LAYOUT AND SHAPE OPTIMIZATION OF ELASTOPLASTIC DISKS WITH BOUNDS ON DEFORMATION AND DISPLACEMENT*,^†

REFERENCES

• Kohn , R.V. and Strang , G. 1986 . Optimal Design and Relaxation of Variational Problems. Commun. Pure Appl. Math. , 36 : 113 – 137 . 139–182, 353–377
   Web of Science ®Google Scholar
• Rozvany , G.I.N . 1977 . Optimization in Structural Mechanics , CISM Courses and Lectures Notes 374 Wien, New York : Springer-Verlag .
   Google Scholar
• Koiter , W.T. 1960 . “ General Theorems for Elasto-Plastic Solids ” . In Progress in Soil Mechanics Edited by: Sneddon , I.N. and Hills , R. 165 – 221 . Amsterdam : North-Holland .
   Google Scholar
• Martin , J.B. 1985 . Bounding Principles and Discrete Time Integration for Statically Loaded Elastic-Plastic Bodies UCT/CSIR Applied Mechanics Unit, University of Cape Town . Report No. 68
   Google Scholar
• Kaliszky , S. 1989 . “ Theory and Application ” . In Plasticity Amsterdam : Elsevier .
   Google Scholar
• Ceradini , G. 1980 . Dynamic Shakedown in Elastic Plastic Bodies . J. Eng. Mech. Div. ASCE , 106 ( EM3 ) : 481 – 499 .
   Google Scholar
• Corradi , L. and Maier , G. 1973 . Inadaptation Theorems in the Dynamics of Elastic–Work Hardening Structures . Ing. Arch. , 43 : 44 – 57 .
   Google Scholar
• Maier , G. 1969 . Shakedown Theory in Perfect Elastoplasticity with Associated and Nonassociated Flow Laws: a Finite Element, Linear Programming Approach . Meccanica , 4 ( 3 ) : 1 – 11 .
   Google Scholar
• König , J.A. 1987 . Shakedown of Elastic-Plastic Structures Amsterdam : Elsevier .
   Google Scholar
• Pycko , S. and Maier , G. 1995 . Shakedown Theorems for Some Classes of Nonassociated Hardening Elastic-Plastic Material Models . Int. J. Plasticity , 11 : 367 – 395 .
   Google Scholar
• Weichert , D. 1986 . On the Influence of Geometrical Nonlinearities on the Shakedown of Elastic-Plastic Structures . Int. J. Plasticity , 2 : 135 – 148 .
   Google Scholar
• Pycko , S. 1994 . “ An Indirect Incremental Method for Shakedown Analysis Based on the Min-Max Approach ” . In Inelastic Behavior of Structures Under Variable Loads Edited by: Mroz , Z. , Weichert , D. and Dorosz , S. Amsterdam : Kluwer .
   Google Scholar
• Polizzotto , C. 1982 . A Unified Treatment of Shakedown Theory and Related Bounding Techniques . S.M. Arch. , 7 : 19 – 75 .
   Google Scholar
• Capurso , M. , Corradi , L. and Maier , G. 1978 . “ Bounds on Deformations and Displacements in Shakedown Theory ” . In In Proc. Matériaux et Structures sous Chargement Cyclique 231 – 244 . France : Palaiseau .
   Google Scholar
• Stein , E. , Zhang , G. and König , J. A. 1992 . Shakedown with Nonlinear Strain Hardening Including Structural Computation Using Finite Element Method . Int. J. Plasticity , 8 : 1 – 31 .
   Web of Science ®Google Scholar
• Maier , G. 1969 . Complementary Plastic Work Theorems in Piecewise-Linear Elasto-Plasticity . Int. J. Solids Struct. , 5 : 261
   Google Scholar
• Ponter , A.R.S. 1972 . An Upperbound on the Small Displacements of Elastic,Perfectly Plastic Structures . J. Appl. Mech. , 39 : 959 – 963 .
