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Shape optimization of shallow domes subjected to external pressure

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Abstract

Shallow domes subjected to external pressure are extensively used in missile structures. The critical failure mode for these domes is buckling due to external pressure. Different closed form solutions are available to evaluate buckling pressure of dome shapes like ellipsoid and torisphere. The torisiphere dome is the optimum dome shape among conventional domes. Shape optimization is carried out to find the optimal dome shape among shallow domes subjected to external pressure. Dome geometry is generalized by cubic bezier polynomials. For carrying out shape optimization, a low fidelity model is preferred which can predict the critical buckling pressure of a general dome shape. Towards this a unified model is proposed which meets the above requirement. Using this unified model, shape optimization of dome for minimization of mass is carried out subjected to buckling constraint. The study yielded a dome shape different from conventional dome shapes with a mass saving of 6% over torispherical dome while meeting the buckling constraint. The results of unified model are also validated with high fidelity Finite Element Analysis.

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Abbreviations

a:

Semi major axis of ellipse

b:

Semi minor axis of ellipse

BLF:

Buckling load factor of dome

E:

Young’s modulus of dome material

P:

External pressure acting on dome

P cr :

Critical buckling pressure of dome

R:

Radius of hemispherical dome

R crown :

Crown radius of torispherical dome

R ell :

Equivalent radius of ellipsoidal dome

R knu :

Knuckle radius of torispherical dome

R max :

Equivalent radius of general shape dome

R tor :

Equivalent radius of torispherical dome

s:

Parameter of bezier polynomial

t:

Thickness of dome

X i , Y i :

Control point coordinates of bezier polynomial

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Authors and Affiliations

  1. DRDL, Kanchanbagh, Hyderabad, 500058, India

    Santhosh R, Shaik Ismail, Jain P. C. & Anjaneyulu P. S. R.

Authors
  1. Santhosh R
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  2. Shaik Ismail
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  3. Jain P. C.
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  4. Anjaneyulu P. S. R.
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Correspondence to Santhosh R.

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R, S., Ismail, S., P. C., J. et al. Shape optimization of shallow domes subjected to external pressure. Struct Multidisc Optim 57, 903–908 (2018). https://doi.org/10.1007/s00158-017-1773-6

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  • DOI: https://doi.org/10.1007/s00158-017-1773-6

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