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.

中文翻译：

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使用自适应平滑粒子流体动力学模拟具有各向异性分辨率的板壳结构


在模拟具有大纵横比的板壳结构时，经常采用降维模型，因为与传统的各向同性全维模型相比，降维模型显着减少了计算开销。然而，在涉及厚度方向变化的情况下，需要在该维度上有足够的分辨率，降维模型表现出局限性。为了捕获厚度方向的变化，同时降低计算成本，本研究开发了与自适应平滑粒子流体动力学方法（ASPH）集成的各向异性全维模型，用于模拟板壳结构的行为。在ASPH的总拉格朗日框架内，通过将非各向同性核纳入校正矩阵来相应地修改用于确保一阶一致性的校正矩阵。通过一系列数值算例以及有关由于厚度方向上不均匀内部流体压力导致的多孔膜变形的具体应用，以评估所提出的 ASPH 方法的计算精度和效率。我们的结果与参考数据和传统各向同性 SPH 解决方案的比较分析显示出密切的一致性，证实了当前 ASPH 方法在各种情况下的适用性。