A novel frequency domain numerical method for Very Large Floating Structure (VLFS) hydroelasticity is developed. The problem is formulated in the 2D ocean waveguide, featuring a realistic seabed bathymetry and the presence of inhomogeneous, elastic plates of varying thickness and negligible draft. An in vacuo modal expansion for the elastic body deflection, modelled as a structural plate, is employed to decouple the hydrodynamics from structural mechanics. The inhomogeneous plate is considered to undergo cylindrical bending, while depending on the structure slenderness and excitation wavelength the classical thin plate theory and Mindlin’s model, accounting for first order shear deformation effects are implemented. A weighted residual approach is employed to cast the formulated problems into a mixed weak form for which dimensionality reduction is sought. This is achieved by an enhanced vertical representation for the wave potential, able to accurately account for abrupt bathymetric changes, following Athanassoulis and Belibassakis (1999). The reduced two-field, weak problem is solved by means of the Finite Element Method (FEM). Finally, a series of comparisons are carried out against published results for a range of configurations.

提出了一种用于超大型浮体结构（VLFS）水弹性的新型频域数值方法。该问题由二维海洋波导解决，具有逼真的海底测深法，并且存在厚度不等且可忽略不计的不均匀弹性板。一个真空弹性体挠度的模态膨胀，以结构板为模型，用于将流体力学与结构力学解耦。不均匀板被认为经历了圆柱弯曲，而根据结构的细长度和激发波长，实现了经典的薄板理论和Mindlin模型（考虑了一阶剪切变形效应）。采用加权残差法将制定的问题转换为需要降低维数的混合弱形式。遵循Athanassoulis和Belibassakis（1999）的方法，可以通过增强波势的垂直表示来实现这一点，它能够准确地说明水深的突然变化。简化的两场弱问题通过有限元方法（FEM）解决。最后，