TY - JOUR
T1 - Multi-material topology optimization with multiple volume constraints
T2 - a general approach applied to ground structures with material nonlinearity
AU - Zhang, Xiaojia Shelly
AU - Paulino, Glaucio H.
AU - Ramos, Adeildo S.
N1 - Funding Information:
Acknowledgements The authors acknowledge the financial support from the US National Science Foundation (NSF) under projects #1559594 (formerly #1335160) and #1321661, from the Brazilian agency CNPq (National Council for Research and Development), and from the Laboratory of Scientific Computing and Visualization (LCCV) at the Federal University of Alagoas (UFAL). We are also grateful for the endowment provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology. The information provided in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agencies.
Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - Multi-material topology optimization is a practical tool that allows for improved structural designs. However, most studies are presented in the context of continuum topology optimization – few studies focus on truss topology optimization. Moreover, most work in this field has been restricted to linear material behavior with limited volume constraint settings for multiple materials. To address these issues, we propose an efficient multi-material topology optimization formulation considering material nonlinearity. The proposed formulation handles an arbitrary number of candidate materials with flexible material properties, features freely specified material layers, and includes a generalized volume constraint setting. To efficiently handle such arbitrary volume constraints, we derive a design update scheme that performs robust updates of the design variables associated with each volume constraint independently. The derivation is based on the separable feature of the dual problem of the convex approximated primal subproblem with respect to the Lagrange multipliers, and thus the update of design variables in each volume constraint only depends on the corresponding Lagrange multiplier. Through examples in 2D and 3D, using combinations of Ogden-based, bilinear, and linear materials, we demonstrate that the proposed multi-material topology optimization framework with the presented update scheme leads to a design tool that not only finds the optimal topology but also selects the proper type and amount of material. The design update scheme is named ZPR (phonetically, zipper), after the initials of the authors’ last names (Zhang-Paulino-Ramos Jr.).
AB - Multi-material topology optimization is a practical tool that allows for improved structural designs. However, most studies are presented in the context of continuum topology optimization – few studies focus on truss topology optimization. Moreover, most work in this field has been restricted to linear material behavior with limited volume constraint settings for multiple materials. To address these issues, we propose an efficient multi-material topology optimization formulation considering material nonlinearity. The proposed formulation handles an arbitrary number of candidate materials with flexible material properties, features freely specified material layers, and includes a generalized volume constraint setting. To efficiently handle such arbitrary volume constraints, we derive a design update scheme that performs robust updates of the design variables associated with each volume constraint independently. The derivation is based on the separable feature of the dual problem of the convex approximated primal subproblem with respect to the Lagrange multipliers, and thus the update of design variables in each volume constraint only depends on the corresponding Lagrange multiplier. Through examples in 2D and 3D, using combinations of Ogden-based, bilinear, and linear materials, we demonstrate that the proposed multi-material topology optimization framework with the presented update scheme leads to a design tool that not only finds the optimal topology but also selects the proper type and amount of material. The design update scheme is named ZPR (phonetically, zipper), after the initials of the authors’ last names (Zhang-Paulino-Ramos Jr.).
KW - Design update scheme
KW - Discrete filter
KW - Ground structure method
KW - KKT conditions
KW - Material nonlinearity
KW - Multi-material topology optimization
KW - Multiple load cases
KW - Multiple volume constraints
KW - Potential energy
KW - ZPR update scheme
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U2 - 10.1007/s00158-017-1768-3
DO - 10.1007/s00158-017-1768-3
M3 - Article
AN - SCOPUS:85028885399
SN - 1615-147X
VL - 57
SP - 161
EP - 182
JO - Structural and Multidisciplinary Optimization
JF - Structural and Multidisciplinary Optimization
IS - 1
ER -