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Model reduction and process control of thermomechanical behaviour of non‐linear material deformation
Author(s) -
Grandhi Ramana V.,
Thiagarajan Ramesh
Publication year - 1994
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.1620371808
Subject(s) - reduction (mathematics) , finite element method , subspace topology , viscoplasticity , process (computing) , control theory (sociology) , deformation (meteorology) , mechanical engineering , engineering , structural engineering , computer science , materials science , mathematics , mathematical analysis , geometry , control (management) , composite material , constitutive equation , artificial intelligence , operating system
This paper describes a design procedure for metal forming processes by using the controllable subspace of the full system. The velocity profile of the moving die is designed using the reduced order system. The metal forming processes are simulated using non‐linear finite element methods based on the rigid viscoplastic flow formulation. The balanced model reduction technique is applied to reduce the full state space model to a reduced order model that retains the controllable subspace of the thermomechanical system. The linear quadratic regulator theory with output tracking is used as an off‐line design tool to design the die velocity schedule. The process design is carried out to maintain the strain rate of the critical portion of the billet at a desired value. The procedure for designing the process parameters is demonstrated using two case studies.