Abstract
This paper presents a direct substructuring
method to reduce the computing time of implicit
simulations of single point incremental forming
(SPIF). Substructuring is used to divide the finite element
(FE) mesh into several non-overlapping parts.
Based on the hypothesis that plastic deformation is
localized, the substructures are categorized into two
groups: the plastic—nonlinear—substructures and the
elastic—pseudo-linear—substructures. The plastic substructures
assemble a part of the FE mesh that is in
contact with the forming tool; they are iteratively updated
respecting all nonlinearities. The elastic substructures
model the elastic deformation of the rest of the
FE mesh. For these substructures, the geometrical and
the material behaviour are assumed linear within the
increment. The stiffness matrices and the internal force
vectors are calculated at the beginning of each increment
then they are statically condensed to eliminate
the internal degrees of freedom (DOF). In the iteration
process the condensed stiffness matrices for the elastic
substructures are kept constant. The condensed internal
force vectors are updated by the multiplication of
the condensed stiffness matrices and the displacement
increments. After convergence, any geometrical and material nonlinearity for the elastic substructures are
nonlinearly updated. The categorization of substructures
in plastic and elastic domains is adapted during
the simulation to capture the tool motion. The resulting,
plastic and condensed elastic, set of equations is
solved on a single processor. In an example with 1600
shell elements, the presented substructuring of the SPIF
implicit simulation is 2.4 times faster than the classical
implicit simulation.
Original language | Undefined |
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Pages (from-to) | 181-189 |
Journal | International journal of material forming |
Volume | 2 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2009 |
Keywords
- METIS-262657
- IR-69339