FE‐Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis

Abstract

The partition-of-unity method based on FE-Meshfree QUAD4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain high-order global approximations. This method yields high accuracy and convergence rate without necessitating extra nodes or DOFs. In this study, the FE-Meshfree method is extended to the free and forced vibration analysis of two-dimensional solids. A modified radial point interpolation function without any supporting tuning parameters is applied to construct the composite shape functions. The governing equations of elastodynamic problem are transformed into a standard weak formulation and then discretized into time-dependent equations which are solved via Bathe time integration scheme to conduct the forced vibration analysis. Several numerical test problems are solved and compared against previously published numerical solutions. Results show that the proposed FE-Meshfree QUAD4 element owns greater tolerance for mesh distortion and provides more accurate solutions.

A Gradient Stable Node‐Based Smoothed Finite Element Method for Solid Mechanics Problems

“…where D is the elastic matrix of the isotropic linear elastic material and σ � σ 11 σ 22 σ 12 T . Substituting equations (15) and (17) into equation (10) yields the following:…”

“…Hybrid schemes composed of meshfree and FEM methodologies may encompass the advantages of both while mitigating their respective shortcomings [11][12][13], such as the partition of the unity finite element method (PUFEM) [14], generalized finite element method (GFEM) [15], FEmeshfree [16,17], meshfree-enriched FEM (ME-FEM) [18], and RKPM [5,19]. Zeng and Liu [20] combined the strain-smoothing technique of meshfree methods [21] and the existing FEM technology to establish smoothed finite element methods (S-FEMs) including the CS-SFEM for both 2D and 3D problems [22,23], node-based SFEM (NS-FEM) for both 2D and 3D [24,25], edge-based SFEM (ES-FEN) for 2D and 3D [26,27], face-based SFEM (FS-FEM) for 3D [28], and other hybrid schemes such as αFEM [29,30], βFEM [31], and smoothed FE-meshfree [32].…”

A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

“…ere still exist a variety of gradient term constructions available for different cases [37,40,[62][63][64][65][66][67].…”