aerospace structures Olivia Leo Supervisors: Alberto Pirrera and - PowerPoint PPT Presentation

Modal nudging of aerospace structures Olivia Leão Supervisors: Alberto Pirrera and Rainer Groh Spo Sponsored by 8 th CDT Conference 16 th April 2019

2 Outline • Nonlinearities in design process • Modal nudging • Concept • Stiffened structure example • Limitations • Current/future work • Summary Modal nudging of aerospace structures

3 Well-behaved nonlinear structures [1] • Instabilities ≠ str tructural l failu ilure • Large deformations in material linear elastic range: No Novel l fu functionali lity and lig lighter structures • Well-behaved nonlinearities can be rob obustly controlle led [2] Im Improved str tructural efficiency th through th the in incorporation of f well ll-behaved nonlinearities in in th the design process [1] shellbuckling.com [2] wikipedia.org/wiki/Boeing_Truss-Braced_Wing Modal nudging of aerospace structures

4 Modal nudging [3] No Nonlin linear resp sponse tail ailorin ing method base ased on on pos ost-bucklin ling in information Original Small change Improved structural response: Nonlinear structure in geometry Load-carrying capacity post-buckling Stiffness/compliance response information Sensitivity to imperfections Nonlinear FE Insignificant [4] + change in Numerical continuation mass solver [3] B.S. Cox et al./ J Mech Phys Solids 116 (2017) 135 – 49. [4] R.M.J. Groh et al./ Comput. Methods Appl. Mech. Engrg. 331 (2018) 394 – 426. Modal nudging of aerospace structures

5 Steps and results 1. 1. Id Identify is isolated stable region of f in interest. Higher load-carrying solution Extract deformation mode 𝐯 state . 2. Unstable gap on Superpose to initial geometry 𝐲 𝟏 . 3. original path Region of interest Restart analysis using nudged geometry 𝐲 . 4. (physically unattainable) If necessary, increase nudging factor 𝜃 . Repeat from 3. 5. Buckling Natural physical response Stable orig. path Clamped edge Unstable orig. path 𝑨 Critical point Natural path Clamped edge 𝑦 𝑣 𝑧 Original structure Modal nudging of aerospace structures

6 Steps and results 1. Identify isolated stable region of interest. xtract deformation mode 𝐯 𝐭𝐮𝐛𝐮𝐟 . Higher load-carrying solution 2. Ext 2. Superpose to initial geometry 𝐲 𝟏 . 3. Region of interest Restart analysis using nudged geometry 𝐲 . 4. If necessary, increase nudging factor 𝜃 . Repeat from 3. 5. Stable orig. path Unstable orig. path 𝐯 state Critical point (Scaled up for clarity) Modal nudging of aerospace structures

7 Steps and results 1. Identify isolated stable region of interest. Higher load-carrying solution Extract deformation mode 𝐯 state . 2. initial geometry 𝐲 𝟏 . 3. 3. Superpose to in Region of interest Restart analysis using nudged geometry 𝐲 . 4. If necessary, increase nudging factor 𝜃 . Repeat from 3. 5. 𝐯 state (Scaled up for clarity) 𝐲 = 𝐲 0 + 𝜃ഥ 𝐯 state Stable orig. path 𝜃 : nudging factor Unstable orig. path 𝜃~ thickness Critical point 𝐯 state : normalised 𝐯 state ഥ Modal nudging of aerospace structures

8 Steps and results 1. Identify isolated stable region of interest. Higher load-carrying solution Extract deformation mode 𝐯 state . 2. Nudged load-carrying capacity Superpose to initial geometry 𝐲 𝟏 . 3. 4. Restart analysis using nudged geometry 𝐲 . 4. If necessary, increase nudging factor 𝜃 . Repeat from 3. 5. Nudged geometry 𝐲 Closes unstable gap (Exaggerated nudge: Actual nudge imperceptible) 𝐲 = 𝐲 0 + 𝜃ഥ 𝐯 state Stable orig. path 𝜃 : nudging factor Unstable orig. path 𝜃~ thickness Critical point ഥ 𝐯 state : normalised 𝐯 state Stable nudged path Modal nudging of aerospace structures

9 Limitations and Current/future work Man anufacturabil ilit ity Modal nu nudgin ing Fea eature nu nudging Aerodynamic su surface ch chan ange Geo Geometric ical sur surface ch change NA cha change Modal nudging of aerospace structures

10 Summary • Modal nudging is a robust method for improving structural efficiency • Negligible increase in mass Improvement in load carrying capacity/stiffness • Effective for stiffened structures and can be adapted for different cases Modal nudging of aerospace structures

11 Acknowledgements The authors would like to acknowledge CNPq and Embraer r for their support of this research. Modal nudging of aerospace structures

Thank you! Any questions? olivia.leao@bristol.ac.uk Spo Sponsored by