion Problem

Yang Xiaoping; Zhou Shuzhi; Li Guangyao

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(7): 657-668

Yang Xiaoping, Zhou Shuzhi, Li Guangyao. On an Axially Symmetric Elastic-Plastic Torsion Problem[J]. Applied Mathematics and Mechanics, 1997, 18(7): 657-668.

Citation:

Yang Xiaoping, Zhou Shuzhi, Li Guangyao. On an Axially Symmetric Elastic-Plastic Torsion Problem[J]. Applied Mathematics and Mechanics, 1997, 18(7): 657-668.

Citation:

Yang Xiaoping, Zhou Shuzhi, Li Guangyao. On an Axially Symmetric Elastic-Plastic Torsion Problem[J]. Applied Mathematics and Mechanics, 1997, 18(7): 657-668.

PDF( 2837 KB)

On an Axially Symmetric Elastic-Plastic Torsion Problem

1.
Nanjing University of Science & Technologiy, Nanjing 210094, P.R. China;
2.
Hu'nan University, Changsha 410000, P. R. China;
3.
Guizhou University, Guiyang 550000, P. R. China

Received Date: 1995-11-26
Rev Recd Date: 1996-10-26
Publish Date: 1997-07-15

Abstract

Abstract

This paper discussed an axially symmetric elastic-plastic torsion problem. Invirtue of penalty method, reflection, boundaries, Bernstem estimate and reverse Holderinequality, on account of studying the corresponding complementary boundary problem which had mixed boundary conditions, the regularity of the solutions was established.
- complementary boundary problem,
- penalty method,
- Bernstein estimate,
- regularity

FullText(HTML)

References(15)

References

[1]	M.Biroli and U.Mosco.Stability and homogenization for nonlinear variationalinequalities with irregular obstacles and quadratic growth,Nonli.Anal.,7,1 (1983),41～60.
[2]	J.M.Bony,Principle du maximum dans les espaces de Sobolev,C.R.A.S.,26(1967),333～336.
[3]	C.W.Cryer,The solution of the axisymmetric elastic-plastic torsion of a shaft usingvariational inequalities.J.Math.Anal.Appl.,7(1980),535～570.
[4]	L.C.Evans,A second order elliptic equation with gradient constraint,Communicationsin PDEs.,4(1979),557～572.
[5]	M.Giaquinta,Multiple Integrals in the Calculus of Variations and Nonlinear EllipticSystems,Princeton Univ.Press,Princeton (1983).
[6]	D.Gilbary and N.S.Trudinger.Elliptic Partial Differential Equations of Second Order,Spring-Verlag,New York (1983).
[7]	A.Huber,On the uniqueness of generalized axially symmetric potentials,Ann.of Math.,60,2 (1954),351～358.
[8]	H.Ishii and S.Koike,Boundary regularity and uniqueness for an elliptic equation withgradient constraint.Comm.in PDEs.,8,(1983),317～346.
[9]	D.Kinderlehrer and G.Stampacchia,An Introduction to Variational Inequalities andTheir Applications,Acad.Press.New York (1980).
[10]	T.W.Ting.Elastic-plastic torsion of convex cylindrical bars,J.Math.Mech.,1(1969),531～551.
[11]	T.W.Ting.Elastic-plastic torsion problem over multiply connected domains,Ann.Scuola Norm Sup.,Pisa.4,(1977),291～312.
[12]	M.Wiegner,The C-character of solutions of sccond order elliptic equations withgradient constraint,Comm.in PDEs.,6,3 (1981).361～371.
[13]	杨孝平,关于无界系数的非线性椭圆变分不等式,湖南大学学报(数学专辑),15(1)(1988),222-231.
[14]	周叔子,关于一类轴对称的自由边界问题,应用数学学报,6(4)(1983),420-432.
[15]	周叔子,《变分不等式及其有限元方法》,湖南大学出版社.长沙(isas).