An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function

DOI10.1007/s00466-013-0912-1zbMath1398.74486OpenAlexW1976111545MaRDI QIDQ2512429

Charles E. Augarde, Xiaoying Zhuang, Hehua Zhu

Publication date: 7 August 2014

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: http://dro.dur.ac.uk/13553/1/13553.pdf

zbMATH Keywords

compatibilitypartition of unitymeshlessdelta propertyShepard shape function

Mathematics Subject Classification ID

Related Items (13)

Improved integration scheme for the second-order consistent element-free Galerkin method ⋮ The numerical simulation of the phase field crystal (PFC) and modified phase field crystal (MPFC) models via global and local meshless methods ⋮ A hydro-mechanical-damage fully coupled cohesive phase field model for complicated fracking simulations in poroelastic media ⋮ A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis ⋮ Free element boundary integration method for solving heat conduction and mechanics problems ⋮ Taylor particle-in-cell transfer and kernel correction for material point method ⋮ Detection of multiple flaws in piezoelectric structures using XFEM and level sets ⋮ Error estimate and adaptive refinement in mixed discrete least squares meshless method ⋮ An improved local boundary integral equation method implemented by the transformed MLS approximation with the delta property ⋮ Higher order schemes introduced to the meshless FDM in elliptic problems ⋮ A novel dynamic multilevel technique for image registration ⋮ Transgranular fracturing of crystalline rocks and its influence on rock strengths: insights from a grain-scale continuum-discontinuum approach ⋮ Error analysis of method of lines (MOL) via generalized interpolating moving least squares (GIMLS) approximation

Cites Work

• Unnamed Item
• Unnamed Item
• The cost of continuity: a study of the performance of isogeometric finite elements using direct solvers
• A PU-based meshless Shepard interpolation method satisfying delta property
• Analyzing 2D fracture problems with the improved element-free Galerkin method
• On error control in the element-free Galerkin method
• Reproducing kernel element method. I: Theoretical formulation
• Stable particle methods based on Lagrangian kernels
• Discontinuous modelling of shear bands using adaptive meshfree methods
• Meshless methods: a review and computer implementation aspects
• A meshfree method based on the local partition of unity for cohesive cracks
• Meshless methods: An overview and recent developments
• Reproducing kernel particle methods for large deformation analysis of nonlinear structures
• Consistent pseudo-derivatives in meshless methods
• Analysis of thin shells by the element-free Galerkin method
• Filters, reproducing kernel, and adaptive meshfree method
• A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods
• Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition.
• Numerical analysis of Biot's consolidation process by radial point interpolation method.
• A new cloud-based \(hp\) finite element method
• Analyzing the 2D fracture problems via the enriched boundary element-free method
• A three-dimensional large deformation meshfree method for arbitrary evolving cracks
• A Particle-Partition of Unity Method--Part II: Efficient Cover Construction and Reliable Integration
• Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling
• On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods
• Fracture modeling using meshless methods and level sets in 3D: Framework and modeling
• Coupling Meshfree Methods and FEM for the Solution of the Incompressible Navier-Stokes Equations
• A generalized approximation for the meshfree analysis of solids
• Modelling Elasto-Plasticity Using the Hybrid MLPG Method
• An Analysis for the Elasto-Plastic Fracture Problem by the Meshless Local Petrov-Galerkin Method
• A Local Meshless Shepard and Least Square Interpolation Method Based on Local Weak Form
• Immersed particle method for fluid-structure interaction
• Aspects of the use of orthogonal basis functions in the element-free Galerkin method
• Surfaces Generated by Moving Least Squares Methods
• The dual boundary element method: Effective implementation for crack problems
• Element‐free Galerkin methods
• An improved element free Galerkin formulation
• A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
• Assessment and applications of point interpolation methods for computational mechanics
• A Particle-Partition of Unity Method--Part III: A Multilevel Solver
• Cracking particles: a simplified meshfree method for arbitrary evolving cracks

This page was built for publication: An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function