Journal Article10.1016/J.AML.2021.107084
Generalized finite difference method for electroelastic analysis of three-dimensional piezoelectric structures
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TL;DR: In this article, the generalized finite difference method (GFDM) is applied for numerical solutions of three-dimensional (3D) piezoelectric problems, where the entire computational domain is divided into a set of overlapping subdomains in which the local Taylor series expansion and moving-least square approximation are applied to construct the local systems of linear equations.
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About: This article is published in Applied Mathematics Letters. The article was published on 01 Jul 2021. The article focuses on the topics: Finite difference method & Collocation method.
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Citations
A GFDM with supplementary nodes for thin elastic plate bending analysis under dynamic loading
Wenzhen Qu,Hua He +1 more
TL;DR: In this paper, a meshless generalized finite difference method (GFDM) with supplementary nodes is proposed for the solution of thin elastic plate bending under dynamic loading. But the GFDM is not suitable for the case of large elastic plates.
53
Fracture analysis of ultra-thin coating/substrate structures with interface cracks
Yan Gu,Chuanzeng Zhang +1 more
TL;DR: In this paper, an advanced boundary element method (BEM) is adopted for fracture analysis of ultra-thin coating/substrate structures with interface cracks, and the complex interfacial stress intensity factors (SIFs) can be directly and accurately computed at the collocation points extremely close to the crack-tip by using the proposed computational strategy based on the novel special crack tip elements.
41
A meshless generalized finite difference method for solving shallow water equations with the flux limiter technique
TL;DR: In this article, a meshless stable numerical solver is proposed to solve the non-conservative form of shallow water equations, where discontinuous solutions are allowed to transmit during the simulation, and the upwinding spatial derivatives can be approximated at every node using the half-disk shape of the star and generalized finite difference method.
41
A GFDM with supplementary nodes for thin elastic plate bending analysis under dynamic loading
01 Feb 2022
TL;DR: In this article , a meshless generalized finite difference method (GFDM) with supplementary nodes is proposed for the solution of thin elastic plate bending under dynamic loading. But the GFDM is not suitable for the case of large elastic plates.
34
An upwind generalized finite difference method for meshless solution of two-phase porous flow equations
Anna Rocheva,Jingyu Song +1 more
TL;DR: In this article , the first attempt to apply newly developed upwind GFDM for the meshless solution of two-phase porous flow equations was made, where node cloud is used to flexibly discretize the computational domain, instead of complicated mesh generation.
References
Influence of several factors in the generalized finite difference method
TL;DR: In this paper, the generalized finite difference method (GFD) is used to solve second-order partial differential equations which represent the behavior of many physical processes. And the authors analyze the influences of key parameters of the method, such as the number of nodes of the star, the arrangement of the same, the weight function and the stability parameter in time-dependent problems.
290
A domain-decomposition generalized finite difference method for stress analysis in three-dimensional composite materials
Yuanyuan Wang,Yan Gu,Jianlin Liu +2 more
TL;DR: A new framework for stress analysis of three-dimensional (3D) composite (multi-layered) elastic materials is presented, which yields a sparse and banded matrix system which makes it very attractive for large-scale engineering simulations.
131
Generalized finite difference method for two-dimensional shallow water equations
Po-Wei Li,Chia-Ming Fan +1 more
TL;DR: A new way to determine the shape of star in the GFDM is proposed in this paper to capture the wave transmission and validate the accuracy and the consistency of the proposed meshless numerical scheme.
110
The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems
TL;DR: A new framework for the efficient and accurate solutions of three-dimensional dynamic coupled thermoelasticity problems is presented and a new distance criterion for adaptive selection of nodes in the GFDM simulations is examined.
80
Hybrid FEM–SBM solver for structural vibration induced underwater acoustic radiation in shallow marine environment
TL;DR: In this article, the authors used the finite element method (FEM) to calculate the vibration response of the shell structures and the singular boundary method (SBM) with near-field and far-field Green's functions to simulate the underwater acoustic radiation excited by shell structural vibration in shallow water marine environment.
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