Geometrically nonlinear analysis of thin-walled structures using efficient Shell-based SPH method

• New shell-based SPH model using only 1 layer of particles at the shell mid-surface.
• SSPH model based on Reissner–Mindlin theory, accounting for transverse shearing.
• Vector parameterization of rotations for the treatment of very large 3D rotations.
• CPU time savings compared to the classical continuum SPH method.
• Better results with the new SSPH model compared to the classical continuum SPH.

In this paper a shell-based meshless formulation is proposed for the geometrically nonlinear analysis of thin-walled structures using an explicit dynamics scheme based on the Smoothed Particle Hydrodynamics (SPH) method. In the present investigation the SPH method is modified to deal with shell-like structures, while keeping its character of a strong formulation based on the principle of collocation directly applied on the differential equilibrium equations. The current SPH formulation is an extension of the continuum-improved and stabilized SPH method allowing a thin structure to be modeled using only one layer of particles to represent the shell mid-surface. Application of the present Shell-based SPH (SSPH) formulation for the analysis of several benchmarks including geometrically nonlinear behavior shows its validity and its potential especially in terms of CPU time saving while keeping a very good level of accuracy compared to the classical SPH method and to the Finite Element method.