Buckling-resistant topological design using sensitivities to variations in localised nominal stiffness. (October 2021)

• Record Type: Journal Article
• Authors: Minera, S.; Patni, M.; Pirrera, A.; Weaver, P.M.
• Is Part Of: Thin-walled structures. Volume 167(2021)
• Publication Date: 2021-10
• Subjects: Localised Nominal Stiffness method -- Sensitivity analysis -- Linear buckling -- Unified Formulation -- Cut-out design -- Structural efficiency; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2021.108150
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: Thin-walled structures are extensively used in aerospace, automotive and mechanical engineering applications due to their high strength- and stiffness-to-weight ratios. However, the performance of these structures tends to be heavily influenced by localised features such as manufacturing defects or design details included for non-structural reasons, e.g. inspection cut-outs. Understanding the sensitivity of structural performance to these nominal stiffness variations, and especially their spatial distribution through the volume of the structure, is important to the designer. We propose a new methodology, the Localised Nominal Stiffness method, to quantify the sensitivity of buckling performance to the distribution of nominal stiffness variations across the structure. The underpinning idea involves reducing the stiffness in small localised regions of the structure and quantifying the ensuing variation in linear buckling capacity before returning the stiffness to its original value. The process is repeated for all locations ensuring coverage of the entire structural domain, which leads to a sensitivity map. In practice, each location corresponds to an element in a finite element mesh. Focusing on structures subject to buckling constraints, and with the aim of using highly efficient structural analysis, we identify sensitivities using the hierarchical Unified Formulation. The resulting sensitivity contour maps can be used to identify regions of the structure where defects or removal of material (for lightweighting) would not significantly affect buckling and post-buckling performance. The effectiveness of the method is tested through three examples: a simply-supported plate; a simply-supported, thin-walled box-section column; and a thin shell with simply-supported and clamped boundary conditions. In all cases, the buckling performance of structures can be maintained with reduced structural weight. Highlights: A novel localised nominal stiffness method is proposed. Improved structural efficiency of thin-walled structures in buckling. Unified Formulation framework to improve the computational performance.