First of all, I’d like to thank UQLab developers for such an useful toolbox.
As stated in the title, I have some doubts regarding the cost function in the RBDO.
Particularly, I’m facing the RBDO of a laminated composite plate. The limit state function involves the failure due to buckling of the structure, and the cost function is the structural weight of the plate.
The variables involved are:
Two fibre orientations, the thickness of the laminae and the fibre volume fraction (which affects the longitudinal, transverse and shear moduli, Poisson’s ratios and density of the material). Its input definition is available in the enclosed image.
The four mentioned variables affect the limit state function, whilst the cost function is influenced by the thickness and fibre volume fraction. However, I am considering the latter as an environmental variable since it is affected by the manufacturing processes.
May you have any suggestion on how to solve this issue? Or should I be treating fibre volume fraction as a design variable?
You may define the latter two variables as design parameters directly. Design parameters can be random as well. Basically you assume that there is a small variability around any given design choice and this will be propagated to the model. For instance you may consider that the thickness, denoted by d_1, is in the range [0.125, \, 0.25] if that is the set of possible values. Then you may additionnally assume that for a design choice d_1^{(i)} at iteration i of the optimization, there are some uncertainty (e.g. due to manufacturing) and model it for instance using a Gaussian distribution: X_1(d_1) \sim \mathcal{N}(d_1^{(i)}, \, CoV \cdot d_1^{(i)}), where CoV is the coefficient of variation of the associated random variable. This is obviously just an example and you can decide what is the best distribution in your case for both the thickness and volume fraction.
As of now, UQLab only accounts for uncertainty in the performance function. To compute the cost function, the mean value of the design parameters will be considered.
Please let me know if you had already manged to solve your problem or if this is usefull.
For my case, I finally considered just the thickness to be the design variable that affects the weight. I wanted to consider as well the volume fraction since by just modifying one parameter I can alter all the mechanical properties (Young modulus, Poisson’s ratio, etc.) but, of course, it affects the density.
Following your suggestion, I could have considered volume fraction as a design variable (even if it is not) and imposing a certain range (lets say [0.45,0.75] with a certain COV).
