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针对冲击波作用下水下结构与无限声学水域的流固耦合问题,建立了基于比例边界有限元法和有限元法的瞬态分析方法。无限水域用比例边界有限元法离散,而水下结构等有限域用有限元法模拟。该方法利用声学近似法将无限水域施加给水下结构的载荷分解成冲击波载荷和散射波载荷。冲击波载荷由水下冲击波理论确定,而散射波载荷由比例边界有限元法估值。为改善比例边界有限元法动态质量矩阵的计算效率,发展了动态质量矩阵的时域递推公式。数值算例分析结果表明了所发展的瞬态分析方法和时域递推公式的正确性。
Aimed at the problem of fluid-solid coupling between underwater structure and infinite acoustic waters under shock wave, a transient analysis method based on proportional boundary finite element method and finite element method is established. The infinite waters are discretized by the proportional boundary finite element method, while the finite fields such as the underwater structure are simulated by the finite element method. The method uses acoustic approximation to decompose the load applied to underwater structures in an infinite water area into shock wave loads and scattered wave loads. Shock wave loading is determined by the underwater shock wave theory, while the scattered wave loading is estimated by the proportional boundary finite element method. In order to improve the computational efficiency of the dynamic mass matrix of the proportional boundary finite element method, a time-domain recurrence formula of the dynamic mass matrix is developed. Numerical examples show the correctness of the developed transient analysis method and the time-domain recursion formula.