Abstract
This paper summarizes some developments in limit analysis solutions of structures based on the results obtained by the authors and their associates and students over the past ten years. Plates are first considered. Shells are then treated, including circular cylindrical shells, conical shells and the combined shells. Some new methods for limit analysis are the next subjects with the emphasis on the weighted residual method (WRM) and some numerical methods. Finally the problem of brittle plastic material which is a more general model of limit analysis is taken into account. As a conclusion, the analytical methods of limit analysis remain of value to complement the numerical approaches which are more effective for complicated structures and loading conditions.
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References
M. A. Save and C. F. Massonnet,Plastic Analysis and Design of Plates, Shells and Disks, North-Holland, Amsterdam, London (1972).
B. Y. Xu and X. S. Liu,Limit Analysis of Structures, Chinese Architecture Press, Beijing (1985).
W. Szczepinski,Introduction of the Mechanics of Plastic Forming of Materials, PWN (1979).
Ph. G. Hodge,Limit Analysis of Rotationally Symmetric Plates and Shells, Prentice-Hall (1963).
M. Save,J. Struct, Mech. 13, 343 (1985).
C. Cinquini and P. Zanon,Ingenieur Archive 55, 157 (1985).
F. L. Liu,Chinese J. Appl. Mech 6, 119 (1989).
X. P. Shen, Z. Z. Cen and B. Y. Xu,Chinese Journal of Applied Mechanics 13, 28 (1996).
X. Wu and B.Y. Xu,Acta Mechanica Sinica 21, 131 (1989).
J.C. Tang, S.L. Xing and B.Y. Xu,Comput. Struct. Mech. Appl. 3, 11 (1986).
C. Cinquini, D. O. Lamblin and G. Guerlement,J. Struct. Mech. 9, 145 (1987).
L. G. Pan and B. Y. Xu,J. Tsinghua University 27, 29 (1987).
G. Guerlement, D. O. Lamblin and M. Save,Eng. Struct. 9, 146 (1986).
L. G. Pan and B. Y. Xu,Acta Mechanica Solida Sinica 2, 152 (1986).
B. Yang,Doctoral Thesis, Tsinghua University (1990).
B. Y. Xu and L. Cheng,Arch. Mech. 36, 771 (1984).
L. Cheng, B. Y. Xu and K. C. Hwang,Acta Mechanica Sinica 17, 136 (1985).
Y. Deng, M. D. Xue and K. C. Hwang,Acta Mechanica Solida Sinica 3, 225 (1987).
W. Chen, M. D. Xue and B. Y. Xu,Acta Mechanica Solida Sinica 15, 333 (1994).
D. L. Gao,J. Mechanical Strength 8, 7 (1986).
L. G. Wang and Y. Liu,Acta Mechanica Sinica 24, 619 (1989).
Z. H. Sun, X. S. Liu and B. Y. Xu,Acta Mechanica Sinica 24, 136 (1989).
J. C. Tang, B. Y. Xu and T. G. Wang,J. Shichuan College of Technology 7, 21 (1988).
J. C. Tang, H. R. Li and S. L. Xiong,Eng. Mech. 5, 96 (1988).
L. X. Qian and Z. B. Wang,Comput. Struct. Mech. Appl. 5, 212 (1989).
L. X. Qian and Z. B. Wang,Acta Mechanica Sinica 24, 118 (1989).
P. X. Zhang, M. W. Lu and K. C. Hwang,Acta Mechanica Sinica 23, 433 (1991).
Y. H. Liu, Z. Z. Cen and B. Y. Xu,Int. J. Solids Structures 32, 1645 (1995).
Y. H. Liu, Z. Z. Cen and B. Y. Xu,Int. J. Pres. Ves. and Piping 64, 73 (1995).
Y. H. Liu, Z. Z. Cen and B. Y. Xu,Acta Mechanica Sinica 28, 682 (1996).
V. Carvelli, Y. H. Liu and G. Maier,The XIII Italian National Conference on Fracture Mechanics, Cassino, Italy (1997).
K. Dems and Z. Mroz,J. Struct. Mech. 13, 95 (1985).
W. Z. Liu and B. Y. Xu,Acta Mechanica Sinica, Sup, 192 (1989).
W. Z. Liu and B. Y. Xu,Acta Mechanica Solida Sinica 4, 165 (1989).
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Xu, B., Liu, Y. & Cen, Z. Some developments in limit analysis solutions of structures. Metals and Materials 4, 329–335 (1998). https://doi.org/10.1007/BF03187787
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DOI: https://doi.org/10.1007/BF03187787