Distributed-parametric optimization approach for free-orientation of laminated shell structures with anisotropic materials

  • Yoshiaki Muramatsu
  • Masatoshi ShimodaEmail author
Research Paper


In this study, we propose a distributed-parametric material orientation optimization method for the optimal design of laminated composite shell structures consisting of anisotropic materials. We consider the compliance as the objective function and minimize it under the state-equation constraint. The material orientation in all the layers is treated as the design variable. The optimal design problem is formulated as a distributed-parameter optimization problem based on the variational method, and the sensitivity function with respect to the material orientation variation is theoretically derived. The optimal orientation variations are determined using the H1 gradient method with Poisson’s equation, where the derived sensitivity function is applied as the fictitious internal heat generation under the Robin condition to reduce the objective function while maintaining a smooth material orientation. With the proposed method, we can conventionally obtain the arbitrary optimal distribution of the material orientations of all the layers of complicated large-scale shell structures like aircraft or automotive bodies without design variable parameterization. The optimal results of the design examples show that the proposed optimization method can effectively obtain the optimal distribution of the material orientation in laminated shell structures.


Anisotropic material H1 gradient method Laminated shell structures Orthotropic shells Material orientation Optimization 


Funding information

This work was supported by a Grant-in Aid for Scientific Research, Grant Number 18K03853 given by the Japan Society for the Promotion of Science.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Advanced Science and Technology, Graduate School of EngineeringToyota Technological InstituteNagoyaJapan
  2. 2.Department of Advanced Science and TechnologyToyota Technological InstituteNagoyaJapan

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