Correction to: Optimizing component solution spaces for systems design

Correction to: Struct Multidisc Optim

https://doi.org/10.1007/s00158-019-02456-8

The original version of this article unfortunately contains mistakes introduced during the publishing process. The mistakes and corrections are described in the following list:

• 1. The typographical error in the reference “Daub M (2017) Konvexe Optimierung am Beispiel volumenmaximaler einbeschriebener Rechtecksmengen. Master thesis, Universität Konstanz, Germany, http://nbn-resolving.de/urn:nbn:de:bsz:352-0-420923” was removed.

• 2. The typeface of the following figures was adapted.

Fig. 1

A system composed of n components each specified by a design variable vector x^k, k = 1, . . . , n

Fig. 2

Decomposition of the complete system solution space into component solution spaces

Fig. 3

Example of optimal component solution spaces Ω¹ and Ω² for a system composed of two components with one degree of freedom each

Fig. 4

Vehicle front structure for the simple crash design problem with two components and force-deformation characteristics F¹(s), s ∈ [0 mm, ${\overline{s}}^1$) and F²(s), s ∈ [0 mm, ${\overline{s}}^2$)

Fig. 5

Decomposition of the complete system solution space Ω_c (thick black) for the simple crash design problem with d^k = 1 into ${\Omega}_{\mathrm{bs}}^1$, ${\Omega}_{\mathrm{bs}}^2$ (thin black) and ${\Omega}_{\mathrm{as}}^1$, ${\Omega}_{\mathrm{as}}^2$ (gray)

Fig. 6

Decomposition of the complete system solution space Ω_c for the simple crash design problem with d^k = 2 into ${\Omega}_{\mathrm{bs}}^1$, ${\Omega}_{\mathrm{bs}}^2$ (black) and ${\Omega}_{\mathrm{as}}^1$, ${\Omega}_{\mathrm{as}}^2$ as (gray)

Fig. 7

Component solution spaces Ω^k and their corresponding region of possibly permissible characteristics both bounded by solid gray lines for different d^k. Inside, there are permissible (white dots) or non-permissible (gray dots) force–deformation characteristics. Outside, they are always non-permissible (black dots)

Fig. 8

Total volume (left) and average edge length (right) of box-shaped (bs) and arbitrarily shaped (as) component solution spaces

Fig. 9

CPU time for Intel(R) Xeon(R) CPU E5-1660 v4 @ 3.20 GHz to calculate box-shaped (bs) and arbitrarily shaped (as) component solution spaces with analytically calculated volume

Fig. 10

Vehicle front structure for the realistic crash design problem with eight components. The gray parts indicate deformable structure and the black parts non-deformable structure

Fig. 11

Regions of possibly permissible characteristics from optimal component solution spaces for optimal arbitrarily shaped component solution spaces (gray) and lower and upper bounds of the optimal box-shaped component solution spaces (black)