文档介绍：Computers and Structures 78 (2000) 133±148
pstruc
Recent developments on the analysis and optimum design of
sheet metal forming parts using a simpli®ed inverse approach
. Guo, . Batoz *, H. Naceur, S. Bouabdallah, F. Mercier, O. Barlet
Labo. LG2mS/UPRESA 6066 RS, Departement GSM, Universite de Technologie piegne, . 20529, piegne
Cedex, France
Received 30 November 1998; accepted 17 July 1999
Abstract
A simpli®ed ecient ®nite element method called the inverse approach (IA) has been developed to estimate the large
elasto-plastic strains in thin metallic panels obtained by deep drawing. This paper deals with the main recent devel-
opments introduced by the authors on the IA to improve its eciency in the analysis and optimum design of blank
contours plicated industrial parts. The IA mainly exploits the knowledge of the 3D shape of the ®nal workpiece.
An iterative scheme is used to ®nd the original position of each material point in the initial ¯at blank after which it is
possible to estimate the strains and stresses in the ®nal workpiece. Important assumptions are adopted regarding the
constitutive equations (the deformation theory of plasticity) and the action of the tools (the punch, die and blank
holders). The IA implies only two degrees of freedom per node even if bending eects are considered. In this paper, we
present several recent developments: (1) The bending eects are taken into account using a simple triangular shell el-
ement without increasing the number of dof per node. (2) Some analytical formulas are introduced to consider the
restraining forces due to the drawbeads. (3) Some improvements of resolution algorithms such as the introduction of a
relaxation coecient, a damping factor and a good initial solution are realized. (4) Shape optimization of blank
contours is performed using a numerical procedure based on the coupling of the IA and a sequential quadratic pro-
gramming method (SQP). In this work, all sensi