Dynamic modeling of a three-dimensional braided compositethin plate considering braiding directions

doi:10.1007/s10483-025-3205-8

Abstract

Abstract:

Currently, there are a limited number of dynamic models available for braided composite plates with large overall motions, despite the incorporation of three-dimensional (3D) braided composites into rotating blade components. In this paper, a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established. Based on Kirchhoff's plate assumptions, the displacement variables of the plate are expressed. By incorporating the braiding directions into the constitutive equation of the braided composites, the dynamic model of the plate considering braiding directions is obtained. The effects of the speeds, braiding directions, and braided angles on the responses of the plate with fixed-axis rotation and translational motion, respectively, are investigated. This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions. It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.

Key words: three-dimensional (3D) braided composite, braiding direction, composite thin plate, large overall motion, dynamic model

2010 MSC Number:

O313.7

Chentong GAO, Huiyu SUN, Jianping GU, W. M. HUANG. Dynamic modeling of a three-dimensional braided compositethin plate considering braiding directions. Applied Mathematics and Mechanics (English Edition), 2025, 46(1): 123-138.

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Figures/Tables 17

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Table 1

Mechanical parameters of the matrix and yarn[34]"

Property	Matrix	Carbon fiber
$E 11$ /GPa	2.74	231
$E 22$ /GPa	–	15
$G 12$ /GPa	–	24
$G 23$ /GPa	–	5.03
$μ 12$	0.35	0.28

Table 1

Table 2

Calculation of elastic constants for the composite with 12° braided angle"

Method	$E x$ /GPa	$E y$ /GPa	$G x y$ /GPa	$G y z$ /GPa	$μ x y$	$μ y z$
Homogenization method	84.21	9.11	13.55	3.98	0.29	0.47
Fabric geometry model^[34]	98.50	12.12	16.46	4.23	0.34	0.48

Table 2

Table 3

Predicted values of the interior unit cell"

Braided angle/(°)	$E x$ /GPa	$E y$ /GPa	$G x y$ /GPa	$G y z$ /GPa	$μ x y$	$μ y z$
12	102.041	8.871	16.472	4.756	0.264	0.548
20	98.039	11.881	17.042	5.066	0.294	0.391
30	71.945	16.647	19.723	7.346	0.401	0.360
40	37.886	20.124	21.053	13.555	0.422	0.251

Table 3

Table 4

Predicted values of the surface unit cell"

Braided angle/(°)	$E x$ /GPa	$E y$ /GPa	$G x y$ /GPa	$G y z$ /GPa	$μ x y$	$μ y z$
12	80.002	9.893	12.672	3.545	0.326	0.408
20	71.947	10.406	12.932	3.991	0.280	0.330
30	61.733	13.818	13.554	4.675	0.264	0.260
40	43.676	20.162	21.651	6.257	0.213	0.181

Table 4

Fig. 6

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Fig. 13

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