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UBC-constrained non-probabilistic reliability-based optimization of structures with uncertain-but-bounded parameters

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Abstract

A new UBC-constrained (ultimate-bearing-capacity-constrained) non-probabilistic reliability-based optimization method for structures with uncertain-but-bounded parameters is proposed. Different from the traditional stress-constrained optimization, the ultimate bearing capacity (UBC) is taken as the constraints in the non-probabilistic reliability-based optimization, which reflect the system safety of structures. Based on the interval mathematics, the UBC constraint is transformed into the format of non-probabilistic reliability, in which a novel measuring index, namely, the UBC, is defined by an interval interference model. Thus, structural optimization is converted by the lightweight design problem with UBC reliability constraints. Moreover, the gradient-based Taylor expansion method is employed to obtain the lower and upper bounds of the UBC, which transforms a double-layer optimization into an efficient single-layer one. Finally, 2D and 3D structural examples are given to illustrate the effectiveness of the proposed method.

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Funding

The work of this article is supported by the National Nature Science Foundation of China (No. 11872089) and the Defense Industrial Technology Development Program (Nos. JCKY2017601B001, JCKY2017208B001, and JCKY2019203A003).

Author information

Authors and Affiliations

  1. Institute of Solid Mechanics, School of Aeronautics Science and Engineering, Beihang University, Beijing, 100083, China

    Zhenxian Luo, Xiaojun Wang & Dongliang Liu

  2. School of Materials and Engineering, Jiangsu University of Technology, Changzhou, 213001, Jiangsu, China

    Qinghe Shi

Authors
  1. Zhenxian Luo
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  2. Xiaojun Wang
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  3. Qinghe Shi
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Correspondence to Xiaojun Wang.

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The raw data required to reproduce these findings are available to download from DOI: https://doi.org/10.17632/xbvw9g78gr.1

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Appendix

Appendix

Structural components may have different cross-section shapes, and the expressions of the full plastic force of different cross sections are different. The full plastic force of five common cross sections (shown in Fig. 17) is given in this appendix. The full plastic force of the five cross-section shapes is shown in Eqs. 41 ~ 45, respectively. In these equations, NPx, MPy, and MPz are full plastic axial forces, bending moment in y and z direction, respectively.

  1. (1)

    Rectangle cross section

Fig. 17
figure 17

The geometry of different cross sections: (a) rectangle cross section; (b) circular cross section; (c) I-shaped cross section; (d) rectangle hollow cross section; (e) circular hollow cross section; and (f) coordinate system

Full size image
$$ {N}_{Px}= bh{\sigma}_s,{M}_{Py}=\frac{1}{4}b{h}^2{\sigma}_s,{M}_{Pz}=\frac{1}{4}{b}^2h{\sigma}_s $$
(41)
  1. (2)

    Circular cross section

$$ {N}_{Px}=\pi {\sigma}_s{r}^2,{M}_{py}={M}_{Py}=\frac{4}{3}{\sigma}_s{r}^3 $$
(42)
  1. (3)

    I-shaped cross section

$$ {N}_{Px}={A}_f\left(2+\lambda \right){\sigma}_s,{M}_{Py}={A}_fh\left(1+\frac{\lambda }{4}\right){\sigma}_s,{M}_{Pz}=\frac{1}{2}{A}_f{b}_f{\sigma}_s $$
(43)

where λ presents the ratio of the area of flange Af and the area of web Aw, i.e., λ = Af/Aw.

  1. (4)

    Rectangle hollow cross section

$$ {\displaystyle \begin{array}{c}\left\{\begin{array}{c}{N}_{Px}=\left[ bh-\left(b-2{t}_2\right)\left(h-2{t}_1\right)\right]{\sigma}_s\\ {}{M}_{Py}=\left[\frac{1}{2}{t}_2{h}^2+\left(b-2{t}_2\right)\left(h-{t}_1\right){t}_1\right]{\sigma}_s\\ {}{M}_{Pz}=\left[\frac{1}{2}{t}_1{b}^2+\left(h-2{t}_1\right)\left(b-{t}_2\right){t}_2\right]{\sigma}_s\end{array}\right.\\ {}\end{array}} $$
(44)
  1. (5)

    Circular hollow cross section

$$ {N}_{Px}=4\pi rt{\sigma}_s,{M}_{Py}={M}_{Pz}=\frac{4}{3}\left[{\left(r+0.5t\right)}^3-{\left(r-0.5t\right)}^3\right]{\sigma}_s $$
(45)

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Luo, Z., Wang, X., Shi, Q. et al. UBC-constrained non-probabilistic reliability-based optimization of structures with uncertain-but-bounded parameters. Struct Multidisc Optim 63, 311–326 (2021). https://doi.org/10.1007/s00158-020-02697-y

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