Dynamically loaded rigid-plastic analysis under large deformation
Author:
Yang Gao
Journal:
Quart. Appl. Math. 48 (1990), 731-739
MSC:
Primary 73G20; Secondary 73E20
DOI:
https://doi.org/10.1090/qam/1079916
MathSciNet review:
MR1079916
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Abstract: Extended bounding theorems on maximum deformation and minimum response time are developed for dynamically loaded rigid-plastic structures in the range of large deformations. It is proved that the existence of bounds is directly related to a so-called complementary gap function and its directional-derivative.
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J. B. Martin, The determination of upper bounds on displacements resulting from static and dynamic loading by the application of energy methods, IVth National U.S. Congress of Applied Mechanics, 1966, p. 221
A. R. S. Ponter, An upper bound on the displacements of elastic-perfectly plastic structures, J. Appl. Mech. 39, 959 (1972)
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- Yang Gao and Gilbert Strang, Geometric nonlinearity: potential energy, complementary energy, and the gap function, Quart. Appl. Math. 47 (1989), no. 3, 487–504. MR 1012271, DOI https://doi.org/10.1090/qam/1012271
- Yang Gao and Gilbert Strang, Dual extremum principles in finite deformation elastoplastic analysis, Acta Appl. Math. 17 (1989), no. 3, 257–267. MR 1040379, DOI https://doi.org/10.1007/BF00047073
- Yang Gao and Tomasz Wierzbicki, Bounding theorem in finite plasticity with hardening effect, Quart. Appl. Math. 47 (1989), no. 3, 395–403. MR 1012265, DOI https://doi.org/10.1090/qam/1012265
- Yang Gao, Opposite principles in nonlinear conservative systems, Adv. in Appl. Math. 10 (1989), no. 3, 370–377. MR 1008563, DOI https://doi.org/10.1016/0196-8858%2889%2990021-3
- Yang Gao, Bound theorem on finite dynamic deformations of plasticity, Mech. Res. Comm. 17 (1990), no. 1, 33–39. MR 1031437, DOI https://doi.org/10.1016/0093-6413%2890%2990030-G
Yang Gao, Extended dual bounding theorems for nonlinear plastic limit analysis, to appear in Internat. J. Solids and Structures 1990
- Ivar Ekeland and Roger Temam, Analyse convexe et problèmes variationnels, Dunod; Gauthier-Villars, Paris-Brussels-Montreal, Que., 1974 (French). Collection Études Mathématiques. MR 0463993
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Yang Gao, Panpenalty finite element programming for limit analysis, Comput. and Structures 28, 749–755 (1988)
- Yang Gao and Y. K. Cheung, On the extremum complementary energy principles for nonlinear elastic shells, Internat. J. Solids Structures 26 (1990), no. 5-6, 683–693. MR 1049287, DOI https://doi.org/10.1016/0020-7683%2890%2990039-X
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J. B. Martin, A displacement bound technique for elastic continua subjected to a certain class of dynamic loading, J. Mech. Phys. Solids 12, 165 (1964)
J. B. Martin, The determination of upper bounds on displacements resulting from static and dynamic loading by the application of energy methods, IVth National U.S. Congress of Applied Mechanics, 1966, p. 221
A. R. S. Ponter, An upper bound on the displacements of elastic-perfectly plastic structures, J. Appl. Mech. 39, 959 (1972)
W. J. Stronge, Lower bound on deformation for dynamically loaded rigid-plastic structures, Internat. J. Solids and Structures 19, 1049–1063 (1983)
G. Maier and L. Corradi, Upper bounds on dynamic deformations of elastoplastic continua, Meccanica 9 30 (1974)
M. Capurso, Extended displacements bound theorems for continua subjected to dynamic loading, J. Mech. Phys. Solids 23, 113 (1975)
T. Wierzbicki, Bounds on large dynamic deformations of structures, J. Eng. Mech. Div. Proc. ASCE EM, 267–276 (1970)
J. Ploch and T. Wierzbicki, Bounds for large plastic deformations of dynamically loaded continua and structures, Internat. J. Solids and Structures 17, 183–195 (1981)
Yang Gao and G. Strang, Geometric nonlinearity: Potential energy, complementary energy and the gap function, the 17th International Congress of the Theoretical and Applied Mechanics, Grenoble, France, 1988 (Quart. Appl. Math. 48, 487–504 (1989)
Yang Gao and Gilbert Strang, Dual extremum principles in finite deformation elastoplastic analysis, Acta Appl. Math. 17 257–267 (1989)
Yang Gao and Tomasz Wierzbicki, Bounding theorem in finite plasticity with hardening effect, Quart. Appl. Math. 48 395–403 (1989)
Yang Gao, Opposite principles in nonlinear conservative systems, 4th Int. Conf. on System Research, Informatics and Cybernetics, Baden-Baden, W. Germany, 1988 (Adv. in Appl. Math. (3) 10 370–377 (1989))
Yang Gao, Bounding theorem on finite dynamic deformations of plasticity, Mech. Research Commu. (1) 17, 33–39 (1990)
Yang Gao, Extended dual bounding theorems for nonlinear plastic limit analysis, to appear in Internat. J. Solids and Structures 1990
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, 1976
P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, 1985
Yang Gao, (1988) On the complementary bounding theorems of limit analysis, Internat. J. Solids and Structures 24 545–556 (1988)
Yang Gao, Panpenalty finite element programming for limit analysis, Comput. and Structures 28, 749–755 (1988)
Yang Gao and Y. K. Cheung, On the extremum complementary energy principles for geometrical nonlinear thin elastic shell, Internat. J. Solids and Structures 26 (5-6), 683–693 (1990)
Yang Gao, On the extreme variational principles for nonlinear elastic plates, Quart. Appl. Math. 48, 361–370 (1990)
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Article copyright:
© Copyright 1990
American Mathematical Society