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Application of upper bound method to the powder‐forging of cup‐shaped axisymmetric preforms for estimating punch load
Author(s) -
Cho J. R.,
Jeong H. S.
Publication year - 2001
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.158
Subject(s) - rotational symmetry , forging , discretization , finite element method , upper and lower bounds , die (integrated circuit) , domain (mathematical analysis) , structural engineering , process (computing) , mathematics , engineering , mechanical engineering , computer science , geometry , mathematical analysis , operating system
This paper is concerned with the analytic derivation of the punch load required to forge cup‐shaped axisymmetric porous preforms. Splitting the two‐dimensional preform domain into three rectangular regions, we assumed the kinematically admissible velocity fields to apply the upper bound method. According to the resulting formulas, we developed an incremental numerical algorithm for computing time‐discretized step‐wise punch loads and preform volumes. In order to illustrate the validity of the proposed estimate, we compared the numerical results obtained by the present analysis with those by the finite element simulation. From the comparison made through different preform dimensions, we observed that the present analysis expects the reliable upper bounds of process step‐wise punch loads. Copyright © 2001 John Wiley & Sons, Ltd.