Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T05:38:22.481Z Has data issue: false hasContentIssue false

Optimum design for buckling of arbitrary shaped ribs under uncertain loadings

Published online by Cambridge University Press:  03 February 2016

A. C. Conrado
Affiliation:
Instituto Tecnológico de Aeronáutica, São José dos Campos, Brazil
A. R. de Faria
Affiliation:
Instituto Tecnológico de Aeronáutica, São José dos Campos, Brazil
S. F. M. de Almeida
Affiliation:
Instituto Tecnológico de Aeronáutica, São José dos Campos, Brazil

Abstract

Typically, aircraft wing structural panels are designed against buckling for a very large number of possible loadings that may occur during the operation of the aircraft. If the optimisation procedure accounts only for a limited number of design loads, the structure may be vulnerable to a specific type of loading that may cause the structure to fail. A novel approach for the optimisation of ribs or plates of arbitrary shapes under uncertain loads is proposed. The geometry of the rib is defined by a single closed spline or several connected splines. The loading distribution is not considered to be uniform but it is allowed to vary within an admissible set, conferring uncertainty to the applied loads. The admissible load space comprises distributed normal and shear loadings that can be represented through a collection of piecewise linear functions defined along the plate boundary. A special procedure is applied to handle the constraint that the loading must be self equilibrating. A minimax strategy is used to deal with the loading variability such that the resulting optimal design is able to withstand an entire class of linear piecewise loadings along the rib boundary. The refinement of the loading representation may be completely independent of the refinement of finite element mesh. The validity of the proposed approach is assessed by applying it to an aeronautical wing rib.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2005 

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. Chao, C.C., Koh, S.L. and Sun, C.T.. Optimization of buckling and yield strengths of laminated composites, AIAA J, 1975, 13, (9), pp 11311132.Google Scholar
2. Hirano, Y.. Optimum design of laminated plates under axial compression, AIAA J, 1979, 17, (9), pp 10171019.Google Scholar
3. Haftka, R.T. and Walsh, J.L.. Stacking sequence optimization for buckling of laminated plates by integer programming, AIAA J, 1992, 30, (3), pp 814819.Google Scholar
4. Foldager, J.P.. Design of Composite Structures 1999, PhD thesis, Aalborg University, Institute of Mechanical Engineering, Denmark.Google Scholar
5. Miki, M. and Sugiyama, Y.. Optimum design of laminated composite plates using lamination parameters, AIAA J, 1993, 31, (5), pp 921922.Google Scholar
6. Sun, G. and Hansen, J.S.. Optimal design of laminated-composite circular-cylindrical shells subjected to combined loads, J Applied Mechanics, 1988, 55, (3), pp 136142.Google Scholar
7. Bruhn, E.F., Analysis and Design of Flight Vehicle Structures, 1973, Tri-State Offset, Cincinnati, OH.Google Scholar
8. Niu, M.C.Y. Airframe Stress Analysis and Sizing, 2001, Hong Kong Conmilit Press, Hong Kong.Google Scholar
9. Faria, A.R.De and Hansen, J.S.. On buckling optimization under uncertain loading combinations, Structural and Multidisciplinary Optimization J, 2001, 21, (4), pp 272282.Google Scholar
10. Faria, A.R. de and Almeida, S.F.M. De. Buckling optimization of plates with variable thickness subjected to nonuniform uncertain loads, Int J Solids and Structures, 2003, 40, (15), pp 39553966.Google Scholar
11. Faria, A.R. De and Almeida, S.F.M. De. Buckling optimization of variable thickness composite plates subjected to nonuniform loads, AIAA J, 2004, 42, (2), pp 228231.Google Scholar
12. Powell, M.J.D.. An efficient method for finding the minimum of a function of several variables without calculating derivatives, Computers J, 1964, 7, pp 155162.Google Scholar
13. Gerald, C.F. and Wheatley, P.O., Applied Numerical Analysis, 1985, Addison-Wesley Publishing.Google Scholar