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摘要: 为了研究冲击载荷作用下考虑应力波效应弹性矩形薄板的动力屈曲，根据动力屈曲发生瞬间的能量转换和守恒准则，导出板的屈曲控制方程和波阵面上的补充约束条件，真实的屈曲位移应同时满足控制方程和波阵面上的附加约束条件。满足上述条件，建立了该问题的完整数值解法，对屈曲过程中冲击载荷、屈曲模态和临界屈曲长度之间的关系进行研究，定量计算了横向惯性效应对提高薄板动力屈曲临界应力的贡献。研究表明：板的厚宽比一定时，临界屈曲长度随冲击载荷的增大而减小；由于屈曲时的横向惯性效应，应力波作用下薄板一阶临界力参数是相应边界板的静力失稳临界力参数的1.5倍；随着边界约束逐渐减弱，板临界力参数逐渐减小，动力特征参数逐渐增大。Abstract: Dynamic buckling of thin rectangular plates under elastic compression waves caused by unaxial impact was investigated. Governing equations and a supplementary restraint-equation at compression wave front were obtained on the basis of energy transformation and conservation during buckling of plates; the real buckling displacement must fulfill the governing equations and the supplementary restraint-equation. Based on the requirements of above relations, a numerical method was established to solve the problem, and the relations of the amplitude of impulsive loads, buckling modes and critical buckling length were studied. Research results indicate that: critical buckling length decreases with the increase of impact load when the ratio of width to thickness of plate is fixed; the first order parameter of dynamic critical force is about 1.5 times of the same order parameter of static compression critical force; with weakening of boundary constraints, a smaller buckling load is required to cause the plate to buckle and transverse inertia increase gradually.
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图 1 矩形薄板受冲击载荷作用
Figure 1. The rectangular thin plate subjected to in-plane impact load
图 3 边界条件CCCC下薄板屈曲模态
Figure 3. The buckling modes of thin plate under boundary condition CCCC
表 1 临界力参数和动力特征参数
Table 1. Critical-load parameters and dynamic characteristic parameters
边界条件 σ/MPa Λ1(0) Λ1(1) Λ2(1) Λ1(2) Λ2(2) Λ1(3) Λ2(3) 180 9.35 14.34 3.56 19.95 6.92 26.34 10.21 CCCC 150 8.77 13.25 3.01 18.70 6.14 24.41 9.03 120 8.36 12.05 2.26 16.93 5.02 - - 180 9.04 14.10 3.87 19.79 7.42 26.26 10.66 CSCS 150 8.31 13.12 3.48 18.57 6.65 24.22 9.58 120 7.64 11.90 2.99 16.88 5.78 - - 180 8.81 13.87 4.18 19.71 7.90 25.56 11.26 CFCF 150 7.99 12.73 3.83 17.99 7.20 23.44 10.32 120 7.17 11.12 3.34 15.95 6.38 - - 
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