Coupled topology and shape optimization using an embedding domain discretization method - Stankiewicz, Gabriel; Dev, Chaitanya; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2021)
Density-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.
CRIS-Team Scopus Importer:2021-08-27
Keywords: Coupled topology and shape optimization; Embedding domain discretization; Structural optimization

Geometrically nonlinear design of compliant mechanisms: Topology and shape optimization with stress and curvature constraints - Stankiewicz, Gabriel; Dev, Chaitanya; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2022)
In this work, we exploit a sequential topology and shape optimization framework to design compliant mechanisms. We pay particular attention to a refined and exact design of flexure hinges via shape optimization in a geometrically nonlinear setting. We propose improved adaptive shape and domain refinement strategies for the embedding domain discretization method (EDD) to achieve numerically and geometrically accurate designs of the flexure hinges. Furthermore, to account for durability and manufacturability of the flexure hinges, we employed local stress constraints and a curvature constraint. The local stress constraints are integrated into an augmented Lagrange functional together with the output displacement to form a combined objective response. The design update is realized by employing and adapting the traction method for the specifics of the embedded boundary. Hence, the curvature constraint does not appear in a standard response form, but is rather introduced into the auxiliary boundary value problem (BVP) of the traction method via a penalty functional. The novelties of this work include: (1) enhanced adaptive shape and domain refinement strategies for EDD; (2) geometrically nonlinear shape optimization using EDD; (3) adapted traction method with curvature constraint.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
CRIS-Team WoS Importer:2022-07-15

On the influence of free space in topology optimization of electro-active polymers - Dev, Chaitanya; Stankiewicz, Gabriel; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2023)
This study investigates the impact of the surrounding free space on the topology optimization (TO) of electro-active polymers (EAPs). It is well understood that, under the application of an electric field, the deformation of an EAP is not solely determined by the field distribution within the body, but also by the distribution in the free space surrounding it. This is particularly true for electronic EAP, which are emerging as leading candidates for developing artificial muscles. Our study specifically focuses on understanding the influence of the free space in the context of density-based TO. We model the free space as an extended void region around the design domain. Our numerical experiments focus on EAP actuators and take into account their geometrical nonlinear behavior. The results show that incorporating the surrounding free space has a significant impact on the performance of the optimized EAPs with low electric permittivity. This makes it essential to consider in real-world applications.
CRIS-Team Scopus Importer:2023-08-18
Keywords: Electro-active polymers; Free space; Topology optimization

Sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints - Dev, Chaitanya; Stankiewicz, Gabriel; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2022)
We present a sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints. In our approach, a density-based topology optimization method is used to generate the configuration of the mechanisms. Afterwards, a node-based shape optimization is invoked to obtain an exact boundary representation. A specialized, optimality criteria-based design update is formulated for the shape optimization. To avoid impractical hinges with point connections, stress constraints are imposed. The stress constraints are imposed using two strategies: Local stress constraints on the nodes of the boundary or global P-norm stress constraints in the domain. Further, an adaptive shape refinement strategy is adopted to increase the design space of shape optimization and to capture the fine-scale details of the geometry. Finally, numerical experiments are presented, showing that the proposed approach can be effectively applied to the design of compliant mechanisms with stress constraints.
CRIS-Team WoS Importer:2022-06-24

Towards advanced piezoelectric metamaterial design via combined topology and shape optimization - Stankiewicz, Gabriel; Dev, Chaitanya; Weichelt, Michelle; Fey, Tobias; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2024)
Metamaterials open up a spectrum of artificially engineered properties otherwise unreachable in conventional bulk materials. For electromechanical energy conversion systems, lightweight materials with high hydrostatic piezoelectric coupling coefficients and negative Poisson’s ratio can be obtained. Thus, in this contribution, we explore the possibilities of piezoelectric metamaterials design by employing structural optimization. More specifically, we apply a sequential framework of topology and shape optimization to design piezoelectric metamaterials with negative Poisson’s ratio for electromechanical energy conversion under uniform pressure. Topology optimization is employed to generate the initial layout, whereas shape optimization fine tunes the design and improves durability and manufacturability of the structures with the help of a curvature constraint. An embedding domain discretization (EDD) method with adaptive domain and shape refinement is utilized for an efficient and accurate computation of the state problem in the shape optimization stage. Multiple case studies are conducted to determine the importance of desired stiffness characteristics, symmetry conditions and objective formulations on the design of piezoelectric metamaterials. Results show that the obtained designs are highly dependent on the desired stiffness characteristics. Moreover, the addition of the EDD-based shape optimization step introduces significant changes to the designs, confirming the usability of the sequential framework.
CRIS-Team Scopus Importer:2024-03-01
Keywords: Cellular materials; Manufacturing constraints; Microstructure design; Piezoelectric metamaterials; Shape optimization; Topology optimization