基于双向密度函数的空天轴对称结构拓扑优化

doi:10.7527/S1000-6893.2024.30585

Abstract

Abstract:

The structure optimization configuration obtained by topology optimization is often difficult to meet the manufacturing constraints due to the existence of internal closed holes. To control the specific shape of topology optimization results， a bidirectional density distribution function is proposed based on variable density method for axisymmetric structures in aerospace equipment. By converting the design variables from the pseudo density of each element to the control parameters of the bidirectional density distribution function， the structural materials will change along a specific direction in the process of topology optimization. The final pseudo density field distribution will also change with the specific expression of bidirectional density distribution function. Then， a linear weighted filtering method is used to filter the design variables to obtain a smoother material boundary. Furthermore， the sensitivity analysis of the structural mass and the maximum von Mises stress response to the design variables is carried out respectively， and the topology optimization framework of minimizing the maximum von Mises stress of the structure under the mass constraint is established. Meanwhile， to avoid the topology optimization from falling into the local optimal solution too early， the extension updating method is adopted for the grey element control parameters and the stress P-norm coefficient in the iterative process. Finally， typical aero-engine disks with aerospace axisymmetric structure are used to carry out the example verification. Under the premise of meeting the quality constraints， the material distribution gradually evolves towards the direction of stress minimization in the optimization process. The obtained topology optimization configuration has clear solid space interface， uniform stress distribution and high material utilization rate， demonstrating the effectiveness of the proposed method.

Key words: topology optimization, bidirectional density distribution function, aerospace axisymmetric structure, sensitivity analysis, manufacturing constraint

CLC Number:

V214.5

Yongxin SHI, Kuo TIAN, Bo WANG. Topology optimization of aerospace axisymmetric structures based on bidirectional density function[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(S1): 730585.

Figures/Tables 20

Fig.1

Fig.2

Fig.3

Table 1

Expressions of radial density distribution functions

线段	η	$ρ 1 r k, η$	$∂ ρ 1 / ∂ r k$
a	$η < r k$	0	0
b	$r k ≤ η < r k + R s i n θ$	$R - R c o s α$	$t a n α$
c	$r k + R s i n θ ≤ η < r k + w - R s i n θ$	$1 - R + R c o s θ - k (η - r k - R s i n θ)$	k
d	$r k + w - R s i n θ ≤ η ≤ r k + w$	$1 - R + R c o s α$	$t a n α$
e	$η > r k + w$	1	0

Table 1

Table 2

Expressions of axial density distribution functions

线段	ξ	$ρ 2 b i, ξ$	$∂ ρ 2 / ∂ b i$
a	$ξ ≥ b i + w$	0	0
b	$b i + w - R s i n θ ≤ ξ < b i + w$	$R - R c o s α$	$t a n α$
c	$b i + R s i n θ ≤ ξ < b i + w - R s i n θ$	$1 - R + R c o s θ - k (ξ - b i - R s i n θ)$	k
d	$b i ≤ ξ ≤ b i + R s i n θ$	$1 - R + R c o s α$	$t a n α$
e	$ξ < b i$	1	0

Table 2

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

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Topology optimization of aerospace axisymmetric structures based on bidirectional density function

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