Topology optimization of continuum structures subjected to uncertainties in material properties

• Published in: International journal for numerical methods in engineering Vol. 106; no. 3; pp. 192 - 212
• Main Authors: da Silva, G. A., Cardoso, E. L.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 20.04.2016; Wiley Subscription Services, Inc
• Subjects: Continuums; Correlation; Mathematical models; Minimization; Optimization; random field; robust; Standard deviation; Topology optimization; uncertainties; Uncertainty
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.5126

Summary This work addresses the use of the topology optimization approach to the design of robust continuum structures under the hypothesis of uncertainties with known second‐order statistics. To this end, the second‐order perturbation approach is used to model the response of the structure, and the midpoint discretization technique is used to discretize the random field. The objective function is a weighted sum of the expected compliance and its standard deviation. The optimization problem is solved using a traditional optimality criteria method. It is shown that the correlation length plays an important role in the obtained topology and statistical moments when only the minimization of the standard deviation is considered, resulting in more and thinner reinforcements as the correlation length decreases. It is also shown that the minimization of the expected value is close to the minimization of the deterministic compliance for small variations of Young's modulus. Copyright © 2016 John Wiley & Sons, Ltd.