Analysis of multi-layers insulated sandwich panel with flexible shear connectors

Figures & data

Figure 1. Multi-Layers Insulated Sandwich Panel with Shear Connectors (Insulated cores are removed for illustration purpose).

Figure 2. Box plate-section with shear connectors for multi-layers sandwich panel.

Figure 3. Slip between layers.

Figure 4. Strain distribution.

Figure 5. Axial and bending moment on multi-layers sandwich panel.

Figure 6. Shear force distribution on 5-layers sandwich panel (a) side view, (b) plate-section, (c) typical shear force diagram.

Figure 7. WF section.

Figure 8. Multi-cell box section [10].

Figure 9. FE model for 4-layers 2-cell sandwich panel.

Table 1. Shear connector stiffness for single box.

	3-Layers		4-Layers		5-Layers
DCA %	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)
25%	2.64	18.64	2.19	15.43	1.91	13.47
50%	8.98	63.28	7.42	52.3	6.47	45.60
75%	37.66	265.2	30.97	218.08	26.88	189.32
100%	27006	190162	21133	148807	16288	114692

Table 2. Shear connector stiffness for WF.

	3-Layers		4-Layers		5-Layers
DCA %	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)
25%	5.5	38.6	4.58	32.25	3.96	27.87
50%	19.1	134.6	16.01	112.72	13.72	96.60
75%	89.4	629.6	75.14	529.10	62.22	438.15
100%	1.16E + 10	8.14E + 10	521545	3672440	123456	869310

Table 3. Shear connector stiffness for cantilever.

	3-Layers		4-Layers		5-Layers
DCA %	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)
25%	8.55	433.51	6.86	347.91	5.92	300.41
50%	30.30	1536.33	23.70	1201.79	20.27	1027.87
75%	150	7618	105	5348	87	4404
100%	1.00E + 10	5.07E + 11	9.92E + 09	5.03E + 11	9.97E + 09	5.06E + 11

Table 4. Shear connector stiffness for 2-cell.

	3-Layers		4-Layers		5-Layers
DCA %	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)	Analytical (N/mm^2)	FE (N/mm)
25%	3.54	24.90	2.92	20.55	2.55	17.95
50%	12.01	84.54	9.89	69.64	8.63	60.74
75%	50.40	354.88	41.18	290	35.76	251.78
100%	9.77 × 10^9	6.88 × 10^10	3.8 × 10^9	2.68 × 10^10	1.44 × 10^9	1.015 × 10^10

Figure 10. Stress distribution for 3-layers (single box).

Figure 11. Stress distribution for 3-layers (WF).

Figure 12. Stress distribution for 3-Layers (Cantilever).

Figure 13. Stress distribution for 3-layers (2-Cell).

Figure 14. Connector shear forces for 4-layers (2-cell) with different DCA: (a) 100%, (b) 75%, (c) 50% and (d) 25%.

Figure 15. Connector shear forces for 4-layers (2-cell) with 100% DCA (Layer elements are not shown for clarity).

Table 5. Average stress for single box (MPa).

Analytical				FE			Diff. between analytical and FE
DCA	3-Layers	4-Layers	5-Layers	3-Layers	4-Layers	5-Layers	3	4	5
25%	−1.14	−0.71	−0.50	−1.15	−0.73	−0.52	0.5%	2.4%	4.1 %
50%	−2.29	−1.42	−0.99	−2.29	−1.47	−1.07	0%	3.6%	7.1 %
75%	−3.42	−2.13	−1.48	−3.41	−2.20	−1.63	0.5%	3.5%	8.7 %
100%	−4.45	−2.71	−1.82	−4.32	−2.68	−1.85	3%	−1.1%	1.9 %

Table 6. Average stress for WF (MPa).

Analytical				FE			Diff. between analytical and FE
DCA	3-Layers	4-Layers	5-Layers	3-Layers	4-Layers	5-Layers	3	4	5
25%	−0.59	−0.37	−0.25	−0.59	−0.38	−0.27	1.1%	3.2%	5.1%
50%	−1.17	−0.73	−0.51	−1.18	−0.76	−0.55	0.3%	4%	7.7%
75%	−1.76	−1.10	−0.76	−1.75	−1.13	−0.83	0.6%	3.3%	7.9%
100%	−2.23	−1.35	−0.91	−2.16	−1.34	−0.92	3.3%	1.3%	1.7%

Table 7. Average stress for cantilever (MPa).

Analytical				FE			Diff. between analytical and FE
DCA	3-Layers	4-Layers	5-Layers	3-Layers	4-Layers	5-Layers	3	4	5
25%	−0.38	−0.23	−0.16	−0.33	−0.24	−0.17	12 %	4.8%	7.1%
50%	−0.75	−0.46	−0.32	−0.68	−0.48	−0.35	9.1%	4.6%	8.8%
75%	−1.11	−0.67	−0.47	−1.05	−0.70	−0.51	5.3%	3.8%	8.9%
100%	−1.32	−0.80	−0.54	−1.32	−0.82	−0.57	0.2%	2.2%	5.4%

Table 8. Average stress for 2-cell (MPa).

Analytical				FE			Diff. between analytical and FE
DCA	3-Layers	4-Layers	5-Layers	3-Layers	4-Layers	5-Layers	3	4	5
25%	−0.86	−0.71	−0.37	−0.86	−0.73	−0.39	0.3%	2.4%	4.0 %
50%	−1.72	−1.42	−0.74	−1.71	−1.47	−0.80	0.7%	3.6%	7.0 %
75%	−2.57	−2.13	−1.11	−2.54	−2.20	−1.20	1.2%	3.5%	8.0 %
100%	−3.35	−2.71	−1.35	−3.23	−2.68	−1.38	3.6%	1.1%	2.3 %

Figure 16. Mid-span deflection of 2-cell for multi-layers configurations.

Figure 17. Geometry of multi-layers.

Table 9. Geometry of different number of layers.

# of Layer	Layer Thickness (mm)	Insulation Core Thickness (mm)	Total Thickness (mm)
2-Layers	76.2 × 2	102 × 1	254.4
3-Layers	50.8 × 3	51 × 2	254.4
4-Layers	38.1 × 4	34 × 3	254.4

Figure 18. Pressure load applied.

Figure 19. CFRP geometry.

Table 10. Material properties.

Material	Young’s Modulus (MPa)	Poisson’s Ratio
Concrete	29,323	0.15
CFRP- (Long.)	262,000	0.30
CFRP- (Trans.)	186,158	0.30

Figure 20. Deflection of multi-layers with CFRP shear connector.

Figure 21. Stress on top surface of multi-layers with CFRP shear connector.

Table 11. Shear stiffness of multi-layers sandwich panels.

# of Layers	Displacement (mm)	Stiffness “K” (N/mm^2)
2-layers	1.49 × 10^-3	47.83
3-layers	5.03 × 10^-4	76.88
4-layers	2.55 × 10^-4	123.67

Table 12. Deflection and stress results of multi-layers with CFRP.

# of Layers	Deflection (mm)		Stress (MPa)		DCA %
	Analytical	FE	Analytical	FE
2-Layers	39	42	2.84	3.02	64%
3-Layers	41	44	4.82	4.94	74%
4-Layers	40	45	6.21	6.45	81%

M. Yossef, and A. Chen, A solution considering partial degree of composite action for insulated sandwich panels with general configuration flexible shear connectors, Eng. Struct., vol. 162, pp. 135–150, 2018. https://www.sciencedirect.com/science/article/pii/S0141029617314979.

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