Numerical solution of transient heat conduction problems using improved meshless local Petrov–Galerkin method

Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach

“…One of its significant advantages is that solution of the approximation is constructed in terms of a set of nodes over the computational domain instead of producing a body-fitted mesh and involving re-meshing at every step during the evolution of the simulation. Based on different approximation functions, various element-free methods have been proposed, including the element-free Galerkin method [1], the SPH method [2], the reproducing kernel particle method [3], the improved complex variable element-free Galerkin method [4][5][6][7][8], the kp-Ritz method [9,10], the local Kriging meshless method [11], the improved element-free Galerkin method [12][13][14][15][16][17], the IMLS-Ritz method [18][19][20], the DSC method [21], the generalized moving least-squares method [22], the meshless local weak and strong method [23], the radial point interpolation method [24][25][26], and many others [27][28][29]. The focus of this paper is to explore the IMLS-Ritz method to study the buckling behavior of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations.…”

The complex variable meshless local Petrov–Galerkin method for elasticity problems of functionally graded materials

“…According to the published literature, the meshless methods can be classified into two general classes, namely the element free Galerkin (EFG) method [3] based on the global weak formulation and the meshless local Petrov-Galerkin (MLPG) method [4] based on the local weak formulation. Up to now, a wide range of meshless methods have been successfully used in most cases [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. However, the computational cost of meshless methods is generally higher than that of corresponding numerical methods.…”

Nonlinear numerical analysis of convective-radiative fin using MLPG method

“…The method was further elaborated and developed by Sladek et al [41], Atluri and Shen [42], Qian and Batra [43], Xue-Hong et al [44], Baradaren and Mahmoodebadi [45], Thakur et al [46], Dai et al [47] and Zhang et al [48] and concluded that MLPG has a very high rate of convergence, it does not need any post processing technique and also not exhibit any volumetric locking. MLPG method works on Petrov-Galerkin formulation i.e.…”

“…According to Atluri and Shen [42], the MLPG method is classified into six sub-methods, based on the way the test function is chosen as MLPG 1 (MLS weight function); MLPG 2 (Dirac's Delta function); MLPG 3 (discrete least sqaures); MLPG 4 (fundamental solution); MLPG 5 (Heaviside unit step function); MLPG 6 (identical to trial function). Although, all the MLPG methods possess higher accuracy, still MLPG 1 is claimed as one of the strongest method to address complicated heat transfer problems as it yields the better results and higher rate of convergence than the established methods [40][41][42][43][44][45][46][47]. Hence MLPG 1 is employed in this study.…”