Fig.1

Typical cases of stiffened aerospace structures

Fig.2

Static analysis conditions of bypass engine casing

Fig.3

Buckling analysis conditions of bypass engine casing

Table 1

Material properties of titanium alloy

Table 2

Stress status of bypass engine casing critical position under ultimate load conditions

Fig.4

Simplification of bypass engine casing and design domain definition

Table 3

Topology optimization results of bypass engine casing under different load conditions

载荷工况	拓扑优化结果	加筋布局特点
F1		斜置正交/轴向加筋
F3		轴向加筋
M1		轴向/交叉加筋
P1		周向加筋
全工况		混合加筋

Fig.5

Initial arrangements of stiffening ribs at different segments of bypass engine casing

Fig.6

Stiffened cylinders and buckling load conditions

Table 4

Comparison of critical buckling loads of stiffened cylinder under different conditions

Fig.7

Comparison of buckling resistance of different stiffened patterns

Fig.8

Stiffened bypass engine casing and buckling load conditions

Table 5

Comparison of critical buckling loads of stiffened bypass engine casing under different conditions

加筋构型	轴向压力/N	弯矩/（N∙m）	扭矩/（N∙m）	外部压强/MPa
矩形加筋	4.91×105	9.55×104	1.36×105	0.199
斜置正交加筋	4.44×105	8.70×104	1.51×105	0.204
三角形加筋	4.06×105	8.05×104	1.51×105	0.217
六边形加筋	5.95×105	11.5×104	1.12×105	0.133
三角形加筋 屈曲模态
失效模式	局部屈曲	局部屈曲	整体屈曲	整体屈曲

Fig.9

Initial arrangements of hierarchical stiffening ribs of bypass engine casing

Fig.10

First principal stress field of initial bypass engine casing under ultimate load condition

Fig.11

Response surfaces of stress level and critical buckling load of bypass engine casing

Fig.12

Response surfaces of stiffening ribs geometry and mechanical performance indices of bypass engine casing

Table 6

Symbol meaning comparison table

Fig.13

Response surface of stiffening optimization model of bypass engine casing

Fig.14

Geometry model of optimized bypass engine casing

Fig.15

First principal stress field of the optimized bypass engine casing under ultimate load condition

Fig.16

First-order buckling modes of the optimized bypass engine casing

Table 7

Performance comparison of the optimized bypass engine casing with reference one