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Rigid plastic model of incremental sheet deformation using second‐order cone programming
Author(s) -
Raithatha A.,
Duncan S. R.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2512
Subject(s) - second order cone programming , finite element method , upper and lower bounds , shell (structure) , cone (formal languages) , limit analysis , software , deformation (meteorology) , limit (mathematics) , mathematics , computer science , structural engineering , algorithm , mathematical optimization , geometry , mathematical analysis , engineering , materials science , mechanical engineering , composite material , regular polygon , convex optimization , programming language
This paper describes a method for numerically modelling the incremental plastic deformation of shells and applies the method to incremental sheet forming (ISF). An upper bound finite element shell model is developed based on sequential limit analysis under the rigid plastic assumption, which is solved by manipulating the problem into the form of a second‐order cone program (SOCP). Initially, the static upper bound plate problem is investigated and the results are compared with the existing literature. The approach is then extended to a shell formulation using a linearized form of the Ilyushin yield condition and two methods for treating the Ilyushin condition are presented. The model is solved efficiently using SOCP software. The resulting model shows good geometric agreement when validated against an elasto‐plastic model produced using existing commercial software and with measurements from a real product produced using ISF. Copyright © 2008 John Wiley & Sons, Ltd.