Issue 37

R. Sepe et alii, Frattura ed Integrità Strutturale, 37 (2016) 369-381; DOI: 10.3221/IGF-ESIS.37.48 375     1 1 0 1 , 1 , , 0 , x x,k x k y,k y k x k y y k μ μ μ G μ μ μ G μ μ            (14) The SDI technique is based on the assumption that the cloud of points corresponding to the results obtained from a set of MC trials can be moved toward a desired position in the N-dimensional space such as to give the desired result (target), and that the amplitude of the required displacement can be forecast through a close analysis of the points that are in the same cloud (Fig. 2): in effects, it is assumed that the shape and the size of the cloud don’t change greatly if the displacement is small enough; it is therefore immediate to realize that an SDI process is composed by several sets of MC trials (runs) with intermediate estimates of the required displacement (Fig. 3). Figure 2 : initial and final structural responses. Figure 3 : SDI process. It is also clear that the assumption about the invariance of the cloud can be maintained just in order to carry out the multivariate regression which is needed to perform a new step – i.e. the evaluation of the G matrix – but that subsequently a new and correct evaluation of the cloud is needed; in order to save time, the same evaluation can be carried out every k steps, but of course, as k increases, the step amplitude has to be correspondently decreased. It is also immediate that the displacement is obtained by changing the statistics of the design variables and, in particular, by changing their mean (nominal) values, as in the now available version of the method all distributions are assumed to be