Numerical simulations of large deformation of thin shell structures using meshfree methods

Abstract

In this paper, meshfree simulations of large deformation of thin shell structures is presented. It has been shown that the window function based meshfree interpolants can be used to construct highly smoothed (high order``manifold'') shape functions for three-dimensional (3-D) meshfree discretization/interpolation, which can be used to simulate large deformation of thin shell structures while avoiding ill-conditioning as well as stiffening in numerical computations.The main advantage of such 3-D meshfree continuum approach is its simplicity in both formulation and implementation as compared to shell theory approach, or degenerated continuum approach. Moreover, it is believed that the accuracy of the computation may increase because of using 3-D exact formulation. Possible mechanism to relieve shear/volumetric locking due to the meshfree interpolation is discussed. Several examples have been computed by using a meshfree, explicit, total Lagrangian formulation. Towards to developing a self-contact algorithm, a novel meshfree contact algorithm is proposed in the end.

Mesh‐free simulation of ductile fracture

“…The RKPM is a further development of the original SPH method [17,18]. Comprehensive development and application of the method have been performed by the computational mechanics group at Northwestern University, [22][23][24][25][26]. The basic idea of RKPM and the other so-called corrective SPH methods is to 'correct' the original SPH kernel (hereafter called window function), (X − X I ), to make the method a partition of unity so that rigid body motion can be correctly represented.…”

FEM and EFG Quasi-Static Explicit Buckling Analysis for Thin-Walled Members

“…Lu [15] developed an adaptive enrichment mesh-free method to capture wrinkling and post-buckling behavior in sheet metal forming. Li [16] used mesh-free method for numerical simulations of large deformation of thin shell structures, which showed simplicity in both formulation and implementation as compared to shell theory approach. Lin [17] used a non-linear dynamic explicit scheme for the post-buckling analysis of thin-walled structure based on the meshless shell formulation.…”

A meshfree thin shell method for non‐linear dynamic fracture

“…However, the shell was developed for small deformations, small strains and elasticity. Three dimensional modelling of shear deformable shells and degenerated shells in a meshfree context was studied by Noguchi et al [2], Li et al [3] and Kim et al [4]. Usually, a low order polynomial basis was used, e.g.…”

“…Usually, a low order polynomial basis was used, e.g. in [3], a trilinear polynomial basis was applied and the method was applied to several non-linear problems. However, for thin structures, three dimensional modelling of shell structures is computationally expensive.…”