Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-22T11:20:03.858Z Has data issue: false hasContentIssue false
  • English
  • Français

Shape optimisation in the design of thin-walled shells as components of aerospace structures

Published online by Cambridge University Press:  27 January 2016

P. A. Suarez Espinoza ,
K-U. Bletzinger ,
H. R. E. M. Hörnlein ,
F. Daoud ,
G. Schuhmacher  and
M. Klug
P. A. Suarez Espinoza*
Affiliation:
Technische Universität München, Munich, Germany
K-U. Bletzinger*
Affiliation:
Technische Universität München, Munich, Germany
H. R. E. M. Hörnlein*
Affiliation:
EADS, Manching, Germany
F. Daoud*
Affiliation:
EADS, Manching, Germany
G. Schuhmacher*
Affiliation:
EADS, Manching, Germany
M. Klug*
Affiliation:
Premium Aerotec, Augsburg, Germany
*
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

One of the most resent efforts in aircraft design is the replacement of aluminium structures by carbon fibre reinforced polymer composites. Due to lower material and manufacturing costs, doubly curved shapes covering big areas are preferred over simpler surfaces which integrate stiffening profiles. In this context, CAD parameterisation of surfaces allows design solutions by means of classical shape optimisation. Related geometrical parameters are manipulated towards optimal design, generating innovative geometries and detailing.

The presented structure is optimised by reducing the overall weight. The final optimum is guided using stability and strength restrictions in order to assure the safety of the component. Geometrical considerations are also included due to operational reasons. A hierarchical design procedure is developed which results in a work flow from preliminary ‘parameter-free’ form finding motivated by solving the minimal surface problem. The geometrical model for optimisation is recovered by generating B-Spline surface patches to preserve continuity requirements over large regions. The number of geometrical coefficients are defined by the accuracy in surface generation and the required freedom in surface control. The hierarchical approach reduces the possibilities of ending with an unsatisfactory optimum when several local minima characterise the non-linear problem, as it is usually the case in shape optimal design. A geometrical non-linear analysis is used to verify the performance of the optimum.

