Topology optimization of continuum structures with stress constraints and uncertainties in loading

Author(s)

da Silva, G. A. ^[1] ; Beck, A. T. ^[1] ; Cardoso, E. L. ^[2]

Affiliation

^[1] Univ Sao Paulo, Sao Carlos Sch Engn, Dept Struct Engn, BR-13566590 Sao Carlos, SP - Brazil

^[2] Univ Estado Santa Catarina, Dept Mech Engn, BR-89219710 Joinville, SC - Brazil

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING; v. 113, n. 1, p. 153-178, JAN 6 2018.
• Web of Science Citations: 8

Abstract

Topology optimization using stress constraints and considering uncertainties is a serious challenge, since a reliability problem has to be solved for each stress constraint, for each element in the mesh. In this paper, an alternative way of solving this problem is used, where uncertainty quantification is performed through the first-order perturbation approach, with proper validation by Monte Carlo simulation. Uncertainties are considered in the loading magnitude and direction. The minimum volume problem subjected to local stress constraints is formulated as a robust problem, where the stress constraints are written as a weighted average between their expected value and standard deviation. The augmented Lagrangian method is used for handling the large set of local stress constraints, whereas a gradient-based algorithm is used for handling the bounding constraints. It is shown that even in the presence of small uncertainties in loading direction, different topologies are obtained when compared to a deterministic approach. The effect of correlation between uncertainties in loading magnitude and direction on optimal topologies is also studied, where the main observed result is loss of symmetry in optimal topologies. (AU)

• FAPESP's process: 15/25199-0 - Topology Optimization under Uncertainties with Stress Failure Criteria
• Grantee: Gustavo Assis da Silva
• Support Opportunities: Scholarships in Brazil - Doctorate