Topological Optimization and Dynamic Response of Periodic Porous Sandwich Structure under Impact Load
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摘要: 在等效静力方法框架下基于双向渐进结构优化硬杀法构建了冲击载荷下周期性多孔夹芯结构的拓扑优化方法。采用ABAQUS有限元软件，研究了周期性优化夹芯结构与梯形波纹芯层、矩形波纹芯层和随机Voronoi芯层夹芯梁在刚体以100 m/s的速度撞击下的变形失效模式。在载荷作用前期，优化夹芯结构的上半部分芯层被完全压缩，能量吸收优于其他3种结构；在载荷作用后期，由于优化夹芯结构的最终塑性变形较小，在整个响应过程中总能量吸收略小于其他3种结构。为检验单一载荷工况下优化夹芯结构在其他载荷作用下的性能，采用不同速度的刚体以3种不同类型的脉冲载荷加载，比较了4种夹芯结构的能量吸收性能。综合考虑夹芯结构上下面板的跨中挠度、比吸能、芯层吸能占比和平均冲击力后发现：在刚体冲击下，优化夹芯结构具有更好的能量吸收性能和抗冲击性能；在矩形脉冲下，优化夹芯结构的比吸能小于矩形波纹芯夹芯结构，未能体现结构优化的优势。研究表明，单一工况下优化所得的结构不能在任意载荷下均表现出最优异的性能，因此，针对不同的载荷工况，需要进一步的研究。Abstract: In this study, under the frame of equivalent static loads (ESL) method structural optimization and based on hard-kill bi-directional evolutionary structural optimization (hard-kill BESO), the topological optimization method for periodic porous sandwich structure under impact load was carried out. The commercial software ABAQUS was used to investigate the deformation patterns of the optimized periodic sandwich structure and the sandwich structures with trapezoidal, rectangular and random Voronoi cores under the impact load imposed by a rigid body with an initial velocity of 100 m/s. In the early stage of load, the upper half of the core layer of the optimized periodic sandwich structure is completely compressed and the energy absorption is higher than the other three structures. However, the total energy absorption of the optimal sandwich structure is slightly less than the other three due to the small plastic deformation at the end stage of load. To study the capabilities of the topologically optimized structure under different load conditions, the energy absorption performance of the four sandwich structures subjected to the rigid body impact loads at different velocities and three impulse loads were compared. After comprehensively considering the deflection at the centers of top and bottom panels, the specific energy absorption, the ratio of energy absorption of core layer, as well as the mean impact load, it shows that the optimized sandwich periodic structure performs higher energy absorption capability and resistance under the rigid body impact. The specific energy absorption of the optimal sandwich structure is less than the sandwich structure with rectangular core under rectangular impulse, losing advantages of the structural optimization. It indicates that the optimization design obtained under a single load condition cannot get the best performance for any load condition, and further research is required for different load conditions.
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Key words:
- topology optimization /
- impact load /
- sandwich periodic structure /
- energy absorption
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图 2 典型的具有m1× m2个单胞的二维周期结构
Figure 2. Representative two dimensional periodic structure with m1× m2 cells
图 3 冲击载荷下固支梁结构示意图
Figure 3. Schematic diagram of fixed sandwich structure subjected to impact load
图 6 不同芯层的夹芯结构示意图
Figure 6. Schematic diagram of sandwich structures with different cores
图 8 冲击载荷下不同夹芯结构的吸能时程曲线
Figure 8. Energy absorption of differnet sandwich structures versus time under impact load
图 9 不同速度的刚体撞击下不同结构上下面板的跨中挠度
Figure 9. Deflections at the center points of top and bottom panels of different sandwich structures under the rigid body impact at different velocities
图 10 不同速度的刚体撞击下夹芯结构的比吸能和芯层吸能占比EC/EW
Figure 10. Comparison of specific energy absorption and EC/EW of sandwich structures under the rigid body impact at different velocities
图 11 不同速度刚体撞击下结构受到的平均冲击力
Figure 11. Mean impact load received by sandwich structures under the rigid body impact at different velocities
图 12 不同脉冲下夹芯结构的变形
Figure 12. Deformations of sandwich structures under different impulse loads
图 13 不同脉冲下不同夹芯结构上下面板的跨中挠度
Figure 13. Deflections at the center points of top and bottom panels of sandwich structures under different impulse loads
图 14 不同脉冲下夹芯结构的吸能性能比较
Figure 14. Comparison of energy absorption of sandwich structures under different impulse loads
表 1 优化结构的上面板挠度与其他3种结构中上面板挠度的最大值的对比
Table 1. Comparison of top panel deflection of optimal structure and the maximum value of other three structures
v0/(m∙s−1) Core with the maximum deflection of the
top panel for other three structuresUt,max/mm $U{_{\rm {t} }^{ {\rm{op} } } }$/mm (Ut,max−$U{_{\rm {t} }^{ {\rm{op} } } }$)/mm Error/% 30 Rectangular core 5.20 4.17 1.03 19.8 50 Trapezoidal core 11.57 9.84 1.73 15.0 70 Rectangular core 21.28 16.73 4.55 21.4 100 Trapezoidal core 41.90 27.36 14.54 34.7 120 Trapezoidal core 54.28 35.86 18.42 33.9 150 Trapezoidal core 75.40 51.56 23.84 31.6 
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表 2 优化结构的下面板挠度与其他3种结构中最大值的对比
Table 2. Comparison of bottom panel deflection of optimal structure and the maximum value of other three structures
v0/(m∙s−1) Core with the maximum deflection of the
bottom panel for other three structuresUb,max/mm $U{_{\rm {t} }^{ {\rm{op} } } } $/mm (Ub,max−$U{_{\rm {t} }^{ {\rm{op} } } } $)/mm Error/% 30 Rectangular core 5.05 1.32 3.73 73.9 50 Rectangular core 10.96 3.46 7.50 68.4 70 Rectangular core 18.20 7.08 11.12 61.1 100 Trapezoidal core 30.62 14.86 15.76 51.5 120 Trapezoidal core 49.75 21.47 28.28 56.8 150 Rectangular core 63.48 34.96 28.52 44.9
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