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

TL;DR

This paper introduces a novel SPH formulation for analyzing thin plate and shell structures undergoing large deformations and rotations, using a single-layer surface-particle approach with stability-enhancing techniques.

Contribution

It develops a reduced-dimensional SPH method based on Uflyand-Mindlin theory, incorporating correction matrices, damping, and hourglass control for improved stability and accuracy.

Findings

Accurately models finite deformation and large rotation in thin structures.

Demonstrates stability and accuracy through comprehensive tests.

Outperforms existing methods in capturing complex behaviors.

Abstract

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.