TY - JOUR
T1 - A maximum filter for the ground structure method
T2 - An optimization tool to harness multiple structural designs
AU - Sanders, Emily D.
AU - Ramos, Adeildo S.
AU - Paulino, Glaucio H.
N1 - Funding Information:
The authors acknowledge support provided by the National Science Foundation (NSF) project CMMI 1559594 (formerly 1335160). We also acknowledge support from the Raymond Allen Jones endowment at Georgia Institute of Technology. Additionally, the authors would like to thank Dr. Tomas Zegard for the Lotte Tower ground structure generation and 3D truss plotting routines, which were borrowed from reference [12] . We are grateful to Bill Baker and Dr. Tomas Zegard of Skidmore, Owings & Merrill for insights provided on the first example in the manuscript. The information presented in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agencies. Appendix A
Publisher Copyright:
© 2017
PY - 2017/11/15
Y1 - 2017/11/15
N2 - The ground structure method seeks to approximate Michell optimal solutions for real-world design problems requiring truss solutions. The single solution extracted from the ground structure is typically too complex to realize directly in practice and is instead used to inform designer intuition about how the structure behaves. Additionally, a post-processing step required to filter out unnecessary truss members in the final design often leads to structures that no longer satisfy global equilibrium. Here, a maximum filter is proposed that, in addition to guaranteeing structures that satisfy global equilibrium, leads to several design perspectives for a single problem and allows for increased user control over the complexity of the final design. Rather than applying a static filter in each optimization iteration, the maximum filter employs an interval reducing method (e.g., bisection)to find the maximum allowable filter value that can be imposed in a given optimization iteration such that the design space is reduced while preserving global equilibrium and limiting local increases in the objective function. Minimization of potential energy with Tikhonov regularization is adopted to solve the singular system of equilibrium equations resulting from the filtered designs. In addition to reducing the order of the state problem, the maximum filter reduces the order of the optimization problem to increase computational efficiency. Numerical examples are presented to demonstrate the capabilities of the maximum filter, including a problem with multiple load cases, and its use as an end-filter in the traditional plastic and nested elastic approaches of the ground structure method.
AB - The ground structure method seeks to approximate Michell optimal solutions for real-world design problems requiring truss solutions. The single solution extracted from the ground structure is typically too complex to realize directly in practice and is instead used to inform designer intuition about how the structure behaves. Additionally, a post-processing step required to filter out unnecessary truss members in the final design often leads to structures that no longer satisfy global equilibrium. Here, a maximum filter is proposed that, in addition to guaranteeing structures that satisfy global equilibrium, leads to several design perspectives for a single problem and allows for increased user control over the complexity of the final design. Rather than applying a static filter in each optimization iteration, the maximum filter employs an interval reducing method (e.g., bisection)to find the maximum allowable filter value that can be imposed in a given optimization iteration such that the design space is reduced while preserving global equilibrium and limiting local increases in the objective function. Minimization of potential energy with Tikhonov regularization is adopted to solve the singular system of equilibrium equations resulting from the filtered designs. In addition to reducing the order of the state problem, the maximum filter reduces the order of the optimization problem to increase computational efficiency. Numerical examples are presented to demonstrate the capabilities of the maximum filter, including a problem with multiple load cases, and its use as an end-filter in the traditional plastic and nested elastic approaches of the ground structure method.
KW - Filtering
KW - Max filter
KW - Nested elastic formulation
KW - Plastic formulation
KW - Reduced order model
KW - Tikhonov regularization
KW - Topology optimization of trusses
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U2 - 10.1016/j.engstruct.2017.07.064
DO - 10.1016/j.engstruct.2017.07.064
M3 - Article
AN - SCOPUS:85028057792
SN - 0141-0296
VL - 151
SP - 235
EP - 252
JO - Engineering Structures
JF - Engineering Structures
ER -