TY - JOUR
T1 - Topology optimization with local stress constraints
T2 - a stress aggregation-free approach
AU - Senhora, Fernando V.
AU - Giraldo-Londoño, Oliver
AU - Menezes, Ivan F.M.
AU - Paulino, Glaucio H.
N1 - Funding Information:
F.V.S., O.G.-L., and G.H.P. acknowledge the financial support from the US National Science Foundation under grant #1663244 and the endowment provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology. F.V.S. and I.F.M.M. acknowledge the support provided by Brazilian agencies CNPQ and FAPERJ, and Tecgraf/PUC-Rio (Group of Technology in Computer Graphics), Rio de Janeiro, Brazil. Acknowledgments
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - This paper presents a consistent topology optimization formulation for mass minimization with local stress constraints by means of the augmented Lagrangian method. To solve problems with a large number of constraints in an effective way, we modify both the penalty and objective function terms of the augmented Lagrangian function. The modification of the penalty term leads to consistent solutions under mesh refinement and that of the objective function term drives the mass minimization towards black and white solutions. In addition, we introduce a piecewise vanishing constraint, which leads to results that outperform those obtained using relaxed stress constraints. Although maintaining the local nature of stress requires a large number of stress constraints, the formulation presented here requires only one adjoint vector, which results in an efficient sensitivity evaluation. Several 2D and 3D topology optimization problems, each with a large number of local stress constraints, are provided.
AB - This paper presents a consistent topology optimization formulation for mass minimization with local stress constraints by means of the augmented Lagrangian method. To solve problems with a large number of constraints in an effective way, we modify both the penalty and objective function terms of the augmented Lagrangian function. The modification of the penalty term leads to consistent solutions under mesh refinement and that of the objective function term drives the mass minimization towards black and white solutions. In addition, we introduce a piecewise vanishing constraint, which leads to results that outperform those obtained using relaxed stress constraints. Although maintaining the local nature of stress requires a large number of stress constraints, the formulation presented here requires only one adjoint vector, which results in an efficient sensitivity evaluation. Several 2D and 3D topology optimization problems, each with a large number of local stress constraints, are provided.
KW - Aggregation-free
KW - Augmented Lagrangian
KW - Consistent topology optimization
KW - Stress constraints
KW - Stress relaxation
KW - von Mises stress
UR - http://www.scopus.com/inward/record.url?scp=85089680362&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85089680362&partnerID=8YFLogxK
U2 - 10.1007/s00158-020-02573-9
DO - 10.1007/s00158-020-02573-9
M3 - Article
AN - SCOPUS:85089680362
SN - 1615-147X
VL - 62
SP - 1639
EP - 1668
JO - Structural Optimization
JF - Structural Optimization
IS - 4
ER -