Optimization of Combining Fiber Orientation and Topology for Constant-Stiffness Composite Laminated Plates

  • Xinxing TongEmail author
  • Wenjie GeEmail author
  • Xinqin Gao
  • Yan Li


This paper deals with an efficient optimization method of combining fiber orientation and topology for constant-stiffness composite laminated plates. The optimal topology and fiber orientation can be simultaneously obtained, using the proposed method. To overcome the non-monotonous behaviors derived from directly optimizing fiber orientation, the lamination parameters are selected as design variable. The proposed method mainly includes two steps. Initially, lamination parameters and density are taken as the design variables for determining the fiber orientation and topology shape. A combined optimization model is built based on the penalization theory. The optimal lamination parameter and topology shape can be achieved simultaneously in this step. Then, solving nonlinear equations is transformed into a least squares optimization problem. The optimal fiber orientation is obtained and matched with the optimal lamination parameter. Finally, numerical examples of designing short cantilever beam and compliant inverter are performed to illustrate the validity of this method.


Topology optimization Fiber orientation optimization Constant-stiffness composite laminated plates Lamination parameters 

Mathematics Subject Classification

49J35 74E30 74P05 74P15 



The paper was revised by Prof. Xinqin Gao for mathematical expositions and Prof. Yan Li for English service authors, which helped us to improve the paper. Author would like to thank for the support provided by the National Natural Science Foundation of China (Grant Numbers 51375383 and 51575443) and Doctor’s Research Foundation of Xi ’an University of Technology (Grant Number 102-451118017).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mechanical and Precision Instrument EngineeringXi’an University of TechnologyXi’anChina
  2. 2.School of Mechanical EngineeringNorthwestern Polytechnical UniversityXi’anChina

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