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In this paper, we propose a reduced-dimensional smoothed particlehydrodynamics (SPH) formulation for quasi-static and dynamic analyses of plateand shell structures undergoing finite deformation and large rotation. Byexploiting Uflyand-Mindlin plate theory, the present surface-particleformulation is able to resolve the thin structures by using only one layer ofparticles at the mid-surface. To resolve the geometric non-linearity andcapture finite deformation and large rotation, two reduced-dimensionallinear-reproducing correction matrices are introduced, and weightednon-singularity conversions between the rotation angle and pseudo normal areformulated. A new non-isotropic Kelvin-Voigt damping is proposed especially forthe both thin and moderately thick plate and shell structures to increase thenumerical stability. In addition, a shear-scaled momentum-conserving hourglasscontrol algorithm with an adaptive limiter is introduced to suppress themismatches between the particle position and pseudo normal and those estimatedwith the deformation gradient. A comprehensive set of test problems, for whichthe analytical or numerical results from literature or those of thevolume-particle SPH model are available for quantitative and qualitativecomparison, are examined to demonstrate the accuracy and stability of thepresent method.

An SPH formulation for general plate and shell structures with finite deformation and large rotation