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针对坝体在水平向激励下的瞬态耦合问题和基于比例边界有限元法,推导了等横截面半无限水库的动态刚度矩阵,其值用贝赛尔函数计算。基于该动态刚度矩阵,建立了有限元法与比例边界有限元法的耦合方程,分析了水平向激励下任意几何形状的半无限水库的瞬态响应。其中,半无限水库分解成用有限元离散的任意几何形状的近场域和用比例边界有限元法模拟的远场域即等横截面半无限水库。通过比较动态刚度矩阵和动态质量矩阵模拟等横截面半无限水库的计算效率,发现它们计算精度相同,但动态刚度矩阵效率更高。数值算例表明了所发展的动态刚度矩阵与其耦合方程的正确性。
Aiming to the transient coupling problem of horizontal dam under dam and the finite element method based on proportional boundary method, the dynamic stiffness matrix of half-infinite reservoirs with equal cross-section is deduced and its value is calculated by Bessel function. Based on the dynamic stiffness matrix, the coupled equations of finite element method and proportional boundary finite element method are established, and the transient response of a semi-infinite reservoir with arbitrary geometry under horizontal excitation is analyzed. Semi-infinite reservoirs are decomposed into near-field with arbitrary geometric shape discrete by finite element and far-field with equal-boundary finite element method. By comparing the dynamic stiffness matrix and the dynamic mass matrix to simulate the computational efficiency of semi-infinite reservoirs with equal cross-section, we found that the computational accuracy is the same, but the dynamic stiffness matrix is more efficient. Numerical examples show the correctness of the developed dynamic stiffness matrix and its coupled equations.