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

Modal nudging of aerospace structures

Olivia Leão

Supervisors: Alberto Pirrera and Rainer Groh

8th CDT Conference 16th April 2019

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Outline

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• Nonlinearities in design process
• Modal nudging
• Concept
• Stiffened structure example
• Limitations
• Current/future work
• Summary

Modal nudging of aerospace structures

Well-behaved nonlinear structures

3

• 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
• bustly controlle

led

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 [1] [2]

Modal nudging of aerospace structures

[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

4

[3]

Original structure Nonlinear post-buckling response information Small change in geometry

Improved structural response:

Load-carrying capacity Stiffness/compliance Sensitivity to imperfections

Nonlinear FE + Numerical continuation solver

Insignificant change in mass

[4]

No Nonlin linear resp sponse tail ailorin ing method base ased on

• n pos
• st-bucklin

ling in information Modal nudging of aerospace structures

1.

• 1. Id

Identify is isolated stable region of f in interest.

2. Extract deformation mode 𝐯state. 3. Superpose to initial geometry 𝐲𝟏. 4. Restart analysis using nudged geometry 𝐲. 5. If necessary, increase nudging factor 𝜃. Repeat from 3.

Steps and results

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𝑣 𝑦 𝑧 𝑨

Clamped edge Clamped edge

Higher load-carrying solution Unstable gap on

• riginal path

Region of interest (physically unattainable) Stable orig. path Unstable orig. path Critical point Natural path Natural physical response Buckling Original structure

Modal nudging of aerospace structures

1. Identify isolated stable region of interest.

2.

• 2. Ext

xtract deformation mode 𝐯𝐭𝐮𝐛𝐮𝐟.

3. Superpose to initial geometry 𝐲𝟏. 4. Restart analysis using nudged geometry 𝐲. 5. If necessary, increase nudging factor 𝜃. Repeat from 3.

6 𝐯state

(Scaled up for clarity)

Higher load-carrying solution Region of interest Stable orig. path Unstable orig. path Critical point

Steps and results

Modal nudging of aerospace structures

1. Identify isolated stable region of interest. 2. Extract deformation mode 𝐯state.

3.

• 3. Superpose to in

initial geometry 𝐲𝟏.

4. Restart analysis using nudged geometry 𝐲. 5. If necessary, increase nudging factor 𝜃. Repeat from 3.

7 𝐲 = 𝐲0 + 𝜃ഥ 𝐯state

𝜃: nudging factor 𝜃~thickness ഥ 𝐯state: normalised 𝐯state

𝐯state

(Scaled up for clarity)

Higher load-carrying solution Region of interest Stable orig. path Unstable orig. path Critical point

Steps and results

Modal nudging of aerospace structures

1. Identify isolated stable region of interest. 2. Extract deformation mode 𝐯state. 3. Superpose to initial geometry 𝐲𝟏.

4.

• 4. Restart analysis using nudged geometry 𝐲.

5. If necessary, increase nudging factor 𝜃. Repeat from 3.

8

Stable orig. path Unstable orig. path Critical point Stable nudged path Nudged geometry 𝐲

(Exaggerated nudge: Actual nudge imperceptible)

Nudged load-carrying capacity Higher load-carrying solution

𝐲 = 𝐲0 + 𝜃ഥ 𝐯state

𝜃: nudging factor 𝜃~thickness ഥ 𝐯state: normalised 𝐯state Closes unstable gap

Steps and results

Modal nudging of aerospace structures

Limitations and Current/future work

9 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

Summary

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• 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

Acknowledgements

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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?

• livia.leao@bristol.ac.uk

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