# Discrete material selection and structural topology optimization of composite frames for maximum fundamental frequency with manufacturing constraints

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## Abstract

This paper proposes a methodology for simultaneous optimization of composite frame topology and its material design considering specific manufacturing constraints for the maximum fundamental frequency with a bound formulation. The discrete material optimization (DMO) approach is employed to couple two geometrical scales: frame structural topology scale and microscopic composite material parameter scale. The simultaneous optimization of macroscopic size or topology of the frame and microscopic composite material design can be implemented within the DMO framework. Six types of manufacturing constraints are explicitly included in the optimization model as a series of linear inequality or equality constraints. Sensitivity analysis with respect to variables of the two geometrical scales is performed using the semi-analytical sensitivity analysis method. Corresponding optimization formulation and solution procedures are also developed and validated through numerical examples. Numerical study shows that the proposed simultaneous optimization model can effectively enhance the frame fundamental frequency while including specific manufacturing constraints that reduce the risk of local failure of the laminated composite. The proposed multi-scale optimization model for the maximum fundamental frequency is expected to provide a new choice for the design of composite frames in engineering applications.

## Keywords

Topology optimization Maximum fundamental frequency Semi-analytical sensitivity analysis Manufacturing constraints Discrete material selection Jacket composite frames## Notes

### Funding information

Financial supports for this research were provided by the National Natural Science Foundation of China (nos. 11672057, 11711530018, and 11372060), the National Key R&D Program of China (2017YFC0307203), Program (LR2017001) for Excellent Talents at Colleges and Universities in Liaoning Province, the 111 project (B14013), the Fundamental Research Funds for the Central Universities (DUT19ZD204), the Korea Institute of Energy Technology Evaluation and Planning, and the Ministry of Trade Industry & Energy of the Republic of Korea (no. 20172010000830). These supports are gratefully recognized.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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