On the optimal layout of structures subjected to probabilistic or multiply loading

The loading uncertainties can be expressed by the stochastic nature of any part of the load determination. If any information is probabilistic among the three independent data of the load determination (the magnitude, the line of action and/or the point of application) a more precise design requires to elaborate a probabilistic method. This goal can be obtained by the use of an appropriate approximation technique, in which the original stochastic mathematical programming problem is substituted by a deterministic one. A similar technique can be followed in case of a multiple loading. In addition to the numerical modelling a parametric study is given where the influence of the multiple loading is investigated to determine the optimal layout in function of the initial layout. The application is illustrated by numerical examples.