Abstract
In the present study a shell contact problem with geometric and material nonlinearities is efficiently formulated by utilizing the mathematical programming method. The contact surface is assumed unbonded and frictionless. An incremental analysis by the updated Lagrangian approach is used. Two representative problems are treated to show modeling of the shell contact and the proposed solution method. The results are compared with existing solutions and those calculated by a commerical package.
Similar content being viewed by others
References
Bathe, K.J. and Bolourchi, S., 1980, “A Geometric and Material Nonlinear Plate and Shell Element”, Comp. Struct., Vol. 11, pp. 23–48.
Bathe, K.J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs.
Chaudhary, A. and Bathe, K.J., 1986, “A Solution Method for Static and Dynamic Analysis of Three-Dimensional Contact Problems with Friction”, Comp. Struct., Vol. 24, pp. 855–873.
Cheng, J.H. and Kikuchi, N., 1985, “An Analysis of Metal Forming Processes Using Large Deformation Elastic-Plastic Formulations”, Comp. Meth. Appl. Mech. Engng., Vol 49, pp. 71–108.
Fung, Y.C., 1965, Foundations of Solid Mechanics, Prentice-Hall Englewood Cliffs.
Haug, E.J. and Kwak, B.M., 1978, “Contact Stress Minimization by Contour Design”, Int. J. Num., Meth. Engng., Vol. 12, pp. 917–930.
Hibbitt, H.D. et al., 1988, ABAQUS User’s Manual Version 4.7, HKS Inc., Providence.
Hung, N.D. and de Saxce, G., 1980, “Frictionless Contact of Elastic Bodies by Finite Element Method and Mathematical Programming Technique”, Comp. Struct., Vol. 11, pp. 55–67.
Joo, J.W. and Kwak, B.M., 1986, “Analysis and Applications of Elasto-Plastic Contact Problems Considering Large Deformation”, Comp. Struct., Vol. 24, pp. 953–961.
Kwak, B.M., 1989, “Complementarity Problem Formulation and Implementation of Three-Dimensional Frictional Contact”, to appear in J. Applied Mechanics, Trans. ASME.
Kikuchi, N. and Skalski, K., 1981, “An Elasto-Plastic Rigid Punch Problem Using Variational Inequalities”, Arch. Mech., Vol. 33, pp. 865–877.
Lee, G.B., 1988, “Contact Analysis of Beam and Shell Structures with Geometric and Material Nonlinearities,”, Ph. D. Dissertation, KAIST, Seoul.
Lee, G.B. and Kwak, B.M., 1989, “Formulation and Implementation of Beam Contact Problems under Large Displacement by a Mathematical Programming”, Comp. Struct., Vol. 31, pp. 365–376.
Nagtegaal, J.C. and de Jong, J.E., 1981, “Some Computational Aspects of Elastic-Plastic Large Strain Analysis”, Int. J. Num. Meth. Engng., Vol. 17, pp. 15–41.
Oden, J.T. and Pires, E.B., 1984, “Algorithms and Numerical Results for Finite Element Approximations of Contact Problems with Non-Classical Friction Laws”, Comp. Struct., Vol. 19, pp. 137–147.
Panagiotopoulos, P.D., 1985, Inequality Problems in Mechanics and Applications, Birkhaeuser, Boston.
Tielking J.T. and Schapery, R.A., 1981, “A Method for Shell Contact Analysis”, Comp. Meth. Appl. Mech. Engng., Vol. 26, pp. 181–195
Updike, D.P. and Kalnins, A., 1972, “Contact Pressure Between an Elastic Spherical Shell and a Rigid Plate”, J. Appl. Mech., Trans. ASME, Vol. 39, pp. 1110–1114.
Yamada, Y., Yoshimura, N. and Sakurai, T., 1967, “Plastic Stress Strain Matrix and Its Application for the Solution of Elasto-Pastic Problems by the Finite Element Method”, Int. J. Mech. Sci. 10, 343–354.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lee, G.B., Kim, Y.G. & Kwak, B.M. Contact analysis of nonlinear shell structures using a mathematical programming method. KSME Journal 3, 130–138 (1989). https://doi.org/10.1007/BF02953598
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02953598