The stacking sequence optimisation of a filament wound composite bicycle frame using the data-driven evolutionary algorithm EvoDN2

Figures & data

Figure 1. Bicycle frame geometry 3D.

Figure 2. Beam model based on 3D geometry.

Table 1. Parameters of the bicycle frame beam model.

Element	Nodes	d [mm]	Name	Material
I	1,9	56	Down Tube	UMS40_55
II	9,7	56
III	7,2	56
IV	2,3	58	Head Tube	UMS40_53
V	3,4	48	Top Tube	t700_55
VI	4,1	40	Seat Tube	t700_55
VII	5,9	22	Chain Stay Right	UMS40_50
VIII	6,9	22	Chain Stay Left	UMS40_50
IX	5,8	18	Seat Stay	UMS40_50
X	6,8	18	Seat Stay	UMS40_50
XI	7,8	10	Damper	Steel
XII	8,9	18	Seat Stay	UMS40_50
XIII	8,9	18	Seat Stay	UMS40_50

Table 2. Composite material mechanical properties.

Material property	Symbol	Unit	UMS40_55	UMS40_53	UMS40_50	t700_55
Longitudinal Young’s modulus	E1	MPa	218600	210760	199000	130600
Transversal Young’s modulus	E2	MPa	7376	7184	6907	7376
Shear modulus	G12	MPa	5672	5419	5071	5672
Poisson’s ratio	ν12	–	0.345	0.347	0.35	0.345
Longitudinal tensile strength	XT	MPa	1950	1950	1950	1950
Longitudinal compressive strength	XC	MPa	1480	1480	1480	1480
Transversal tensile strength	YT	MPa	48	48	48	48
Transversal compressive strength	YC	MPa	200	200	200	200
Shear strength	S	MPa	80	80	80	80

Figure 3. Position of loaded points.

Table 3. Starting load case definition (Forces Fx, Fy, Fz [N] and moments Mx, My, Mz [Nmm]).

Table 4. Uphill load case definition (Forces Fx, Fy, Fz [N] and moments Mx, My, Mz [Nmm]).

Figure 4. Refining objectives through sequential cycles (Uphill): 1ply and TW.

Figure 5. Refining objectives through sequential cycles (Starting): 1ply and TW.

Table 5. Bicycle frame parameters obtained as a result of cyclic optimisation (Starting LC, 1ply winding).

		Tube 1		Tube 2		Tube 3		Tube 4
		α [DEG]	T [mm]	α [DEG]	T [mm]	α [DEG]	T [mm]	α [DEG]	T [mm]
Selected member parameters	Layer 1	0.1	0.33	0.1	1.10	1.2	0.33	2.1	1.27
	Layer 2	1.4	0.50	89.6	2.20	3.9	0.47	20.4	0.40
	Layer 3	6.5	0.85			0.9	0.41
TOTAL THICKNESS [mm]			1.68		3.30		1.21		1.67
F1	6787	[mJ]	Starting 1ply only
F2	0.21	[-]
F3	1.22	kg

Table 6. Modified parameters and corresponding objectives (Starting LC, 1ply winding).

		Tube 1		Tube 2		Tube 3		Tube 4
		α [DEG]	T [mm]	α [DEG]	T [mm]	α [DEG]	T [mm]	α [DEG]	T [mm]
Selected member parameters	Layer 1	0.8	0.83	0.1	1.10	2.1	1.21	2.1	1.27
	Layer 2	6.5	0.85	89.6	2.20			20.4	0.40
	Layer 3
TOTAL THICKNESS [mm]			1.68		3.30		1.21		1.67
F1	6794	[mJ]	Starting 1ply only – corr.
F2	0.21	[-]
F3	1.22	kg

Table 7. Isotropic material mechanical properties.

	Steel	Aluminium	Titanium
Modulus of Elasticity E [GPa]	210	68.9	100
Poissons Ratio [-]	0.3	0.33	0.34
Ultimate Tensile Strength (UTS)[MPa]	900	310	620
Shear Strength [MPa]	540	207	430
Density [g/cm^3]	7.8	2.7	4.48

Table 8. Objectives comparison (starting load case).

Objective starting	Composite	Steel		Aluminium		Titanium
	Value	Value	Ratio	Value	Ratio	Value	Ratio
F1	6787	6776		6799		6760
F2	0.21	0.52	2.48	0.36	1.71	0.37	1.76
F3	1.22	1.90	1.56	1.56	1.28	2.05	1.68

Table 9. Objectives comparison (uphill load case).

Objective uphill	Composite	Steel		Aluminium		Titanium
	Value	Value	Ratio	Value	Ratio	Value	Ratio
F1	1172	1158		1178		1178
F2	0.09	0.18	2.02	0.24	2.67	0.17	1.89
F3	1.21	2.04	1.69	2.34	1.93	2.19	1.81

Figure 6. Comparison of normalised stiffness and strength ratios for various materials.