Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads

Static and vibration analysis of functionally graded beams using refined shear deformation theory

“…Many theoretical models and beam theories have been developed to solve this complicated problem. By using a meshless local Petrov-Galerkin method, Ching and Yen [1] presented numerical solutions for two-dimensional (2D) FG solids such as simply-supported beams. In terms of Airy stress function, Zhong and Yu [2] presented a general 2D solution for a cantilever FG beam with arbitrary variations of material properties.…”

Optimal material distribution for heat conduction of FGM based on meshless weighted least-square method

“…Liu and Gu [5] introduced meshless methods and their programming, such as the element-free Galerkin (EFG) method, the hp-clouds method, the meshless local Petrov-Galerkin (MLPG) method, meshless Galerkin method using radial basis functions, the least-square method and meshless point collocation method. The main advantage of the MLPG method [6,7] compared with regular Galerkin-based methods is that no background mesh is used to evaluate various integrals appearing in the local weak formulation of problem, but it requires a high order quadrature rule to obtain converged results and thus needs much more computational effort in terms of CPU time than that for the FEM. A meshless algorithm of fundamental solution coupling with radial basis functions based on analog equation theory was proposed to conduct steady-state and transient thermal analysis of FGMs [8,9] and to simulate the static thermal stress distribution in 2D FGMs [10].…”

“…Compared with the above mentioned FEM, FDM and BEM, the meshless methods [4][5][6][7][8][9][10][11][12][13][14] is associated with a class of numerical techniques that approximate a given differential equation or a set of differential equations using global interpolations on an unstructured distribution of nodes, exhibiting the advantages of avoiding mesh generation, simple data preparation, easy post-processing and so on. Liu and Gu [5] introduced meshless methods and their programming, such as the element-free Galerkin (EFG) method, the hp-clouds method, the meshless local Petrov-Galerkin (MLPG) method, meshless Galerkin method using radial basis functions, the least-square method and meshless point collocation method.…”

Bending analysis of thin functionally graded plates using generalized differential quadrature method

“…Originally, the concept of FGMs was introduced as an alternative to conventional thermal barriers to relax the residual stresses and improving bonding strength [2], because the large stresses induced by the abrupt change in material properties across the interface could cause detachment of coating and substrate. As well as the advancement in manufacturing technologies, FGM has been the subject of a large amount of researches in various engineering fields, specifically thermoelastic loadings [3][4][5][6][7], fracture mechanics [8][9][10][11][12] and processing methodologies [13,14]. Recently, behavior of functionally graded (FG) plates under mechanical and thermal loads has received more attention ( [15][16][17][18][19]).…”