On the implementation of a nonlinear shell-based SPH method for thin multilayered structures

Abstract

An efficient Smoothed Particle Hydrodynamics method is developed in this paper for bending and buckling analysis of laminated composite plates and shells. The governing differential equations of thin structures is based on the First-order Shear Deformation Theory considering the geometrically nonlinear behavior. The Total Lagrangian Formulation is employed to avoid tensile instabilities, which represents one of the major defects of the original SPH method. Another drawback called boundary deficiency is alleviated by developing a Corrective Smoothed Particle Method, which combines with the Taylor series expansion. In order to demonstrate the effectiveness of the present shell-based SPH method, several numerical applications involving geometrically nonlinear behavior are carried out using the explicit dynamics scheme for the time integration. The results are compared with reference solutions and Finite Element results obtained using ABAQUS© commercial software. It has been shown, through the numerical applications that the shell-based SPH method using only one layer of particles is suitable for the study of laminated composite structures undergoing large transformations and therefore may constitute a good alternative to the FE method.