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Article
A meshfree unification: reproducing kernel peridynamics
This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel parti...
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Article
An XFEM/Spectral element method for dynamic crack propagation
A high-order extended finite element method based on the spectral element method for the simulation of dynamic fracture is developed. The partition of unity for the discontinuous displacement is constructed by...
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Article
Tailoring the Load Carrying Capacity of MWCNTs Through Inter-shell Atomic Bridging
Recent studies have finally produced accurate measurements of the mechanical properties of carbon nanotubes, confirming the anticipated results computed from quantum and molecular mechanics. Several studies ha...
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Article
Application of Particle Methods to Static Fracture of Reinforced Concrete Structures
Particle methods for modeling reinforced concrete are described. The reinforcements are modeled by finite elements and are coupled to the particle method by Lagrange multipliers. The method is applicable to no...
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Article
Biological Structures Mitigate Catastrophic Fracture Through Various Strategies
Gao et al. (PNAS, 100, 5597–5600 (2003)) have argued that load-bearing mineralized hard tissues, including bones, shells, and teeth, are nanocomposites, in which the mineral phase has nanoscale dimensions that en...
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Article
Material stability analysis of particle methods
Material instabilities are precursors to phenomena such as shear bands and fracture. Therefore, numerical methods that are intended for failure simulation need to reproduce the onset of material instabilities...
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Article
An extended finite element method with higher-order elements for curved cracks
A finite element method for linear elastic fracture mechanics using enriched quadratic interpolations is presented. The quadratic finite elements are enriched with the asymptotic near tip displacement solutio...
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Chapter and Conference Paper
The Extended Finite Element and Level Set Methods for Non-Planar 3D Crack Growth
A methodology for treating non-planar three-dimensional cracks with geometries that are independent of the mesh is described. The method is based on the extended finite element method, in which the crack disco...
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Chapter and Conference Paper
A Combined Element-Free Galerkin Method/ Arbitrary Lagrangian-Eulerian Formulation for Dynamic Crack Propagation
The Element Free Galerkin (EFG) method is an alternative to the finite element method (FEM) which is an industrial standard tool for solving a wide variety of mechanics problems. However, for some highly nonli...
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Article
An introduction to programming the meshless Element F reeGalerkin method
A detailed description of the Element Free Galerkin (EFG) method and its numerical implementation is presented with the goal of familiarizing scientists and engineers with the new computational technique. In t...
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Article
An error estimate in the EFG method
In this paper, local and global error estimates for the element-free Galerkin (EFG) method are proposed. The essence of proposed error estimates is to use the difference between the values of the projected st...
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Article
An element-free Galerkin method for three-dimensional fracture mechanics
The application of a coupled finite element– element-free Galerkin (EFG) method to problems in three-dimensional fracture is presented. The EFG method is based on moving least square (MLS) approximations and ...
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Article
A Petrov-Galerkin Diffuse Element Method (PG DEM) and its comparison to EFG
The diffuse element method (DEM) pioneered␣by B. Nayroles, G. Touzot and P. Villon is a meshless method for solving partial differential equations. The original version does not pass the patch test. Here an i...
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Article
Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations
A proof of stability is developed for an explicit multi-time step integration method of the second order differential equations which result from a semidiscretization of the equations of structural dynamics. T...
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Article
Continuous meshless approximations for nonconvex bodies by diffraction and transparency
Continuous meshless approximations are developed for domains with non-convex boundaries, with emphasis on cracks. Two techniques are developed in the context of the element-free Galerkin method: a transparency...
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Article
Selected works in applied mechanics and mathematics
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Article
Overview and applications of the reproducing Kernel Particle methods
Multiple-scale Kernel Particle methods are proposed as an alternative and/or enhancement to commonly used numerical methods such as finite element methods. The elimination of a mesh, combined with the properti...
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Article
Advances in multiple scale kernel particle methods
A novel approach to multiresolution analysis based on reproducing kernel particle methods (RKPM) and wavelets is presented. The concepts of reproducing conditions, discrete convolutions, and multiple scale ana...
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Article
Analysis of thin plates by the element-free Galerkin method
A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which ...
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Article
A coupled finite element-element-free Galerkin method
A procedure is developed for coupling meshless methods such as the element-free Galerkin method with finite element methods. The coupling is developed so that continuity and consistency are preserved on the in...
