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CivilComp Proceedings
ISSN 17593433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 21
A Technique for Optimally Designing FibreReinforced Laminated Plates for Minimum Weight with Manufacturing Uncertainty M. Walker and R. Hamilton
Centre for Advanced Materials, Design & Manufacture Research, Durban Institute of Technology, South Africa M. Walker, R. Hamilton, "A Technique for Optimally Designing FibreReinforced Laminated Plates for Minimum Weight with Manufacturing Uncertainty", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 21, 2004. doi:10.4203/ccp.79.21
Keywords: design technique, composite plates, minimum mass, manufacturing uncertainty.
Summary
Robust design is an approach that explicitly recognizes the
effects of these variations and seeks to minimize their consequences 
without eliminating their sources, but very few researchers have dealt with
the robust design of composite structures. Chiang [1] used a robust design
approach to improve the accuracy of the Iosipescu shear test specimen. The
statistical design of experiments based on the finite element method was
employed, and was able to identify the influential design variables. In two
papers by Walker & Hamilton [2,3], a technique for optimally designing
laminated plates with manufacturing tolerances present in the design
variable (which is the fibre orientation) is described. The objective is to
maximise the buckling load carrying capacity and in the first, a closed form
solution for plates is implemented, whilst in the second, the FEM is used.
The techniques are aimed at optimally designing for the worstcase scenario,
and the results presented (as a means of illustrating the methodology)
demonstrate the importance of accounting for manufacturing uncertainties.
This study deals with a variation on the theme of RDO, and describes a procedure to design symmetrically laminated plates for maximum buckling load with manufacturing uncertainty in the ply angle, which is the design variable. As in Refs [2,3], it is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal. The effects of bendingtwisting coupling are neglected and the Golden Section method is used as the search technique, but the methodology is flexible enough to allow any appropriate problem formulation and search algorithm to be substituted. Three different tolerance scenarios are used to illustrate the methodology, and plates with varying aspect ratios and loading ratios are optimally designed. It is shown that because they are worst case scenario designs, when the resulting plate thicknesses are rounded off to 0.1mm, the corresponding buckling load capacity is still in excess of the minimum requirement.
Optimal Design Problem and Solution Procedure
The objective of the design problem is to maximixe the buckling load
capacity of the symmetrically laminated plate, with manufacturing
uncertainty in the layup angle and laminate thickness accounted for. The
problem can thus be stated as:

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