球对称形式物质点法及其在水下爆炸中的应用

利用物质点法求解三维远场水下爆炸冲击响应问题时，爆炸冲击波到达结构物之前传播过程的计算会消耗大量的计算资源，影响求解效率。针对这一问题，并考虑到水下爆炸冲击波在自由场中的传播特点，提出了一维球对称形式的物质点法，对球形炸药水下爆炸过程进行了数值模拟，并与Cole公式以及DYNA计算结果进行了比较，结果吻合较好，验证了一维球对称形式物质点法的正确性。在此基础上，提出了基于物质点法的重映射算法，将爆炸冲击波在自由场中的传播过程在一维球对称模型中进行计算，并将计算结果映射到三维模型中，以便继续完成计算过程，有效避免了计算资源在冲击波传播过程计算上的消耗。

Spherically-symmetric form of the material point method with applications to underwater explosion

In solving the shock response problems of three-dimensional far-field underwater explosion by the material point method, the calculation of the propagation process of the shock wave before it reaches the structure will cost a large amount of computing resources and affect the computing efficiency. Aimed to this problem, a one-dimensional spherically-symmetric form of the material point method was proposed by taking into account the propagation characteristics of the underwater explosion shock waves in the free field. And the underwater explosion of the spherical explosive was numerically simulated by the proposed material point method. The simulated results are in good agreement with the ones obtained by the Cole formula and DYNA, and it can explain that the proposed material point method is feasible. On the basis of the above results, a re-mapping algorithm was brought forward based on the material point method. The blast wave propagation in the free field was calculated in the one-dimensional spherically-symmetric model, and the calculated results were mapped to the three-dimensional model to complete the calculation process. So the computation efficiency is improved greatly.