Nose-shape optimization and simulation of projectiles penetrating into concrete target based on local interaction theory
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摘要: 以局部相互作用理论为基础，引入与弹体头部形状相关的开坑计算方法和归一化弹体头部形状方程，给出了任意头部形状弹体侵彻混凝土深度的计算模型。利用最大侵深法，得到了无量纲头部形状控制参数表达式及经典变分头部形状优化设计方法。理论计算及弹靶分离仿真模拟计算结果与实验结果吻合较好。研究结果表明：弹体头部相对半径较小时，球头锥形和球头卵形弹体优化后得到的头部形状分别为尖头锥形和尖头卵形；优化截头弹体的侵彻深度大于优化尖头弹体，而优化截锥形弹体的侵彻深度最大；弹体头部形状对弹体侵彻过载的影响显著，优化弹体头部形状可以有效地提高侵彻深度。Abstract: Based on the local interaction theory, we proposed a penetration depth model for projectiles with an arbitrary nose-shape penetrating into a concrete target in consideration of the cratering stage related to nose-shape and normalized nose-shape function. Furthermore, using the method of maximum depth of penetration, we presented an expression about the normalized control parameter of the nose-shape and the classical variational optimization of the nose-shape. The local interaction model prediction and simulation results accord well with the experimental data of different projectile nose shapes. The optimal analysis and simulation show that, when the relative radius of the projectile nose is small, the optimal spherical-tip projectile is similar to corresponding optimal sharp-tip projectile, and the optimized truncated-tip projectiles have better penetration performance than that of the corresponding sharp-tip projectile. Compared with other nose-shaped projectiles, the optimized truncated-conical projectile has a relatively greater penetration depth. As the shape of the projectile nose affects its overload in the penetration process, the optimized shape of the projectile nose can effectively improve the penetration depth of the projectile.
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图 1 任意头部形状弹体局部相互作用模型
Figure 1. Local interaction model of projectile with arbitrary nose-shape
图 4 不同头部形状弹体侵彻混凝土的局部相互作用模型计算结果与实验数据对比
Figure 4. Comparison of local interaction model calculation with experimental results for projectiles with different nose shapes penetrating into concrete
图 5 典型回转形弹体头部形状控制参数最优值
Figure 5. Optimized control parameters of nose-shape for typical revolution projectiles
图 6 相对球头半径与头部形状控制参数的变化关系
Figure 6. Control parameter of nose-shape vs. normalized spherical radius
图 8 基于弹靶分离方法的弹体模型
Figure 8. Projectile model based on projectile-target separation method
图 9 弹体侵彻混凝土的模拟结果与实验数据对比
Figure 9. Comparison of simulation with experiment for projectiles penetrating into concrete
图 11 不同头部形状弹体速度与侵彻深度的关系
Figure 11. Penetration velocity vs. penetration depth for different optimal projectiles
图 12 不同头部形状弹体以800 m/s的初速度侵彻混凝土时加速度和瞬时侵彻深度时程曲线
Figure 12. Curves of acceleration and instantaneous penetration depth for projectiles with different nose shapes penetrating into concrete at an initial velocity of 800 m/s
表 1 弹体模型参数及混凝土材料参数
Table 1. Parameters for projectile geometry model and concrete material
弹体头部形状 实验编号 弹体模型参数 混凝土材料参数 m/kg dp/mm 弹体头形方程 σc/MPa ρt/(kg·m-3) 尖卵形 1[24] 4.43 57.0 Φ=[228.02-(x-110.4)2]1/2-199.5 35 2 450 2[25] 12.90 76.2 Φ=[228.62-(x-126.4)2]1/2-190.5 39 2 300 截卵形 3[26] 0.28 25.3 Φ=[90.12-(x-33.2)2]1/2-83.8 40 2 300 尖锥形 4[27] 0.08 10.0 Φ=x tan22.5° 44 2 200 5[27] 0.08 10.0 Φ=x 44 2 200 
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