A variational differential quadrature formulation for buckling analysis of anisogrid composite lattice conical shells

doi:10.1007/s10483-025-3310-9

Abstract

Abstract:

Anisogrid composite lattice conical shells, which exhibit varying stiffness along their cone generators, are widely used as interstage structures in aerospace applications. Buckling under axial compression represents one of the most hazardous failure modes for such structures. In this paper, the smeared stiffness method, which incorporates the effect of component torsion, is used to obtain the equivalent stiffness coefficients for composite lattice conical shells with triangular and hexagonal patterns. A unified framework based on the variational differential quadrature (VDQ) method is established, leveraging its suitability for asymptotic expansion to determine the critical buckling loads and the $b$ -imperfection sensitivity parameter of lattice conical shells with axially varying stiffness due to rib layout. The influence of pre-buckling deformation is taken into account to enhance the accuracy of predictions on the linear buckling loads. The feasibility of the present equivalent continuum model is verified, and the differences in buckling behaviors for composite lattice conical shells with both triangular and hexagonal unit cells are numerically evaluated through the finite element (FE) simulations and the VDQ method.

Key words: lattice conical shell, smeared stiffness method, variational differential quadrature (VDQ) method, parametric finite element (FE) model, buckling

2010 MSC Number:

O317

Yongqi LIU, Jianwei WANG, Dong DU, Guohua NIE. A variational differential quadrature formulation for buckling analysis of anisogrid composite lattice conical shells. Applied Mathematics and Mechanics (English Edition), 2025, 46(11): 2155-2176.

TrendMD

Figures/Tables 15

Fig.?1

Fig.?2

Fig.?3

Fig.?4

Fig.?5

Table?1

Critical buckling loads Pcr (kN) obtained from the continuum model"

$ϕ 1 / (∘)$	$H = 2$ mm, $b h = b c = 8$ mm	$H = 4$ mm, $b h = b c = 4$ mm	$H = 8$ mm, $b h = b c = 2$ mm
16.47	87.47	189.03	420.20
24.40	126.83	271.11	595.33
32.01	162.45	344.70	746.34
37.83	186.74	393.57	844.49
44.73	212.29	443.88	942.19

Table?1

Table?2

Critical buckling loads Pcr (kN) of triangular lattice shells obtained from FE simulations"

$ϕ 1 / (∘)$	$H = 2$ mm, $b h = b c = 8$ mm	$H = 4$ mm, $b h = b c = 4$ mm	$H = 8$ mm, $b h = b c = 2$ mm
16.47	78.12	177.32	182.68*
24.40	118.88	261.65	334.54*
32.01	155.93	338.09	502.24*
37.83	185.05	392.08	640.50*
44.73	213.07	448.34	796.11*
* local in-plane buckling

Table?2

Table?3

Critical buckling loads Pcr (kN) for hexagonal lattice shells obtained from FE simulations"

$ϕ 1 / (∘)$	$H = 2$ mm, $b h = b c = 8$ mm	$H = 4$ mm, $b h = b c = 4$ mm	$H = 8$ mm, $b h = b c = 2$ mm
16.47	76.84	163.20	339.64
24.40	116.71	241.91	496.42
32.01	154.33	315.71	645.72
37.83	181.23	369.71	755.76
44.73	210.70	426.78	870.87

Table?3

Table?4

Comparison of VDQ-predicted buckling loads with FE results"

$ϕ 1 / (∘)$	$H = 2$ mm, $b h = b c = 8$ mm	$H = 4$ mm, $b h = b c = 4$ mm	$H = 8$ mm, $b h = b c = 2$ mm
16.47	$P V > P T > P H$	$P V > P T > P H$	$P V > P H > P T$
24.40	$P V > P T > P H$	$P V > P T > P H$	$P V > P H > P T$
32.01	$P V > P T > P H$	$P V > P T > P H$	$P V > P H > P T$
37.83	$P V > P T > P H$	$P V > P T > P H$	$P V > P H > P T$
44.73	$P T > P V > P H$	$P T > P V > P H$	$P V > P H > P T$
* $P V$ denotes the critical buckling load calculated by the VDQ method based on the equivalent continuum model; $P T$ and $P H$ refer to the results by the FE model of composite lattice conical shells with triangular unit cell and hexagonal unit cell, respectively

Table?4

Fig.?6

Fig.?7

Fig.?8

Fig.?9

Fig.?10

Fig.?11

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