Abstract
This paper presents an approach to design composite panels via multiple stacking sequence tables (SST) such that the continuity constraints between adjacent regions are maintained. Traditional SST methods determine all the stacking sequences with only one SST, but this simplification limits the design option space. To increase the design freedom, this research utilizes multiple SSTs to blend the stacking sequences of a laminated structure. In the design process of the proposed approach, the monotonicity property of predicted laminate thicknesses is employed to determine the number of SSTs, and an SST rebuilding method is developed to satisfy the blending constraints. In the implementation of the simulated annealing algorithm for solving the optimal design problem, an SST difference code is introduced to represent feasible solutions, and a particular neighborhood structure is proposed to sufficiently explore the solutions in design space. Finally, the 18-region benchmark problem is chosen to validate the efficiency and accuracy of the proposed method. The results reveal that, compared with other existing methods, the proposed method can generate manufacturable solutions with lower weights under the symmetry and balance constraints.
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Acknowledgments
The authors would like to thank Mr. Kuan Fan for his support in programming work. In addition, we thank the anonymous reviewers for their comments and suggestions, which are valuable for improving the manuscript.
Funding
This project is supported by the National Natural Science Foundation of China (Grant Nos. 51775202 and 51475186).
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Appendices
Appendix 1. Calculation of buckling load factor
In this work, buckling of symmetrical and balanced laminates, simply supported on boundaries, under normal compressions (Fx,Fy) is analyzed. The formulation of buckling load factor λcb is as follows:
Here, m and n are the numbers of half wavelengths along x and y directions respectively, a and b are the length and width of region respectively, and D11, D12, D66, and D22 are bending stiffness obtained by classical lamination theory. The same formulation is used in (Soremekun et al. 2002; Adams et al. 2004; Irisarri et al. 2014; Yang et al. 2016; Jing et al. 2016a; Seresta et al. 2009; Fan et al. 2016; Ijsselmuiden et al. 2009; Park et al. 2008).
Appendix 2. Laminate thickness prediction
According to Eq. (4), λcb is a linear function of bending stiffness parameters, and reaches an extreme value with the same ply orientation at all stacking positions (Jing et al. 2016b). The multi-panel sequential permutation table (MSPT) method was developed in (Jing et al. 2016a, b) to predict the minimum thickness without considering the blending requirement. The algorithm for obtaining the minimum-thickness distribution with MSPT is summarized in Algorithm A1.
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Zeng, J., Huang, Z., Chen, Y. et al. A simulated annealing approach for optimizing composite structures blended with multiple stacking sequence tables. Struct Multidisc Optim 60, 537–563 (2019). https://doi.org/10.1007/s00158-019-02223-9
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DOI: https://doi.org/10.1007/s00158-019-02223-9