Simulating plate and shell structures with anisotropic resolution using adaptive smoothed particle hydrodynamics

When simulating plate and shell structures characterized by large aspect ratios, reduced-dimensional models are frequently employed due to their notable reduction in computational overhead in contrast to traditional isotropic full-dimensional models. However, in scenarios involving variations in the thickness direction, where adequate resolution in this dimension is required, reduced-dimensional models exhibit limitations. To capture variations in the thickness direction while simultaneously mitigating computational costs, an anisotropic full-dimensional model, integrated with an adaptive smoothed particle hydrodynamics method (ASPH), is developed for simulating behaviors of plate and shell structures in this study. The correction matrix, which is applied to ensure the first-order consistency, is modified accordingly by incorporating the nonisotropic kernel into it within the total Lagrangian framework of ASPH. A series of numerical examples, along with a specific application concerning the deformation of a porous film due to nonuniform internal fluid pressure in the thickness direction, are conducted to assess the computational accuracy and efficiency of the proposed ASPH method. Comparative analyses of our results against reference data and traditional isotropic SPH solutions demonstrate close agreements, affirming the suitability of the present ASPH method across various scenarios.