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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 207
Optimisation of Anisotropic Cylinders Accounting for Manufacturing Tolerances P.Y. Tabakov and M. Walker
Center for Advanced Materials, Design & Manufacture, Research, Durban Institute of Technology, South Africa Full Bibliographic Reference for this paper
P.Y. Tabakov, M. Walker, "Optimisation of Anisotropic Cylinders Accounting for Manufacturing Tolerances", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 207, 2006. doi:10.4203/ccp.83.207
Keywords: manufacturing tolerance, optimal design, anisotropic pressure vessel, genetic algorithm.
Summary
Accurate optimal design solutions for most engineering structures present
considerable difficulties due to the complexity and multi-modality of the
functional design space. The situation is made even more complex when
potential manufacturing tolerances must be accounted for in the optimizing
process. Though the deviations can be relatively small, their impact on the overall
performance of the structure can be significant.
A few researchers have described methods for dealing with manufacturing tolerances. For example, Bauer and Latalski [1] consider the issue of manufacturing tolerances in dimensions with regard design optimization, when the objective is minimum weight. In two papers by Walker and 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 present study provides an in-depth analysis of the multi-dimensional problem and then a technique for determining the optimal design of engineering structures, with manufacturing tolerances in the design variables accounted for, is proposed and demonstrated. The examples used to demonstrate the technique involve the design optimisation of anisotropic laminated pressure vessels based on an exact three-dimensional elasticity solution [4]. The technique is simple, easy to implement and, at the same time, very efficient. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, can be equal, and thus it is a worst-case scenario approach. In addition, the technique is non-probabilistic. A genetic algorithm with fitness sharing, including a micro-genetic algorithm, has been found to be very suitable to use, and implemented in the technique. Numerical examples clearly demonstrate the impact of manufacturing tolerances on the overall performance of a structure and emphasize the importance of accounting for such tolerances in the design optimisation phase. The results show that when the example tolerances are accounted for, the maximum design pressure can be reduced by more than 60% if the nominal fibre orientations are implemented and the example tolerances are incurred during fabrication.
For the purpose of visual illustration one- and two-layered cylinders are used here.
The material properties are those for a typical T300/5208 graphite/epoxy
material and the ratios of the external radius to internal in the cylinder
used in the example are
The exact values of the maximum critical pressure are
It is assumed in this research that there can be an upper and lower
tolerance in each case, and thus for a problem with These examples clearly demonstrate how important it is to take the manufacturing tolerances into account in the design optimisation stage. It also illustrates that it is much safer to use a few layers instead of one. However, calculations show that after about 10 layers there is not much improvement in the performance of the pressure vessel. References
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