Keywords: design technique, composite plates, minimum mass, manufacturing uncertainty.

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 worst-case 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 bending-twisting 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:

where is the closed-form solution for the critical buckling load. When composite laminates are manufactured, the desired fibre orientation in different plies may deviate from their intended design values by a few degrees. These deviations are referred to as manufacturing tolerances. Assume that for the interval a manufacturing tolerance in the layup angle is incurred, and must be accounted for during the design stage, if optimal performance is required. Furthermore, assume that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal. Extensive research has been performed in the field of manufacturing tolerances but not incorporating it as part of the design optimization process. For example, for there may be a maximum variation band of or , with In addition, when accounted for, it is assumed that and . In order to illustrate the problem, consider the following scenario. For a eight layer symmetric plate with , assume that on the intervals and a manufacturer incurs the following maximum tolerances in the layup angle: and ; viz. when trying to achieve the value , the actual value that results is . The optimization procedure involves the stages of determining the buckling load at , and at the three other points which occur when the tolerances of the fibre orientation are accounted for, viz. and The lowest of these is then selected, and the orientation and thickness values improved to maximise the load. Thus, the computational solution consists of successive stages of analysis and optimization until convergence is obtained and the optimal angle and thickness is determined within specified accuracy. In the optimization stage here, the Golden Section method is employed.

1

Y J. Chiang, "Robust design of the iosipescu shear test specimen for composites", Journal of testing and evaluation, JTEVA, 24(1), 1-11, 1996. doi:10.1520/JTE11282J

2

M. Walker & R. Hamilton, "A technique for optimally designing fibre-reinforced laminated plates with manufacturing uncertainties for maximum buckling strength", to appear in Journal of Engineering Optimization. doi:10.1080/03052150412331298371

3

M. Walker & R. Hamilton, "A methodology for optimally designing fibre-reinforced laminated structures with design variable tolerances for maximum buckling strength", submitted to Elsevier: Thin Walled Structures. doi:10.1016/j.tws.2004.07.001

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