The dimension splitting element-free Galerkin method for 3D transient heat conduction problems

Portal crane is the most commonly used equipment for cargo handling of large mixed loading ships with its advantages of flexible and convenient operation, wide adaptability, and high loading and unloading efficiency. The reasonable modeling and optimization of the pulling point position of luffing jib of portal crane can reduce the rack force of portal crane and the power consumption output of the rack and pinion during the luffing process. Based on penalty function optimization, the interior point method is used to optimize the pulling point position of luffing jib. Compared with the initial design, the race force of the luffing jib is reduced to a certain extent. In addition, the consistency between the finite element analysis results and the optimization results can be verified, and the effectiveness of the optimization design is also proved through the finite element analysis of portal crane.

Section: Introductionmentioning

confidence: 99%

Modeling and Optimization of Pulling Point Position of Luffing Jib on Portal Crane

Jiao

Qin

Han³

et al. 2021

“…Cheng et al proposed the improved moving least-squares (IMLS) approximation to develop the improved element-free Galerkin (IEFG) method [33][34][35] and the interpolating element-free Galerkin method [36][37][38]. By introducing the dimension splitting method into the reproducing kernel particle method, a new meshless method was developed to solve three-dimensional potential problems [39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Sine-Gordon Equation with the Local Kriging Meshless Method

Guo

Boldbaatar

et al. 2020

This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions. Based on the local Petrov–Galerkin formulation and the center difference method for time discretization, a system of nonlinear discrete equations is obtained. The numerical examples are presented and the numerical solutions are found to be in good agreement with the results in the literature to validate the ability of the present meshless method to handle the 2 + 1-dimensional sine-Gordon equation related problems.

“…By combining the dimension splitting method and meshless methods, the hybrid complex variable EFG method [27][28][29][30][31], the dimension split EFG method [32][33][34][35], and the dimension splitting reproducing kernel particle method [36] for 3D problems are proposed, respectively, and those new methods can improve the computational speed of traditional meshless methods for solving 3D problems greatly.…”

Section: Introductionmentioning

confidence: 99%

Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method

Cheng

Guo-dong

2020

Self Cite

In this paper, the improved element-free Galerkin (IEFG) method is used for solving 3D advection-diffusion problems. The improved moving least-squares (IMLS) approximation is used to form the trial function, the penalty method is applied to introduce the essential boundary conditions, the Galerkin weak form and the difference method are used to obtain the final discretized equations, and then the formulae of the IEFG method for 3D advection-diffusion problems are presented. The error and the convergence are analyzed by numerical examples, and the numerical results show that the IEFG method not only has a higher computational speed but also can avoid singular matrix of the element-free Galerkin (EFG) method.