Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov–Galerkin (MLPG) method

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

“…To further validate the effectiveness of SSDQM, the transverse displacement and in-plane normal stress for FGM square plates (h/a=0.3) with various boundary conditions and various E h /E 0 are computed using 30 layers in the ALM and 9 × 9 discrete points and presented in Table 1, where the exact solutions [15] for SSSS plate, 3D MLPG, and finite element method (FEM) results [20] for all plates are also listed. Apparently, the present results coincide very well with these 3D solutions.…”

“…In detail, all boundary conditions should be rearranged in terms of the state variables, i.e., the state variables at four edges are either zero or algebraically related to other state variables unknown with respect to ζ. Therefore, the differential equations of the state variables at the edges should be eliminated [20] . Upon incorporating all boundary conditions, the state equation (6) is further reduced to…”

“…Hence, analytical solutions are impossible. Recently, Vaghefi et al [20] used the meshless local Petrov-Galerkin (MLPG) method to derive a 3D elasticity solution for bending of generally supported FGM plates. However, their solution is restricted to exponential law variations of Young's modulus.…”

“…Due to the hypotheses and simplification concerning the deformation field along the thickness direction, the applicability of the 2D plate theories is always confined to the plates with lower thickness-to-length ratios. To account for the deformation field as complete as possible, three-dimensional (3D) elasticity solutions were widely exploited for FGM plates [11][12][13][14][15][16][17][18][19][20] . Since the spatial variation of material properties, it is rather difficult to derive analytical solutions for FGM plate based on the 3D elasticity theory.…”

Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

“…They derived the equations of motion and boundary conditions using Hamilton's principle. Vaghefi et al [41] have presented three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov-Galerkin (MLPG) method. Hosseini-Hashemi et al [42] have presented an analytical closed-form solution in explicit forms to investigate small-scale effects on the buckling and the transverse vibration behavior of Levy-type rectangular nanoplates based on Reddy's nonlocal third-order shear deformation plate theory.…”