Topological-derivative-based design of stiff fiber-reinforced structures with optimally oriented continuous fibers

Desai, A and Mogra, M and Sridhara, S and Kumar, K and Sesha, G and Ananthasuresh, GK (2020) Topological-derivative-based design of stiff fiber-reinforced structures with optimally oriented continuous fibers. In: Structural and Multidisciplinary Optimization . (In Press)

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Abstract

We use topological derivatives to obtain fiber-reinforced structural designs with non-periodic continuous fibers optimally arranged in specific patterns. The distribution of anisotropic fiber material within isotropic matrix material is determined for given volume fractions of void and material as well as fiber and matrix simultaneously, for maximum stiffness. In this three-phase material distribution approach, we generate a Pareto surface of stiffness and two volume fractions by adjusting the level-set plane in the topological sensitivity field. For this, we utilize topological derivatives for interchanging (i) isotropic material and void; (ii) fiber material and void; and (iii) isotropic and fiber materials, during iterative optimization. While the isotropic topological derivative is well known, the latter two required modification of the anisotropic topological derivative. Furthermore, we used the polar form of the topological derivative to determine the optimal orientation of the fiber at every point. Thus, in the discretized finite element model, we get element-wise optimal fiber orientation in the portions where fiber is present. Using these discrete sets of orientations, we extract continuous fibers as streamlines of the vector field. We show that continuous fibers are aligned with the principal stress directions as first reported by Pedersen. Three categories of examples are presented: (i) embedding fiber everywhere in the isotropic matrix without voids; (ii) selectively embedding fiber for a given volume fraction of the fiber without voids; and (iii) including voids for given volume fractions of fiber and matrix materials. We also present an example with multiple load cases. Additionally, in view of practical implementation of laying up or 3D-printing of fibers within the matrix material, we simplify the dense arrangement of fibers by evenly spacing them while retaining their specific patterns. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

Item Type:	Journal Article
Publication:	Structural and Multidisciplinary Optimization
Publisher:	Springer Science and Business Media Deutschland GmbH
Additional Information:	copyright for this article belongs to Springer Science and Business Media Deutschland GmbH
Keywords:	3D printers; Anisotropy; Embeddings; Pareto principle; Reinforced plastics; Stiffness; Stiffness matrix; Structural design; Topology; Void fraction; Volume fraction, Anisotropic fiber; Continuous fibers; Isotropic materials; Iterative Optimization; Multiple load case; Optimal orientation; Topological derivatives; Topological sensitivity, Fibers
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	04 Nov 2020 11:01
Last Modified:	04 Nov 2020 11:01
URI:	http://eprints.iisc.ac.in/id/eprint/67014

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