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Yumin Cheng - One of the best experts on this subject based on the ideXlab platform.

  • the interpolating element free galerkin method for three dimensional Elastoplasticity problems
    Engineering Analysis With Boundary Elements, 2020
    Co-Authors: Fengbin Liu, Yumin Cheng
    Abstract:

    Abstract In this paper, the interpolating element-free Galerkin (IEFG) method for solving the three-dimensional (3D) Elastoplasticity problems is presented. By using the improved interpolating moving least-squares method to form the approximation function, and using the Galerkin weak form of 3D Elastoplasticity problems to obtain the discretilized equations, we present the formulae of the IEFG method for the 3D Elastoplasticity problems. The method can apply the displacement boundary conditions directly, which results in higher computational efficiency and accuracy. Numerical examples are given to discuss the influences of node distributions, scale parameters of influence domains and the loading steps on the computational accuracy of numerical solutions of the IEFG method. The numerical results show that, comparing with the element-free Galerkin method, the IEFG method for 3D Elastoplasticity problems in this paper has higher computational efficiency and accuracy.

  • the improved element free galerkin method for three dimensional Elastoplasticity problems
    Engineering Analysis With Boundary Elements, 2019
    Co-Authors: M J Peng, H Cheng, Yumin Cheng
    Abstract:

    Abstract In this study, the improved element-free Galerkin (IEFG) method is presented to the three-dimensional Elastoplasticity problems. The improved least-squares (IMLS) approximation is used to obtain the shape function, the Galerkin weak form of three-dimensional Elastoplasticity problems considering the nonlinear stress–strain relationship is used to form the discrete equation system, and penalty method is applied to the displacement boundary conditions, then the formula of the IEFG method for three-dimensional Elastoplasticity problems are obtained. Some numerical examples are given to discuss the convergence of the IEFG method in this paper and the influences of the weight function, the scaling parameter, the penalty factor, the node distribution and the step number on the computational accuracy of the numerical solutions of the IEFG method. Comparing with the element-free Galerkin (EFG) method, the method in this study has a greater computational efficiency.

  • an improved interpolating element free galerkin method for Elastoplasticity via nonsingular weight functions
    International Journal of Applied Mechanics, 2016
    Co-Authors: Jufeng Wang, Fengxin Sun, Yumin Cheng
    Abstract:

    An improved interpolating element-free Galerkin (IIEFG) method for Elastoplasticity is proposed in this paper. In the IIEFG method, the shape functions are constructed by the improved interpolating...

  • analysis of Elastoplasticity problems using an improved complex variable element free galerkin method
    Chinese Physics B, 2015
    Co-Authors: Yumin Cheng, Chao Liu, Funong Bai, M J Peng
    Abstract:

    In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin (ICVEFG) method is presented for two-dimensional (2D) Elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D Elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D Elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

  • a novel interpolating element free galerkin iefg method for two dimensional Elastoplasticity
    Applied Mathematical Modelling, 2014
    Co-Authors: Yumin Cheng, Funong Bai, M J Peng
    Abstract:

    Abstract Using the interpolating moving least-squares (IMLS) method to obtain the shape function, we present a novel interpolating element-free Galerkin (IEFG) method to solve two-dimensional Elastoplasticity problems. The shape function of the IMLS method satisfies the property of Kronecker δ function, then in the meshless methods based on the IMLS method, the essential boundary conditions can applied directly. Based on the Galerkin weak form, we obtain the formulae of the IEFG method for solving two-dimensional Elastoplasticity problems. The IEFG method has some advantages, such as simpler formulae and directly applying the essential boundary conditions, over the conventional element-free Galerkin (EFG) method. The results of three numerical examples show that the computational precision of the IEFG method is higher than that of the EFG method.

H Nguyenxuan - One of the best experts on this subject based on the ideXlab platform.

