modal nudging of aerospace structures
TRANSCRIPT
Modal nudging of
aerospace structures
Olivia Leão
Supervisors: Alberto Pirrera and Rainer Groh
8th CDT Conference
16th April 2019
Sponsored by
Outline2
• Nonlinearities in design process
• Modal nudging • Concept
• Stiffened structure example
• Limitations
• Current/future work
• Summary
Modal nudging of aerospace structures
Well-behaved nonlinear structures3
• Instabilities ≠ structural failure
• Large deformations in material linear elastic range:
Novel functionality and lighter structures
• Well-behaved nonlinearities can be robustly controlled
Improved structural efficiency through the incorporation of well-behaved nonlinearities in 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 nudging4
[3]
Original structure
Nonlinearpost-buckling
response information
Small change in geometry
Improved structural response:
Load-carrying capacity
Stiffness/compliance
Sensitivity to imperfections
Nonlinear FE +
Numerical continuationsolver
Insignificant change in
mass
[4]
Nonlinear response tailoring method based on post-buckling information
Modal nudging of aerospace structures
1. Identify isolated stable region of interest.
2. Extract deformation mode 𝐮state.
3. Superpose to initial geometry 𝐱𝟎.
4. Restart analysis using nudged geometry 𝐱.
5. If necessary, increase nudging factor 𝜂. Repeat from 3.
Steps and results5
𝑢 𝑥 𝑦
𝑧
Clamped edge
Clamped edge
Higher load-carrying solution
Unstable gap onoriginal path Region of interest
(physically unattainable)
Stable orig. pathUnstable orig. pathCritical pointNatural path
Natural physicalresponse
Buckling
Original structure
Modal nudging of aerospace structures
1. Identify isolated stable region of interest.
2. Extract deformation mode 𝐮𝐬𝐭𝐚𝐭𝐞.
3. Superpose to initial geometry 𝐱𝟎.
4. Restart analysis using nudged geometry 𝐱.
5. If necessary, increase nudging factor 𝜂. Repeat from 3.
66
𝐮state(Scaled up for clarity)
Higher load-carrying solution
Region of interest
Stable orig. pathUnstable orig. pathCritical point
Steps and results
Modal nudging of aerospace structures
1. Identify isolated stable region of interest.
2. Extract deformation mode 𝐮state.
3. Superpose to initial geometry 𝐱𝟎.
4. Restart analysis using nudged geometry 𝐱.
5. If necessary, increase nudging factor 𝜂. Repeat from 3.
77
𝐱 = 𝐱0 + 𝜂ഥ𝐮state𝜂: nudging factor
𝜂~thickness
ഥ𝐮state: normalised 𝐮state
𝐮state(Scaled up for clarity)
Higher load-carrying solution
Region of interest
Stable orig. pathUnstable orig. pathCritical point
Steps and results
Modal nudging of aerospace structures
1. Identify isolated stable region of interest.
2. Extract deformation mode 𝐮state.
3. Superpose to initial geometry 𝐱𝟎.
4. Restart analysis using nudged geometry 𝐱.
5. If necessary, increase nudging factor 𝜂. Repeat from 3.
88
Stable orig. pathUnstable orig. pathCritical pointStable nudged path
Nudged geometry 𝐱(Exaggerated nudge:
Actual nudge imperceptible)
Nudged load-carrying capacity
Higher load-carrying solution
𝐱 = 𝐱0 + 𝜂ഥ𝐮state𝜂: nudging factor
𝜂~thickness
ഥ𝐮state: normalised 𝐮state
Closes unstable gap
Steps and results
Modal nudging of aerospace structures
Limitations and Current/future work9
Manufacturability
Modal nudging Feature nudging
Aerodynamic surface change
Geometrical surface change NA change
Modal nudging of aerospace structures
Summary10
• 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
Acknowledgements11
The authors would like to acknowledge CNPq and Embraer for their support of this research.
Modal nudging of aerospace structures
