Meshfree methods: progress made after 20 years

JS Chen, M Hillman, SW Chi - Journal of Engineering Mechanics, 2017 - ascelibrary.org
In the past two decades, meshfree methods have emerged into a new class of computational
methods with considerable success. In addition, a significant amount of progress has been …

Implementation of different types of meshfree technique in computational solid mechanics: a comprehensive review across nano, micro, and macro scales

Z Al Mahmoud, B Safaei, S Sahmani, M Asmael… - … Methods in Engineering, 2024 - Springer
This work is considered as the first comprehensive review, that covers all types of meshfree
method including the traditional or developed meshless techniques that have been …

A meshfree approach using naturally stabilized nodal integration for multilayer FG GPLRC complicated plate structures

CH Thai, P Phung-Van - Engineering Analysis with Boundary Elements, 2020 - Elsevier
In this study, a meshfree approach using a naturally stabilized nodal integration (NSNI)
integrated with a higher-order shear deformation theory (HSDT) for free vibration analysis of …

Two-phase PFEM with stable nodal integration for large deformation hydromechanical coupled geotechnical problems

YF Jin, ZY Yin - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
The node-based strain smoothed particle finite element method (NS-PFEM) has a high level
of computational efficiency. However, it has not yet been extended to hydromechanical …

A stable node-based smoothed PFEM for solving geotechnical large deformation 2D problems

YF Jin, ZY Yin, XW Zhou, FT Liu - Computer Methods in Applied Mechanics …, 2021 - Elsevier
The strain smoothed nodal integration particle finite element method (NS-PFEM) has a high
level of computational efficiency. However, it suffers from the 'overly soft'problem. This study …

An accuracy analysis of Galerkin meshfree methods accounting for numerical integration

J Wu, D Wang - Computer Methods in Applied Mechanics and …, 2021 - Elsevier
Presently, it has been widely recognized that numerical integration plays a crucial role on
the solution accuracy of Galerkin meshfree methods due to the rational nature of meshfree …

Superconvergent gradient smoothing meshfree collocation method

D Wang, J Wang, J Wu - Computer Methods in Applied Mechanics and …, 2018 - Elsevier
A superconvergent meshfree collocation method with smoothed nodal gradients is
presented. In this method, the first order smoothed gradients of meshfree shape function are …

A truly meshfree method for solving acoustic problems using local weak form and radial basis functions

X You, W Li, Y Chai - Applied Mathematics and Computation, 2020 - Elsevier
It has been known that numerical solutions to Helmholtz problems obtained using several
numerical methodologies (eg finite element approach) are always plagued by the pollution …

A temporal stable smoothed particle finite element method for large deformation problems in geomechanics

WH Yuan, M Liu, N Guo, BB Dai, W Zhang… - Computers and …, 2023 - Elsevier
In this study, a stabilized smoothed particle finite element method (SPFEM) for modeling
nonlinear, large deformation dynamic problems in geomechanics is presented. The …

Upwind reproducing kernel collocation method for convection-dominated problems

J Wang, M Hillman - Computer Methods in Applied Mechanics and …, 2024 - Elsevier
Because of the best approximation property, traditional Bubnov–Galerkin numerical
methods have proven immensely successful in modeling self-adjoint problems, such as heat …