Optimal orientation of fibre composites for strength based on Hashin’s criteria optimality conditions

Ferreira, Rafael T.L.; Ashcroft, Ian A.

Abstract

© 2020, The Author(s). The Hashin’s strength criteria are usually employed in first ply failure and damage-onset analysis of fibre-reinforced composites. This work presents optimality conditions of local material orientations for these criteria, in terms of principal stresses and material strength parameters. Each criterion (matrix tensile/compressive, fibre tensile/compressive modes) has its conditions separately derived, analytically, based on a fixed stress field assumption. The conditions found show that orientations which coincide and do not coincide with principal stress directions may minimise local failure indices. These solutions are employed in a proposed algorithm, named HA-OCM (Hashin Optimality Criteria Method), which selectively satisfies the matrix failure modes (either tensile or compressive), iteratively and finite element-wise in composites. It is demonstrated that the HA-OCM is able to design single-layer plane structures with improved failure loads in comparison with designs following only maximum (in absolute) principal stress orientations. Results show that the material orientations have a trend to end up either aligned or at 90° with maximum in absolute principal stress directions. Global optima for compliance are, however, not guaranteed. To give an idea of gains in terms of failure loads, some HA-OCM designs show improvements of 71% and 140%, for example, in comparison with principal stress design.

Citation

Ferreira, R. T., & Ashcroft, I. A. (2020). Optimal orientation of fibre composites for strength based on Hashin’s criteria optimality conditions. Structural and Multidisciplinary Optimization, 61, 2155–2176. https://doi.org/10.1007/s00158-019-02462-w

• Journal Article Type: Article
• Acceptance Date: Nov 20, 2019
• Online Publication Date: Feb 19, 2020
• Publication Date: 2020-05
• Deposit Date: Nov 29, 2019
• Publicly Available Date: Feb 20, 2021
• Journal: Structural and Multidisciplinary Optimization
• Print ISSN: 1615-147X
• Electronic ISSN: 1615-1488
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 61
• Pages: 2155–2176
• DOI: https://doi.org/10.1007/s00158-019-02462-w
• Keywords: Control and Systems Engineering; Software; Control and Optimization; Computer Graphics and Computer-Aided Design; Computer Science Applications
• Public URL: https://nottingham-repository.worktribe.com/output/3444267
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00158-019-02462-w
• Additional Information: Received: 11 July 2019; Revised: 16 October 2019; Accepted: 20 November 2019; First Online: 19 February 2020; : ; : The authors declare that they have no conflict of interest.