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CORRECTION

Correction to: Gaussian mixture model for robust design optimization of planar steel frames Bach Do 1

&

Makoto Ohsaki 1

Received: 4 November 2020 / Revised: 6 November 2020 / Accepted: 10 November 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020

Correction to: Structural and Multidisciplinary Optimization https://doi.org/10.1007/s00158-020-02676-3 The original version of this paper unfortunately contains two mistakes. The authors wish to revise the mistaken problem (27) and a mistaken statement in Section 5.1; see below corrections. Correction 1: Problem (27) should be corrected to qffiffiffiffiffiffiffiffiffiffiffiffiffi min: f ðx1 ; x2 Þ ¼ ρx1 1 þ x22 subject to  qffiffiffiffiffiffiffiffiffiffiffiffiffi 5Q 8 1 þ g1 ðx1 ; x2 Þ ¼ 1− pffiffiffiffiffi 1 þ x22 ≥0 x1 x1 x2 65 Fy ð27Þ   qffiffiffiffiffiffiffiffiffiffiffiffiffi 5Q 8 1 2 − 1 þ x2 g2 ðx1 ; x2 Þ ¼ 1− pffiffiffiffiffi ≥0 x1 x1 x2 65 Fy

Correction 2: In the second paragraph of Section 5.1, the statement: “Nominal values of the yield stress, tensile strength, and Young’s modulus of the steel material are 200 MPa, 250 MPa, and 400 GPa, respectively” should be corrected to “Nominal values of the yield stress, tensile strength, and Young’s modulus of the steel material are 250 MPa, 400 MPa, and 200 GPa, respectively”.

Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest.

0:2≤ x1 ≤ 20; 0:1 ≤x2 ≤1:6 The numerical results are correct, since this was just a typing error.

Responsible Editor: Ming Zhou The online version of the original article can be found at https://doi.org/ 10.1007/s00158-020-02676-3 * Bach Do [email protected] 1

Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyoto-Daigaku Katsura, Nishikyo, Kyoto 615-8540, Japan

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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