MNSMS  Vol.3 No.4 , October 2013
Numerical Simulation of Stress-Strain State for Nonhomogeneous Shell-Type Structures Based on the Finite Element Method
Abstract: Projective-iterative version of finite element method has developed for numerical simulation of the stress-strain state of nonhomogeneous shell-type structures (shells with openings). Plastic deformation of the material is taken into account when using the method of elastic solutions that reduce the solution of elastoplastic problems to solution of elastic problems. Developed PIV’s significant savings of computer calculation has been compared with the calculation on a fine mesh of traditional FEM. Designed scheme allows analysis of the mutual influence of openings. Analysis of the transformation zone of plastic deformation is developed. For definiteness, the cylindrical shell structures with several rectangular openings are considered.
Cite this paper: E. Hart, V. Hudramovich, S. Ryabokon and E. Samarskaya, "Numerical Simulation of Stress-Strain State for Nonhomogeneous Shell-Type Structures Based on the Finite Element Method," Modeling and Numerical Simulation of Material Science, Vol. 3 No. 4, 2013, pp. 155-157. doi: 10.4236/mnsms.2013.34022.

[1]   V. S. Hudramovich, “Features of Nonlinear Deformation and Critical States of Shell Systems with Geometrical Imperfections,” Journal of Applied Mechanics, Vol. 42, No. 12, 2006, pp. 1323-1355.

[2]   E. Hart and V. Hudramovich, “Applications of the Projective-Iterative Versions of FEM in Problems of Damage for Engineering Structures,” Proceedings of the 2th International Conference “Maintenance 2012”, Zenica, Bosnia and Herzegovina, 13-16 June 2012, pp. 157-163.

[3]   A. A. Il’yushin, “Collected Works in 4 Volumes, Vol. 2: Plasticity (1946-1966),” Fizmatlit, Moscow, 2004.

[4]   M. A. Krasnosel’skii, G. M. Vainikko and P. P. Zabreiko, “Approximate Solution of Operator Equations,” Nauka, Moscow, 1969.

[5]   R. Kluge, “Ein Projektions-Iterationsverfahren bei Fix- punktproblemen und Gleichungen mit Monothonen Operatoren,” Monatsber. Dtsch. Akad. Wissenschaft, Vol. 11, No. 8-9, 1969, pp. 599-609.

[6]   W. Hackbusch, “Multigrid Methods and Applications,” Springer, Berlin, 1985.

[7]   E. L. Hart, “Projection-Iterative Version of the Pointwise Relaxation Method,” Journal of Mathematical Sciences, Vol. 167, No. 1, 2010, pp. 76-88.

[8]   V. Hudramovich, E. Hart and S. Ryabokon, “Elastoplastic Deformation of Nonhomogeneous Plates,” Journal of Engineering Mathematics, Vol. 78, No. 1, 2013, pp. 181- 197.

[9]   V. V. Novozhilov, K. F. Chernych and E. I. Michailovskii, “Linear Theory of Thin Shells,” Politechnica, Leningrad, 1991.