A semi-analytical model of hydroelastic slamming for two-dimensional symmetric flexible bodies is presented in this paper. The hydrodynamic loads are computed using the analytical Modified Logvinovich Model (MLM) with account for elastic deflections of the body surface. The elastic deflections are described by the modal approach. The rigid and elastic motions of the body are computed at the same time together with the wetted part of the body surface. The coupled problem of elastic impact is reduced to a system of nonlinear ordinary differential equations, which is integrated in time by the implicit Newmark method with iterations at each time step. Both free fall and constant water entry cases are considered. The developed model is validated for flexible wedge and cylindrical shell water entry problems. Good agreements with existing experimental and numerical results are achieved. It is shown that the MLM significantly improves predictions of the deflections and stresses cause by the impact compared with the Wagner model of water impact. The developed model is suitable for efficient and accurate computations of water elastic impacts.

提出了一种二维对称弹性体的水弹性撞击的半解析模型。使用分析型修正的Logvinovich模型（MLM）并考虑了车身表面的弹性挠度来计算流体动力载荷。弹性挠度由模态方法描述。同时计算身体的刚度和弹性运动以及身体表面的湿润部分。弹性冲击的耦合问题被简化为一个非线性常微分方程系统，该系统通过隐式Newmark方法在每个时间步长进行迭代，从而及时进行积分。考虑自由落体和持续进水的情况。该开发模型针对柔性楔形和圆柱壳入水问题进行了验证。与现有的实验和数值结果达成了良好的协议。结果表明，与瓦格纳水冲击模型相比，MLM显着改善了由冲击引起的挠度和应力的预测。所开发的模型适用于高效，准确地计算水弹性冲击。