[1] Guo Xiaoming,. On existence and uniqueness of the solutionof elastoplastic contact problems [J]. Journal of Southeast University (English Edition), 2009, 25 (2): 232-235. [doi:10.3969/j.issn.1003-7985.2009.02.019]
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On existence and uniqueness of the solutionof elastoplastic contact problems(
)
一类弹塑性接触问题解的存在惟一性
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 25
- Issue:
- 2009 2
- Page:
- 232-235
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2009-06-30
Info
- Title:
- On existence and uniqueness of the solutionof elastoplastic contact problems
- 一类弹塑性接触问题解的存在惟一性
- Author(s):
- Guo Xiaoming
- School of Civil Engineering, Southeast University, Nanjing 210096, China
- 郭小明
- 东南大学土木工程学院, 南京210096
- Keywords:
- elastoplastic; contact problem; existence; uniqueness; coerciveness; variational extremum form
- PACS:
- O343.3
- DOI:
- 10.3969/j.issn.1003-7985.2009.02.019
- Abstract:
- Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally.First, the coerciveness of the functional is proved.Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated.The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality.A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems.The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.
- 针对弹塑性接触问题所构造的等价变分不等式, 解除了弹塑性本构状态约束方程和接触状态约束方程的约束.首先证明了所构造泛函的强制性, 从而证明了所构造的等价变分不等式解的惟一性, 并根据椭圆型变分不等式解存在的充分条件论证了弹塑性接触问题解的存在性, 为该问题的变分极值原理的建立奠定了数学理论基础.所构造的变分极值形式为运用数学规划法求解弹塑性接触问题提供了理论保证.
References:
[1] Guo Xiaoming, Zhang Roulei, She Yinghe.On the mathematical modeling for elastoplastic contact problem and their solution by quadratic programming[J].Int J Solids and Structures, 2001, 38(45):8133-8150.
[2] Adams R A.Sobolev space[M].Beijing:People’s Education Press, 1984.(in Chinese)
[3] Palmer A C, Maier G, Drucker D C.Normality relations and convexity of yield surfaces for unstable materials or structural elements[J].J Appl Mech, 1967, 34(2):464-470.
[4] Jiang Lishang, Pang Zhiyuan.Finite element methods and their theoretical foundations[M].Beijing:People’s Education Press, 1979:152-159.(in Chinese)
[5] Lions J, Duvaut G.Variational inequalities in mechanics and physics[M].Beijing:Science Press, 1987.(in Chinese)
[6] Cheng Gengdong.Foundations of the optimum design in engineering[M].Beijing:China Water-Power Press, 1984.(in Chinese)
[7] Cocu M.Existence of solutions of Signorini problems with friction[J].Int J Engng Sci, 1984, 22(5):567-575.
[8] Curnier A, Alart P.A generalized Newton method for contact problem with friction[J].Journal de Mecanique Theorique et Appliquee, 1988, 7(1)67-82.
[9] Klarbring A.Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction[J].Ingenieur-Archiv, 1990, 60(8):529-541.
[10] Khludnev A M.The contact between two plates, one of which contains a crack[J].J Appl Mech, 1997, 61(5):851-862.
[11] Fu Mingfu, Wu Hongfei.The existence and uniquenes of solutions of generalized variational inequalities arising from elasticity with friction[J].Appl Math and Mech, 2000, 21(8):836-842.(in Chinese)
Memo
- Memo:
-
Biography: Guo Xiaoming(1965—), male, doctor, professor, xmguo@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10672039), the Key Project of Ministry of Education of China(No.105083).
Citation: Guo Xiaoming.On existence and uniqueness of the solution of elastoplastic contact problems[J].Journal of Southeast University(English Edition), 2009, 25(2):232-235.