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Geometry and topology optimization of sheet metal profiles by using a branch‐and‐bound framework
Author(s) -
Horn B. M.,
Lüthen H.,
Pfetsch M. E.,
Ulbrich S.
Publication year - 2017
Publication title -
materialwissenschaft und werkstofftechnik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.285
H-Index - 38
eISSN - 1521-4052
pISSN - 0933-5137
DOI - 10.1002/mawe.201600762
Subject(s) - topology optimization , topology (electrical circuits) , design for manufacturability , finite element method , relaxation (psychology) , mathematical optimization , shape optimization , mathematics , subdivision , optimal design , lagrangian relaxation , geometry , structural engineering , engineering , mechanical engineering , combinatorics , psychology , social psychology , statistics , civil engineering
In this paper well established procedures from partial differential equation (PDE)‐constrained and discrete optimization are combined in a new way to find an optimal design of a multi‐chambered profile. Given a starting profile design, a load case and corresponding design constraints (e.g. sheet thickness, chamber sizes), the aim is to find an optimal subdivision into a predefined number of chambers with optimal shape subject to structural stiffness. In the presented optimization scheme a branch‐and‐bound tree is generated with one additional chamber in each level. Before adding the next chamber, the geometry of the profile is optimized. Then a relaxation of a topology optimization problem is solved. Based on this relaxation, a best fitting feasible topology subject to manufacturability conditions is determined using a new mixed integer method employing shortest paths. To improve the running time, the finite element simulations for the geometry optimization and topology relaxation are performed with different levels of accuracy. Finally, numerical experiments are presented including different starting geometries, load scenarios and mesh sizes.