TY - JOUR
T1 - Reliability-based topology optimization of trusses with stochastic stiffness
AU - Jalalpour, Mehdi
AU - Guest, James K.
AU - Igusa, Takeru
N1 - Funding Information:
This work was supported by National Science Foundation under Grant No. CMMI-0928613 with Dr. Christina Bloebaum serving as program officer. This support is gratefully acknowledged.
PY - 2013/7
Y1 - 2013/7
N2 - A new method is proposed for reliability-based topology optimization of truss structures with random geometric imperfections and material variability. Such imperfections and variability, which may result from manufacturing processes, are assumed to be small in relation to the truss dimensions and mean material properties and normally distributed. Extensive numerical evidence suggests that the trusses, when optimized in terms of a displacement-based demand metric, are characterized by randomness in the stiffness that follow the Gumbel distribution. Based on this observation, it was possible to derive analytical expressions for the structural reliability, enabling the formulation of a computationally efficient single-loop reliability-based topology optimization algorithm. Response statistics are estimated using a second-order perturbation expansion of the stiffness matrix and design sensitivities are derived so that they can be directly used by gradient-based optimizers. Several examples illustrate the accuracy of the perturbation expressions and the applicability of the method for developing optimal designs that meet target reliabilities.
AB - A new method is proposed for reliability-based topology optimization of truss structures with random geometric imperfections and material variability. Such imperfections and variability, which may result from manufacturing processes, are assumed to be small in relation to the truss dimensions and mean material properties and normally distributed. Extensive numerical evidence suggests that the trusses, when optimized in terms of a displacement-based demand metric, are characterized by randomness in the stiffness that follow the Gumbel distribution. Based on this observation, it was possible to derive analytical expressions for the structural reliability, enabling the formulation of a computationally efficient single-loop reliability-based topology optimization algorithm. Response statistics are estimated using a second-order perturbation expansion of the stiffness matrix and design sensitivities are derived so that they can be directly used by gradient-based optimizers. Several examples illustrate the accuracy of the perturbation expressions and the applicability of the method for developing optimal designs that meet target reliabilities.
KW - Geometric imperfections
KW - Manufacturing defects
KW - Material uncertainties
KW - Perturbations
KW - Topology optimization
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U2 - 10.1016/j.strusafe.2013.02.003
DO - 10.1016/j.strusafe.2013.02.003
M3 - Article
AN - SCOPUS:84879474977
SN - 0167-4730
VL - 43
SP - 41
EP - 49
JO - Structural Safety
JF - Structural Safety
ER -