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Inverse Problems in Science and Engineering Volume 23, 2015 - Issue 1
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Articles

Two-step shape optimization methodology for designing free-form shells

Yang LiuDepartment of Advanced Science and Technology, Toyota Technological Institute, Nagoya, Japan.Correspondence[email protected]
&
Masatoshi ShimodaDepartment of Advanced Science and Technology, Toyota Technological Institute, Nagoya, Japan.
Pages 1-15 | Received 18 Sep 2012, Accepted 31 Mar 2013, Published online: 29 Apr 2013

Figures & data

Fig. 1 Shell geometry assembled by infinitesimal flat surfaces.

Fig. 1 Shell geometry assembled by infinitesimal flat surfaces.

Fig. 2 Shape variation of shell by V.

Fig. 2 Shape variation of shell by V.

Fig. 3 Definition of the notation n in Equations (20) and (21).

Fig. 3 Definition of the notation n in Equations (20) and (21).

Fig. 4 Free-form optimization method.

Fig. 4 Free-form optimization method.

Fig. 5 Schematic of the two-step free-form optimization methodology.

Fig. 5 Schematic of the two-step free-form optimization methodology.

Fig. 6 Boundary conditions of square-plate design problem.

Fig. 6 Boundary conditions of square-plate design problem.

Fig. 7 Obtained shape of square plate problem.

Fig. 7 Obtained shape of square plate problem.

Fig. 8 Iteration histories of step 1 and step 2.

Fig. 8 Iteration histories of step 1 and step 2.

Fig. 9 Comparison of strain energy components.

Fig. 9 Comparison of strain energy components.

Fig. 10 Boundary conditions of L-shaped bracket design problem.

Fig. 10 Boundary conditions of L-shaped bracket design problem.

Fig. 11 Obtained shape of L−shaped bracket problem.

Fig. 11 Obtained shape of L−shaped bracket problem.

Fig. 12 Iteration histories of step 1 and step 2.

Fig. 12 Iteration histories of step 1 and step 2.

Fig. 13 Comparison of strain energy components.

Fig. 13 Comparison of strain energy components.

Fig. 14 Boundary conditions of Spherical Shell design problem.

Fig. 14 Boundary conditions of Spherical Shell design problem.

Fig. 15 Obtained shape of Spherical Shell design problem.

Fig. 15 Obtained shape of Spherical Shell design problem.

Fig. 16 Iteration histories of step 1 and step 2.

Fig. 16 Iteration histories of step 1 and step 2.

Fig. 17 Comparison of strain energy components.

Fig. 17 Comparison of strain energy components.

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