Keywords: optimization, probabilistic loading, multiple load cases, stochastic loading, uncertain point of application, optimal layout, optimality criteria method, optimal design, robust design..

Multiple loading and the loading uncertainty can be modelled in such a way that the later is taken into consideration with the help of a surrogate load model. The loading uncertainties can be given by the stochastic nature of any part of the load determination. If any information is probabilistic among the three independent data of the loadings (the magnitude, the line of action and the point of application), a more precise design requires a probabilistic method to elaborate the design procedure. One of the most convenient solution techniques is to create an appropriate deterministic model as a surrogate for the original stochastic problem. In this way the loading uncertainties require the consideration of multiple load cases to form the surrogate deterministic models. Here probabilistic topology design methods are elaborated where the loads are given randomly. As a result of the probabilistic nature of the loading, the compliance expressions are probabilistic ones. Two equivalent topology optimization algorithms are used: minimization of the maximum structural compliance with respect to a given volume, or minimization of the volume of the structure subjected to compliance constraints. The numerical procedure is based on an iterative formula, which is formed by the use of the first order optimality condition of the Lagrangian function. 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 the function of the initial layout. The application is illustrated by numerical examples.

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