We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Topological-derivative-based design of stiff fiber-reinforced structures with optimally oriented continuous fibers.
- Authors
Desai, Akshay; Mogra, Mihir; Sridhara, Saketh; Kumar, Kiran; Sesha, Gundavarapu; Ananthasuresh, G. K.
- 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.
- Subjects
TOPOLOGICAL derivatives; FIBER orientation; STIFFNESS (Engineering); FIBERS; TOPOLOGICAL fields; VECTOR fields
- Publication
Structural & Multidisciplinary Optimization, 2021, Vol 63, Issue 2, p703
- ISSN
1615-147X
- Publication type
Article
- DOI
10.1007/s00158-020-02721-1