Abstract
This chapter focuses on mixed finite element (FE)-experimental frequency based inverse identification of three-dimensional (3D) elastic behaviour of multilayer unidirectional (UD) carbon fibre reinforced plastic (CFRP) composites using a robust multi-objective evolutionary optimization procedure. This combines numerical sensitivity analysis through FE design of experiments, response surfaces methodology-based meta-modelling and a non-sorting genetic algorithm of second generation. All identifiable 3D elastic behaviours are considered as well as uncertainties of material properties. The sensitivity analyses show that the four engineering constants that describe the two-dimensional (2D) elasticity are dominant for the considered freely vibrating UD CFRP thin plate. Differently from its manufacturer’s assumption as quasi-isotropic and its 2D inverse identification as orthotropic, this sample’s 3D elastic behaviour is identified as transversely isotropic before sensitivity analyses, but orthotropic after the latter, i.e. using the four dominant in-plane engineering constants during the multi-objective optimization.
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Abbreviations
- 2D:
-
Two-dimensional
- 3D:
-
Three-dimensional
- ANOVA:
-
Analysis of variance
- CFRP:
-
Carbon fibre reinforced plastic
- DoE:
-
Design of experiments
- err:
-
Error
- FE:
-
Finite element
- I:
-
Isotropic
- MSE:
-
Mean square error as defined in (28b)
- NSGA II:
-
Non-sorting genetic algorithm of second generation
- orth:
-
Orthotropic
- QI:
-
Quasi-isotropic
- QTI:
-
Quasi-transversely isotropic
- R2 :
-
Determination factor as defined in (28a)
- RSM:
-
Response surface methodology
- TI:
-
Transversely isotropic
- UD:
-
Uni-directional
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Acknowledgment
The second author gratefully acknowledges the support of the Austrian Comet K2 Linz Centre of Mechatronics (LCM).
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Appendices
Appendix A
The plate C eight modal shapes, computed using Table 14.2 nominal data, are shown in Fig. 14.6, where the numbers between brackets indicate number of zero-crossing along width (x-axis) and length (y-axis) directions.
Beyond rigid body first eight modal shapes of plate C (using Table 14.2 nominal data)
Appendix B
Table 14.14 lists the numerical DoE complete factorial plan of size 25 = 32 for the TI behaviour sensitivity analysis and RSM meta-modelling. Notice that this behaviour’s symmetry relations (14.6) and (14.11) are coded within the DoE.
Appendix C
Table 14.15 lists the DoE complete factorial plan of size 24 = 16 for dominant constants-based orthotropic behaviour sensitivity analysis and RSM meta-modelling.
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Hamdi, M., Benjeddou, A. (2017). Robust Multi-objective Evolutionary Optimization-Based Inverse Identification of Three-Dimensional Elastic Behaviour of Multilayer Unidirectional Fibre Composites. In: Araujo, A., Mota Soares, C. (eds) Smart Structures and Materials. Computational Methods in Applied Sciences, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-44507-6_14
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DOI: https://doi.org/10.1007/978-3-319-44507-6_14
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