  • a node based smoothed finite element method ns fem for upper bound solution to visco elastoplastic analyses of solids using triangular and tetrahedral meshes
    Computer Methods in Applied Mechanics and Engineering, 2010
    Co-Authors: T Nguyenthoi, H C Vudo, H Nguyenxuan, Timon Rabczuk
    Abstract:

    Abstract A node-based smoothed finite element method (NS-FEM) was recently proposed for the solid mechanics problems. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh. In this paper, the NS-FEM is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes, respectively. The material behavior includes perfect visco-Elastoplasticity and visco-Elastoplasticity with isotropic hardening and linear kinematic hardening. A dual formulation for the NS-FEM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl–Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacement-dependent. The numerical results show that the NS-FEM has higher computational cost than the FEM. However the NS-FEM is much more accurate than the FEM, and hence the NS-FEM is more efficient than the FEM. It is also observed from the numerical results that the NS-FEM possesses the upper bound property which is very meaningful for the visco-elastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, NS-FEM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.

  • a face based smoothed finite element method fs fem for visco elastoplastic analyses of 3d solids using tetrahedral mesh
    Computer Methods in Applied Mechanics and Engineering, 2009
    Co-Authors: T Nguyenthoi, G R Liu, H C Vudo, H Nguyenxuan
    Abstract:

    Abstract A face-based smoothed finite element method (FS-FEM) using tetrahedral elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the solid mechanics problems. In this paper, the FS-FEM is further extended to more complicated visco-elastoplastic analyses of 3D solids using the von-Mises yield function and the Prandtl–Reuss flow rule. The material behavior includes perfect visco-Elastoplasticity and visco-Elastoplasticity with isotropic hardening and linear kinematic hardening. The formulation shows that the bandwidth of stiffness matrix of FS-FEM is larger than that of FEM, and hence the computational cost of FS-FEM in numerical examples is larger than that of FEM for the same mesh. However, when the efficiency of computation (computation time for the same accuracy) in terms of a posteriori error estimation is considered, the FS-FEM is more efficient than the FEM.

M J Peng - One of the best experts on this subject based on the ideXlab platform.

  • the improved element free galerkin method for three dimensional Elastoplasticity problems
    Engineering Analysis With Boundary Elements, 2019
    Co-Authors: M J Peng, H Cheng, Yumin Cheng
    Abstract:

    Abstract In this study, the improved element-free Galerkin (IEFG) method is presented to the three-dimensional Elastoplasticity problems. The improved least-squares (IMLS) approximation is used to obtain the shape function, the Galerkin weak form of three-dimensional Elastoplasticity problems considering the nonlinear stress–strain relationship is used to form the discrete equation system, and penalty method is applied to the displacement boundary conditions, then the formula of the IEFG method for three-dimensional Elastoplasticity problems are obtained. Some numerical examples are given to discuss the convergence of the IEFG method in this paper and the influences of the weight function, the scaling parameter, the penalty factor, the node distribution and the step number on the computational accuracy of the numerical solutions of the IEFG method. Comparing with the element-free Galerkin (EFG) method, the method in this study has a greater computational efficiency.

  • analysis of Elastoplasticity problems using an improved complex variable element free galerkin method
    Chinese Physics B, 2015
    Co-Authors: Yumin Cheng, Chao Liu, Funong Bai, M J Peng
    Abstract:

    In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin (ICVEFG) method is presented for two-dimensional (2D) Elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D Elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D Elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

  • a novel interpolating element free galerkin iefg method for two dimensional Elastoplasticity
    Applied Mathematical Modelling, 2014
    Co-Authors: Yumin Cheng, Funong Bai, M J Peng
    Abstract:

    Abstract Using the interpolating moving least-squares (IMLS) method to obtain the shape function, we present a novel interpolating element-free Galerkin (IEFG) method to solve two-dimensional Elastoplasticity problems. The shape function of the IMLS method satisfies the property of Kronecker δ function, then in the meshless methods based on the IMLS method, the essential boundary conditions can applied directly. Based on the Galerkin weak form, we obtain the formulae of the IEFG method for solving two-dimensional Elastoplasticity problems. The IEFG method has some advantages, such as simpler formulae and directly applying the essential boundary conditions, over the conventional element-free Galerkin (EFG) method. The results of three numerical examples show that the computational precision of the IEFG method is higher than that of the EFG method.

