Three-dimensional static analysis of rectangular thick plates by using the meshless local Petrov—Galerkin method

Abstract

In this article, a meshless local Petrov—Galerkin (MLPG) approach is developed for three-dimensional (3D) analysis of thick plates. Two different MLPG methods including MLPG1 and MLPG5 are employed to solve the elasto-static problems of thick plates. In MLPG1, a namely fourth-order spline function is considered as test function, while the Heaviside step function is employed as test function in MLPG5. Considering 3D equilibrium equations, the local symmetric weak forms are derived. The moving least-squares approximation is used to interpolate the solution variables and the penalty method is applied to impose the essential boundary conditions. In the present study, brick-shaped domains are chosen as local subdomains and support domains. The integrals appearing in the weak formulation are easily evaluated over brick-shaped subdomains and their boundaries. Considering the present approach, elasto-static deformations and stresses are analysed for thick rectangular plates with various boundary conditions and different aspect ratios. Excellent agreement is seen comparing the present results with the known analytical and numerical solutions in the literature.

A state space augmented generalised RKPM for three-dimensional analysis of thick and laminated composite plates

“…(45) for the state variables, the general form of the equation can be found as [52] 125.66 À14.616 Iyengar et al [54] 125.664 -DQ (13 Â 13 Â 13) [55] 125.0003 À14.1079 MLPG1 [56] 125.0133 À14.1316 ABAQUS (40 Â 40 Â 10) 125.168 À14.2239 0.2 Current study 11.140 À3.8440 Srinivas and Rao [52] 11.208 À3.9135 Iyengar et al [54] 11.20875 -DQ (13 Â 13 Â 13) [55] 11.18575 À3.88135 MLPG1 [56] 11.1865 À3.8322 ABAQUS (40 Â 40 Â 10) 11.1795 À3.8576…”

A completely meshless analysis of cracks in isotropic functionally graded materials

“…Based on the concept of the MLPG, six different methods have been introduced, which are labelled as MLPG1-MLPG6 [8]. These six methods differ on the basis of the type of test function considered in the weak formulation.…”

“…Meshless methods are new approaches for obtaining the solution of partial differential equations in different fields of engineering. These methods are successfully applied for the solution of elastostatic and elastodynamic structural problems [8]. Meshless methods that do not need the burdensome effort of mesh generation and remeshing are highly suitable for the analysis of cracks in structures.…”

Three-dimensional thermo-mechanical analysis of continuous casting and comparison with two-dimensional models

“…22 In meshless methods, which are based on global weak formulations, special techniques should be employed for meshless evaluation of domain integrals. [23][24][25] In recent years, the MLPG method has been developed in solving a wide range of important engineering problems, taking into account both 2D [26][27][28][29][30][31][32] and 3D [33][34][35][36][37][38][39][40] models. Although the MLPG method shows high capability and precision in solving various types of engineering problems, 41 so far, it has been less used in thermo-mechanical analysis of phase change problems.…”

“…In recent years, the MLPG method has been developed in solving a wide range of important engineering problems, taking into account both 2D 26–32 and 3D 33–40 models. Although the MLPG method shows high capability and precision in solving various types of engineering problems, 41 so far, it has been less used in thermo-mechanical analysis of phase change problems.…”