The Improved Complex Variable Element-Free Galerkin Method for Bending Problem of Thin Plate on Elastic Foundations

2019 ◽  
Vol 11 (10) ◽  
pp. 1950105 ◽  
Author(s):  
Binhua Wang ◽  
Yongqi Ma ◽  
Yumin Cheng
Keyword(s):  
Thin Plate ◽  
Complex Variable ◽  
Weak Form ◽  
Discrete Equation ◽  
Computational Accuracy ◽  
Variable Theory ◽  
Elastic Foundations ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Element Free

In this paper, the improved complex variable element-free Galerkin (ICVEFG) method is proposed for solving the bending problem of thin plate on elastic foundations. In the ICVEFG method, the approximation function regarding the deflection of thin plate is formed with the improved complex moving least-squares (ICVMLS) approximation, the discrete equation is obtained from Galerkin weak form of bending problem of thin plate on different elastic foundations, and essential boundary conditions are considered based on penalty method. As the ICVMLS approximation is based on the complex variable theory, it can obtain the shape function quickly with high precision. Three sample problems are used to discuss the advantages of the ICVEFG method, and the numerical results show that the ICVEFG method presented in this paper has a fast convergence speed and great computational accuracy.

The Improved Interpolating Complex Variable Element Free Galerkin Method for Two-Dimensional Potential Problems

2019 ◽  
Vol 11 (10) ◽  
pp. 1950104 ◽  
Author(s):  
Yajie Deng ◽  
Xiaoqiao He ◽  
Ying Dai
Keyword(s):  
Complex Variable ◽  
Basis Function ◽  
Potential Problem ◽  
Shape Function ◽  
Weak Form ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Potential Problems ◽  
Element Free

In this paper, the improved interpolating complex variable moving least squares (IICVMLS) method is applied, in which the complete basis function is introduced and combined with the singular weight function to achieve the orthometric basis function. Then, the interpolating shape function is achieved to construct the interpolating trial function. Incorporating the IICVMLS method and the Galerkin integral weak form, an improved interpolating complex variable element free Galerkin (IICVEFG) method is proposed to solve the 2D potential problem. Because the essential boundary conditions can be straightaway imposed in the above method, the expressions of final dispersed matrices are more concise in contrast to the non-interpolating complex variable meshless methods. Through analyzing four specific potential problems, the IICVEFG method is validated with greater computing precision and efficiency.

A NEW ELEMENT-FREE GALERKIN METHOD BASED ON IMPROVED COMPLEX VARIABLE MOVING LEAST-SQUARES APPROXIMATION FOR ELASTICITY

2012 ◽  
Vol 01 (01) ◽  
pp. 1250011 ◽  
Author(s):  
HONGPING REN ◽  
YUMIN CHENG
Keyword(s):  
Least Squares ◽  
Complex Variable ◽  
Weak Form ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Elasticity Problems ◽  
Element Free

In this paper, by constructing a new functional, an improved complex variable moving least-squares (ICVMLS) approximation is presented. Based on element-free Galerkin (EFG) method and the ICVMLS approximation, a new complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented. Galerkin weak form is used to obtain the discretized equations and the essential boundary conditions are applied with Lagrange multiplier. Then the formulae of the new CVEFG method for two-dimensional elasticity problems are obtained. Compared with the conventional EFG method, the new CVEFG method has greater computational precision and efficiency. For the purposes of demonstration, some selected numerical examples are solved using the ICVEFG method.

THE COMPLEX VARIABLE ELEMENT-FREE GALERKIN (CVEFG) METHOD FOR TWO-DIMENSIONAL ELASTODYNAMICS PROBLEMS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250042 ◽  
Author(s):  
YUMIN CHENG ◽  
JIANFEI WANG ◽  
RONGXIN LI
Keyword(s):  
Complex Variable ◽  
Time Integration ◽  
Time History ◽  
Weak Form ◽  
Implicit Time ◽  
Two Dimensional ◽  
Element Free Galerkin ◽  
History Analysis ◽  
Variable Element ◽  
Element Free

The complex variable moving least-squares (CVMLS) approximation is discussed in this paper, and the mathematical and physical meaning of the complex functional in the CVMLS approximation is presented. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. Then combining the CVMLS approximation and the Galerkin weak form, we investigate the complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems. The penalty method is used to apply the essential boundary conditions, and the implicit time integration method, which is the Newmark method, is used for time history analysis. Then the corresponding formulae of the CVEFG method for two-dimensional elastodynamics problems are obtained. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG method. Compared with the EFG method, the CVEFG method has greater precision.

The Interpolating Complex Variable Element-Free Galerkin Method for Temperature Field Problems

2015 ◽  
Vol 07 (02) ◽  
pp. 1550017 ◽  
Author(s):  
Yajie Deng ◽  
Chao Liu ◽  
Miaojuan Peng ◽  
Yumin Cheng
Keyword(s):  
Temperature Field ◽  
Least Squares ◽  
Complex Variable ◽  
Weak Form ◽  
Equation System ◽  
Moving Least Squares ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Mls Approximation ◽  
Element Free

In this paper, an interpolating complex variable moving least-squares (ICVMLS) method is presented. In the ICVMLS method, the trial function of a two-dimensional problem is formed with a one-dimensional basis function, and the shape function of the ICVMLS method satisfies the property of Kronecker δ function. The ICVMLS method has greater computational efficiency than the moving least-squares (MLS) approximation. Then combining the ICVMLS method with the Galerkin weak form of temperature field problems, an interpolating complex variable element-free Galerkin (ICVEFG) method is proposed. In the ICVEFG method, we can obtain the equation system by applying the essential boundary conditions directly. Compared with the element-free Galerkin (EFG) method and the complex variable element-free Galerkin (CVEFG) method, the ICVEFG method in this paper has higher accuracy and efficiency.

A Meshless Method Based on the Nonsingular Weight Functions for Elastoplastic Large Deformation Problems

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Fengbin Liu ◽  
Qiang Wu ◽  
Yumin Cheng
Keyword(s):  
Large Deformation ◽  
Numerical Solutions ◽  
Weak Form ◽  
Weight Functions ◽  
Computational Accuracy ◽  
Lagrange Formulation ◽  
Element Free Galerkin ◽  
Penalty Factor ◽  
Element Free ◽  
Large Deformation Problems

In this study, based on a nonsingular weight function, the improved element-free Galerkin (IEFG) method is presented for solving elastoplastic large deformation problems. By using the improved interpolating moving least-squares (IMLS) method to form the approximation function, and using Galerkin weak form based on total Lagrange formulation of elastoplastic large deformation problems to form the discretilized equations, which is solved with the Newton–Raphson iteration method, we obtain the formulae of the IEFG method for elastoplastic large deformation problems. In numerical examples, the influences of the penalty factor, scale parameter of influence domain and weight functions on the computational accuracy are analyzed, and the numerical solutions show that the IEFG method for elastoplastic large deformation problems has higher computational efficiency and accuracy.

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