Type
Research Article
Information
The Aeronautical Journal , Volume 116 , Issue 1182 , August 2012 , pp. 793 - 814
Copyright
Copyright © Royal Aeronautical Society 2012 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Bletzinger, K.U. and Wüchner, R. Form- Trägt - Formfindung vorgespannter Membrantragwerke, 2004, Dresdner Baustatik Seminar - Kreative Ideen im Ingenieurbau, 8, Dresden, Germany.Google Scholar
2. Wüchner, R. Mechanik und Numerik der Formfindung und Fluid- Struktur-Interaktion von Membrantragwerken; 2007, PhD thesis; Technische Universität München, Germany.Google Scholar
3. Bushnell, D. Computerized buckling analysis of shells, 1989, Kluwer Academic Publishers.Google Scholar
4. Linhard, J., Wüchner, R. and Bletzinger, K.U. Membranes to shells the ceg rotation free shell element and its application in structural analysis, Finite Elements in Analysis and Design, 2007, 44, pp 63–74.Google Scholar
5. Hughes, T. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, 2000, Dover Publication.Google Scholar
6. Bletzinger, K.U and, Ramm, E. A General finite element approach to the form finding of tensile structures by the updated reference Strategy, Int J of Space Structures, 1999, 14, (2), pp 131–145.Google Scholar
7. Holzapfel, G. Nonlinear Solid Mechanics, 2000, John Wiley & Sons, Chichester: UK.Google Scholar
8. Linhard, J. Numerisch-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken, 2009, PhD thesis, Technische Universität München, Germany.Google Scholar
9. Jarasjarunkiat, A. Nonlinear Analysis of Pneumatic Membranes From Subgrid to Interface, 2009, PhD thesis; Technische Universität München, Germany.Google Scholar
10. Wriggers, P. Nichtlineare Finite-Element-Methoden, 2001, Springer- Verlag, Berlin, Germany.Google Scholar
11. Belytschko, T., Liu, W. and Moran, B. Nonlinear Finite Elements for Continua and Structures, 2000, John Wiley & Sons, Chichester, UK.Google Scholar
12. Riks, E. Some computational aspects of the stability analysis of nonlinear structures, Computer Methods in Applied Mech and Eng, 1984, 47, pp 219–259.Google Scholar
13. Reitinger, R. Stabilität und Optimierung imperfektionsempfindlicher Tragwerke, 1994, PhD thesis, Institut für Baustatik der Universität Stuttgart, Germany.Google Scholar
14. Pontow, J. and Dinkler, D. Impefection sensitivity and limit loads of spherical shells under radial pressure, PAMM Proc, Appl Mech, 2005, 5, pp 253–254, Wiley-VCH Verlag. Weinheim; Germany.Google Scholar
15. Schmidt, H.. Stability of steel shell structures general report, J Constructional Steel Research, 2000, 55, pp 159–181.Google Scholar
16. Lu, Z., Obrecht, H. and Wunderlich, W. Imperfection sensitivity of elastic and elastic-plastic torispherical pressure vessel heads, Thin-Walled Structures, 1995, 23, pp 21–39.Google Scholar
17. Nemeth, M.P., Britt, V.O., Collins, T.J. and Starnes, J.H. Nonlinear analysis of the space shuttle superlight-weight external fuel tank, 1996, Technical Report 3616, National Aeronautics and Space Administration, Lang-ley Research Center, Hampton, VA, USA.Google Scholar
18. Nemeth, M.P., Young, R.D., Collins, T.J. and Starnes, J.H. Effects of initial geometric imperfections on the non-linear response of the space shuttle superlightweight liquid-oxygen tank, Int J Non-linear Mech, 2002, 37, pp 723–744.Google Scholar
19. Piegl, L. and Tiller, W. The NURBS Book, 1997, Springer-Verlag, Berlin, Germany.Google Scholar
20. Farin, G. NURBS, 1999, Peters.Google Scholar
21. Farin, G. Curves and Surfaces for CAGD: a Practical Guide, 2002, Fifth edition, Morgan Kaufmann.Google Scholar
22. Cohen, E., Riesenfeld, R.F. and Elber, G. Geometric Modeling with Splines, 2001, A K Peters.Google Scholar
23. Rogers, D.F. An Introduction to NURBS, 2001, Morgan Kaufmann.Google Scholar
24. Ma, W. and Kurth, J. Parameterization of randomly measured points for least squares fitting of b-spline curves and surfaces, Computer Aided Design, 1995, 27, (9), pp 663–675.Google Scholar
25. Hormann, K. Fitting free form surfaces, Principles of 3D Image Analysis and Synthesis, 2000, International Series in Engineering and Computer Science, 556, Kluwer Academic Publishers, Boston, MA, USA.Google Scholar
26. Hormann, K. From scattered samples to smooth surfaces, Proceedings of Geometric Modeling and Computer Graphics, 2003.Google Scholar
27. Sintef, M.F. and Floater, M.S. Meshless parameterization and b-spline surface approximation, The Mathematics of Surfaces IX, 2000.Google Scholar
28. Piegl, L.A. and Tiller, W. Curve interpolation wiht arbitrary end derivatives, Engineering with Computers, 2000, 16, pp 73–79.Google Scholar
29. Shamsuddin, S., Ahmed, M. and Samian, Y. Nurbs skinning surface for ship hull design based on new parameterization method, Int J Manuf Technology, 2006, 28, pp 936–941.Google Scholar
30. de Boor, C. A Practical Guide to Splines, 1978, New York, Springer-Verlag.Google Scholar
31. Tokuyama, Y. Skinning-surface generation based on spine-curve control, The Visual Computer, 2000, 16, pp 134–140.Google Scholar
32. Piegl, L.A. and Tiller, W. Least-squares b-spline curve approximation with arbitrary end derivatives. Engineering with Computers, 2000, 16, pp 109–116.Google Scholar
33. Schuhmacher, G. Multidisziplinäre, fertigungsgerechte Optimierung von Faservebund-Flchentragwerken, 1995, PhD thesis, Fachbereich Maschinentechnik der Universität-Gesamthochschule Siegen.Google Scholar
34. Piegl, L.A. and Tiller, W. Surface approximation to scanned data methods in applied mechanics and engineering, The Visual Computer, 2000, 16, pp 386–395.Google Scholar
35. Lyche, T. Knot insertion and Deletion Algorithms for B-spline Curves and Surfaces, 1993.Google Scholar
36. Haftka, R. and Gürdal, Z. Elements of Structural Optimization, 1992, Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
37. Bletzinger, K.U., Firl, M. and Daoud, F. Approximation of derivatives in semi-analytical structural optimization, Computers & Structures, 2008, 86, pp 1404–1416.Google Scholar
38. Schittkowski, K. On the convergence of a sequential quadratic programming method with an augmented la-grangian line search function, Operationsforschung und Statistik, Ser Optimization, 1983, 14, (2), pp 197–216.Google Scholar