In this paper, we propose a reduced-dimensional smoothed particle hydrodynamics (SPH) formulation for quasi-static and dynamic analyses of plate and shell structures undergoing finite deformation and large rotation. By exploiting Uflyand-Mindlin plate theory, the present surface-particle formulation is able to resolve the thin structures by using only one layer of particles at the mid-surface. To resolve the geometric non-linearity and capture finite deformation and large rotation, two reduced-dimensional linear-reproducing correction matrices are introduced, and weighted non-singularity conversions between the rotation angle and pseudo normal are formulated. A new non-isotropic Kelvin-Voigt damping is proposed especially for the both thin and moderately thick plate and shell structures to increase the numerical stability. In addition, a shear-scaled momentum-conserving hourglass control algorithm with an adaptive limiter is introduced to suppress the mismatches between the particle position and pseudo normal and those estimated with the deformation gradient. A comprehensive set of test problems, for which the analytical or numerical results from literature or those of the volume-particle SPH model are available for quantitative and qualitative comparison, are examined to demonstrate the accuracy and stability of the present method.

翻译：本文提出了一种降维光滑粒子流体动力学（SPH）公式，用于进行有限变形和大转角下板壳结构的准静态与动力学分析。通过利用Uflyand-Mindlin板理论，本表面粒子公式仅需在中面使用单层粒子即可解析薄壁结构。为处理几何非线性并捕捉有限变形与大转角，引入了两种降维线性重构修正矩阵，并建立了旋转角与伪法向量之间的加权非奇异转换。针对薄壁及中等厚度板壳结构，提出了一种新型非各向同性Kelvin-Voigt阻尼以提高数值稳定性。此外，引入了一种带自适应限制器的剪切缩放动量守恒沙漏控制算法，以抑制粒子位置与伪法向量之间及其与变形梯度估计值之间的不匹配。通过一组涵盖文献中解析解、数值解及体粒子SPH模型可定量与定性对比的综合算例，验证了本方法的精度与稳定性。