Robust Topology Optimization under Uncertain Loads - A Spectral Stochastic Approach
Nilton Cuellar1; Anderson Pereira2; Ivan F. M. Menezes1
1 Pontifical Catholic University of Rio de Janeiro, Department of Mechanical Engineering; 2 Pontifical Catholic University of Rio de Janeiro, Tecgraf / PUC-Rio
doi:10.20906/CPS/CILAMCE2015-0882
Resumo
A spectral stochastic approach for structural topology optimization in the presence of uncertainties in the magnitude and direction of the applied loads is proposed. The application of this approach in the representation and propagation of uncertainties presents a low computational cost compared to classical techniques, such as Monte Carlo simulation. A recent development of spectral representation methods, known as generalized polynomial chaos (gPC), has become one the most widely used methods by exhibiting fast convergence when the solution depends smoothly on the random parameters. Therefore, in this work, gPC is applied to estimate the statistical measures of the compliance of 2D continuum structures, which we call Robust Topology Optimization. To demonstrate the accuracy and applicability of the proposed method, we solve robust topology optimization where we minimize the influence of stochastic variability on the mean design. Representative examples of topology optimization of continuum structures under load uncertainties are presented. The results demonstrate that load uncertainties play an important role in the optimal design. It is also shown that results obtained from the gPC method are in excellent agreement with those obtained from Monte Carlo simulation.
Palavras-chave: Topology Optimization; Spectral Stochastic Approach; Generalized Polynomial Chaos; Uncertain Quantification; Robust Optimization