Inverse determination of local variations of constituent level elastic parameters of FRP composite plates

Figures & data

Figure 1. Flowchart of the optimization algorithm.

Table 1. Material properties for the test plate.

	Fibre volume fraction ($V_f$)	0.10
Fibre outside ‘patch’	Mass density (${\rho }_{fiber}$)	2540 kg m^−3
	Elastic modulus ($E_{fiber}$)	70 GPa
	Poisson’s ratio (${\nu }_{fiber}$)	0.22
Fibres inside ‘patch’	Mass density (${\rho }_{patch}$)	2540 kg m^−3
	Elastic modulus ($E_{patch}$)	66 GPa/77 GPa
	Poisson’s ratio (${\nu }_{patch}$)	0.22
Epoxy matrix	Mass density (${\rho }_{matrix}$)	1200 kg m^−3
	Elastic modulus ($E_{matrix}$)	3 GPa
	Poisson’s ratio (${\nu }_{matrix}$)	0.35

Table 2. First six natural frequencies of the ‘patch’ plate.

Serial number of modes	FRP plate with ‘patch’ (Hz)
1	62.374
2	121.24
3	144.81
4	177.62
5	186.25
6	317.20

Table 3. Difference in frequencies of an example plate with and without the presence of a ‘patch’.

Modes	With patch (Hz)	Without patch (Hz)	Diff. (%)
1	62.374	62.392	0.03
2	121.24	123.64	1.98
3	144.81	145.45	0.44
4	177.62	179.45	1.03
5	186.25	186.35	0.05
6	317.2	318.19	0.31
7	342.14	349.11	2.04
8	380.37	383.98	0.95
9	383.93	385.89	0.51
10	432.12	433.13	0.23

Figure 2. Convergence plots for (a) fibre, (b) matrix and (c) ‘patch’ moduli without noise in ‘test’ data.

Figure 3. Convergence plots for (a) fibre, (b) matrix and (c) ‘patch’ moduli with noise in ‘test’ data.

Figure 4. Convergence plots for (a) fibre, (b) matrix and (c) ‘patch’ moduli with a 20% sized patch and having noise in ‘test’ data.

Figure 5. Convergence of ‘patch’ moduli with noise in ‘test’ data.

Figure 6. Convergence of the ‘patch’ modulus with noise in ‘test’ data using frequency and FRFs.

Figure 7. Dimensions of the test plate with a ‘patch’ having different elastic properties.

Table 4. Natural frequencies of the ‘patch’ plate and the reference plate.

Serial number of modes	FRP plate with ‘patch’ (Hz)	FRP reference plate (Hz)
1	36.87	36.91
2	45.38	44.8
3	87.93	86.95
4	128.49	125.86
5	169.99	166.95
6	279.23	324.08

Figure 8. Measured mode shapes of the ‘patch’ plate and the reference plate.

Figure 9. Comparison of mode 6 for the plates with and without ‘patch’.

Figure 10. Computed FE mode shapes of the ‘patch plate’.

Figure 11. Convergence curves for the elastic modulus of (a) matrix (b) fibre outside the ‘patch’ and (c) fibre within the ‘patch’.

Table 5. Quasi-static characterization test results.

Longitudinal modulus (E1)	39.6 GPa
Transverse modulus (E2)	1.12 GPa
In-plane shear modulus (G12)	0.36 GPa
In-plane Poisson’s ratio (υ12)	0.34