# Coordinative optimization method of composite laminated structures based on system reliability

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## Abstract

This paper develops the coordinative optimization method based on system reliability for laminated structures. The proposed method improves the rough RBO based on first layer failure (FLF) criterion for composite laminates, and the coupling optimization method of thickness and sequence in traditional RBO strategy based on last layer failure criterion (LLF) is improved. In this paper, the finite element analysis is used to obtain the response for the failure based on two-dimension Hashin failure criterion (the limit function). Obviously, the stiffness of composite materials will decline due to destruction of elements. Therefore, stiffness degradation is considered to describe the process of damage evolution. Subsequently, combining with the branch-bound method (B&B), we can complete the search of main failure sequences and calculate the system reliability with the help of the second-order upper bound theory. In order to guarantee the efficiency and accuracy of optimization, the adaptive GA algorithm is introduced in the whole optimization procedure. After the proposed optimization policy is given in detail, two laminated structures are presented and the results are compared with the traditional optimal method based on safety factor, which demonstrates the validity and reasonability of the developed methodology.

## Keywords

System reliability optimization Last layer failure criterion Laminated structures Hashin failure criterion Finite element analysis## Notes

### Acknowledgements

The authors would like to thank the National Key Research and Development Program (No. 2016YFB0200700), the Defense Industrial Technology Development Program (No. JCKY2016601B001, No. JCKY2017601B001) P. R. China (11432002, 11572024, 11872089) and for the financial supports. Besides, the authors wish to express their many thanks to the reviewers for their useful and constructive comments.

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