   Web of Science ®Google Scholar
• Tin-Loi , F. 1980 . Deflection Bounding at Shakedown . J. Struct. Div. Proc. ASCE , 106 : 1209 – 1215 .
   Google Scholar
• Kaliszky , S. 1996 . Elasto-Plastic Analysis with Limited Plastic Deformations and Displacements . Mech. Struct. Mach. , 24 ( 1 ) : 39 – 50 .
   Web of Science ®Google Scholar
• Dorosz , S. 1978 . An Improved Upperbound to Maximum Deflections of Elasto-Plastic Structures at Shakedown . J. Struct. Mech. , 6 : 267 – 287 .
   Web of Science ®Google Scholar
• Capurso , M. 1974 . Displacement Bounding Principle in Dynamic Shakedown of Structures Subjected to Cyclic Loads . Int. J. Solids Struct. , 10 : 77 – 92 .
   Google Scholar
• Capurso , M. 1979 . Some Upper Bound Principles for Plastic Strains in Dynamic Shakedown of Elastoplastic Structures . J. Struct. Mech. , 7 : 1 – 20 .
   Google Scholar
• Maier , G. and Vitello , E. 1974 . Bounds on Plastic Strains and Displacements in Dynamic Shakedown of Workhardening Structures . J. Appl. Mech. , 41 : 443 – 440 .
   Google Scholar
• Polizzotto , C. 1986 . A Convergent Bounding Principle for a Class of Elasto-Plastic Strain-Hardening Solids . Int. J. Plasticity , 2 : 359 – 370 .
   Google Scholar
• Kaliszky , S. and Lógó , J. 1997 . Optimal Plastic Limit and Shakedown Design of Bar Structures with Constraints on Plastic Deformation . Eng. Struct. , 19 ( 1 ) : 19 – 27 .
   Google Scholar
• Lange-Hansen , P. 1988 . Comparative Study of Upper Bound Methods for the Calculation of Residual Deformation After Shakedown , Series R, No. 49 Department of Structural Engineering and Materials. Technical University of Denmark .
   Google Scholar
• Tin-Loi , F. 2000 . Optimum Shakedown Design Under Residual Displacement Constraints . Struct. Multidisc. Optim. , 19 : 130 – 139 .
   Web of Science ®Google Scholar
• Ohkubo , S. and Makino , K. 1992 . Nonlinear Stress and Displacement Analysis of Rigid Frames by Total Energy Minimization . Comp. Struct. , 44 : 193 – 206 .
   Google Scholar
• Lógó , J. 1988 . “ Design of Bar Structures by Multicriterion Optimization ” . In University doctoral thesis Budapest : Technical University of Budapest .
   Google Scholar
• Kaliszky , S. and Lógó , J. 2000 . Plastic Constraints in the Shakedown Analysis and Optimal Design of Bar Structures . Sept 11–14 2000 , Barcelona, Spain. Proceedings of ECCOMAS 2000, European Congress on Computational Methods in Applied Sciences and Engineering , pp. 164
   Google Scholar
• Kaliszky , S. and Lógó , J. 1998 . Discrete Optimal Design of Elasto-Plastic Trusses Using Compliance and Stability Constraints . Struct. Optim. , 15 ( 2–3 ) : 261 – 268 .
   Google Scholar
• König , J.A. and Maier , G. 1981 . Shakedown Analysis of Elastoplastic Structures: Review of Recent Developments . Nucl. Eng. Desi. , 66 : 81 – 95 .
   Web of Science ®Google Scholar
• Maute , K. , Swartz , S. and Ramm , E. 1998 . Adaptive Topology Optimization of Elastoplastic Structures . Struct. Optim. , 15 : 81 – 91 .
   Google Scholar
• Rozvany , G. I. N. , Bendsoe , M. P. and Kirsch , U. 1995 . Layout Optimization of Structures . Appl. Mech. Rev. , 48 : 41 – 119 .
   Google Scholar