Formulation of pseudospectral meshless radial point Hermit interpolation for the Motz problem and comparison to pseudospectral meshless radial point interpolation

Shivanian, Elyas

doi:10.1108/mmms-04-2019-0084

Cited by 2 publications

(1 citation statement)

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“…Discretization and appropriate distribution of nodal points, selection of base functions and their combination in making shape functions in the domains play an important role in the relationship between the known values of variables field and the unknown values at arbitrary points in domains. There are different methods to find shape functions, but the common feature of these methods is the production of shape functions that have; convergence in solution, compatibility condition, differentiability from the order of m or m-complete condition and possessing the Dirac delta property (Shobeyri and Afshar, 2010; Yu-ying and Jing, 2005; Xu et al ., 2010; Zhuang et al ., 2014; Shojaei et al ., 2017; Karamanli, 2020; Wenterodt and von Estorff, 2009; Moussaoui and Bouziane, 2016; Ghaffarzadeh et al ., 2016; Shivanian, 2020; Ariannezhad et al ., 2022). One of methods used for discretization and zoning that allows optimization of the analysis domain is the use of the Voronoi diagram (VD) method.…”

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confidence: 99%

Voronoi discretization to improve the meshless local Petrov–Galerkin method in 3D-computational fracture mechanics

Ariannezhad,

Shahrooi,

Shishesaz

2023

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Purpose1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method.Design/methodology/approachUsing appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane).FindingsBy doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics.Originality/valueThe present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35].

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