Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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TL;DR: A formulation of the alternating direction implicit scheme is proposed into the meshless framework, not constrained by a grid in space and unconditionally stable in time, and is validated by numerical simulations.
24 citations
TL;DR: In this article, an ultra-accurate hybrid smoothed finite element method (HS-FEM) is presented for the analysis of piezoelectric structures, in which the electrostatic equations governing the problem are solved numerically with simplest triangular elements in 2D and tetrahedral elements in 3D.
Abstract: An ultra-accurate hybrid smoothed finite element method (HS-FEM) is presented for the analysis of piezoelectric structures, in which the electrostatic equations governing piezoelectric problem are solved numerically with simplest triangular elements in 2D and tetrahedral elements in 3D. In the present method, the strain field is assumed to be the weighted average between compatible strains from finite element method (FEM) and smoothed strains from node-based smoothed finite element method (NS-FEM). Numerical results demonstrate that the proposed method possesses a novel bound solution in terms of strain energy and eigenfrequencies, which is very important for safety and reliability assessments of piezoelectric structural properties. In addition, the numerical results obtained from HS-FEM are much more accurate than the standard finite element method using the same of nodes. Furthermore, the computational efficiency of HS-FEM is much better than the FEM.
24 citations
TL;DR: This paper presents a parallel computing strategy for the MPM with multiple Graphics Processing Units (GPUs) to boost the method’s computational efficiency in large scale problems.
24 citations
TL;DR: In this paper, a meshless numerical scheme was proposed to solve the inverse heat source time dependent problem, where fundamental solutions of heat equations and radial basis functions (RBFs) were used to obtain a numerical solution.
Abstract: This paper presents a meshless numerical scheme to solve the inverse heat source time dependent problem. Fundamental solutions of heat equations and radial basis functions (RBFs) are used to obtain a numerical solution. Since the coefficient matrix may be ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulting system of linear equations. Therefore, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. The accuracy and efficiency of the proposed method is illustrated by some numerical examples.
24 citations
TL;DR: In this paper, a mesh-free method for nonlinear analysis of two-dimensional reinforced concrete structures subjected to monotonic static loading is presented, which is used to study the nonlinear behavior of reinforced concrete shear walls.
24 citations