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Optimal design of responsive structures

Akerson, Andrew and Bourdin, Blaise and Bhattacharya, Kaushik (2022) Optimal design of responsive structures. Structural and Multidisciplinary Optimization, 65 (4). Art. No. 111. ISSN 1615-147X. doi:10.1007/s00158-022-03200-5.

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With recent advances in both responsive materials and fabrication techniques, it is now possible to construct integrated functional structures, composed of both structural and active materials. We investigate the robust design of such structures through topology optimization. By applying a typical interpolation scheme and filtering technique, we prove existence of an optimal design to a class of objective functions which depend on the compliances of the stimulated and unstimulated states. In particular, we consider the actuation work and the blocking load as objectives, both of which may be written in terms of compliances. We study numerical results for the design of a 2D rectangular lifting actuator for both of these objectives, and discuss some intuition behind the features of the converged designs. We formulate the optimal design of these integrated responsive structures with the introduction of voids or holes in the domain, and show that our existence result holds in this setting. We again consider the design of the 2D lifting actuator now with voids. Finally, we investigate the optimal design of an integrated 3D torsional actuator for maximum blocking torque.

Item Type:Article
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URLURL TypeDescription ReadCube access Paper ItemCode
Akerson, Andrew0000-0002-4382-1226
Bourdin, Blaise0000-0002-1312-9175
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Received 06 December 2021; Revised 06 February 2022; Accepted 11 February 2022; Published 10 March 2022. We are grateful for the financial support of the U.S. National Science Foundation through “Collaborative Research: Optimal Design of Responsive Materials and Structures” (DMS:2009289 at Caltech and DMS:2009303 at LSU and McMaster University). Part of this work was performed while BB was the A.K. & Shirley Barton Professor of Mathematics at Louisiana State University (USA). The authors have no financial or personal relationship with a third party whose interests could be positively or negatively influenced by the article’s content. Replication of results: The authors are willing to share the code on request. The data for the figures are available through GitHub (
Funding AgencyGrant Number
Louisiana State UniversityUNSPECIFIED
Subject Keywords:Responsive materials; Shape-memory alloys; Liquid crystal elastomers; Topology optimization; Sensitivity
Issue or Number:4
Record Number:CaltechAUTHORS:20210831-203942317
Persistent URL:
Official Citation:Akerson, A., Bourdin, B. & Bhattacharya, K. Optimal design of responsive structures. Struct Multidisc Optim 65, 111 (2022).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110658
Deposited By: George Porter
Deposited On:01 Sep 2021 14:20
Last Modified:04 Apr 2022 23:23

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