T Nguyenthoi - One of the best experts on this subject based on the ideXlab platform.

  • a node based smoothed finite element method ns fem for upper bound solution to visco elastoplastic analyses of solids using triangular and tetrahedral meshes
    Computer Methods in Applied Mechanics and Engineering, 2010
    Co-Authors: T Nguyenthoi, H C Vudo, H Nguyenxuan, Timon Rabczuk
    Abstract:

    Abstract A node-based smoothed finite element method (NS-FEM) was recently proposed for the solid mechanics problems. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh. In this paper, the NS-FEM is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes, respectively. The material behavior includes perfect visco-Elastoplasticity and visco-Elastoplasticity with isotropic hardening and linear kinematic hardening. A dual formulation for the NS-FEM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl–Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacement-dependent. The numerical results show that the NS-FEM has higher computational cost than the FEM. However the NS-FEM is much more accurate than the FEM, and hence the NS-FEM is more efficient than the FEM. It is also observed from the numerical results that the NS-FEM possesses the upper bound property which is very meaningful for the visco-elastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, NS-FEM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.

  • a face based smoothed finite element method fs fem for visco elastoplastic analyses of 3d solids using tetrahedral mesh
    Computer Methods in Applied Mechanics and Engineering, 2009
    Co-Authors: T Nguyenthoi, G R Liu, H C Vudo, H Nguyenxuan
    Abstract:

    Abstract A face-based smoothed finite element method (FS-FEM) using tetrahedral elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the solid mechanics problems. In this paper, the FS-FEM is further extended to more complicated visco-elastoplastic analyses of 3D solids using the von-Mises yield function and the Prandtl–Reuss flow rule. The material behavior includes perfect visco-Elastoplasticity and visco-Elastoplasticity with isotropic hardening and linear kinematic hardening. The formulation shows that the bandwidth of stiffness matrix of FS-FEM is larger than that of FEM, and hence the computational cost of FS-FEM in numerical examples is larger than that of FEM for the same mesh. However, when the efficiency of computation (computation time for the same accuracy) in terms of a posteriori error estimation is considered, the FS-FEM is more efficient than the FEM.

Creto Augusto Vidal - One of the best experts on this subject based on the ideXlab platform.

  • tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to Elastoplasticity
    International Journal for Numerical Methods in Engineering, 1994
    Co-Authors: P Michaleris, Daniel A Tortorelli, Creto Augusto Vidal
    Abstract:

    Tangent operators and design sensitivities are derived for transient non-linear coupled problems. The solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods. The derived formulations are suitable for finite element implementations. Analyses of systems, with materials that exhibit history dependent response, may be obtained directly by applying the analyses of transient non-linear coupled systems. Rate-independent Elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes.

  • design sensitivity analysis for rate independent Elastoplasticity
    Computer Methods in Applied Mechanics and Engineering, 1993
    Co-Authors: Creto Augusto Vidal, Robert B Haber
    Abstract:

    Abstract A new incremental, direct differentiation method for design sensitivity analysis of structures with rate-independent elastoplastic behavior is presented. We formulate analytical sensitivity expressions that are consistent with numerical algorithms for Elastoplasticity that use implicit methods to integrate the constitutive equations and return mappings to enforce the consistency conditions. The sensitivity expressions can be evaluated with only a modest increase in computational expense beyond the cost of simulation. Combined with the inherent advantages of implicit integration strategies, this represents a significant improvement over previous sensitivity formulations for history-dependent materials. First-order sensitivity expressions involving the complete set of design variables, including shape design variables, are derived for a generic response functional. The reduced form of the consistent tangent stiffness matrix obtained at the end of each time or load step in the finite element procedure is used to update the response sensitivities for that time step. No iterations are needed in the sensitivity computations. A numerical example demonstrates the accuracy and efficiency of the new sensitivity analysis method for an elastoplastic analysis problem. Explicit sensitivities from the new method are confirmed by finite difference estimates.