Chao Liu’s research while affiliated with Shanghai University and other places

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Publications (2)


Analyzing nonlinear large deformation with an improved element-free Galerkin method via the interpolating moving least-squares method
  • Article

November 2016

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29 Reads

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54 Citations

International Journal of Computational Materials ScieInternational Journal of Computational Materials Science and Engineeringnce and Engineering

Yumin Cheng

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Funong Bai

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Chao Liu

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Miaojuan Peng

Using the interpolating moving least-squares (IMLS) method to form the shape function, a novel improved element-free Galerkin (IEFG) method is presented for solving nonlinear elastic large deformation problems. To obtain the formulae of the IEFG method for elastic large deformation problems, we use the Galerkin weak form to obtain the discretized system equation, and use the penalty method to apply the displacement boundary conditions. Some selected numerical examples of two-dimensional elastic large deformation problems are given, and the numerical results are analyzed. From the examples, it is shown that the IEFG method in this paper has higher computational precision than the element-free Galerkin (EFG) method presented before.


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

April 2015

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24 Reads

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64 Citations

International Journal of Applied Mechanics

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.

Citations (2)


... Ren et al. improved the interpolating MLS method [16], thus the corresponding interpolating EFG method was presented [17]. Additionally, some mechanics problems [18][19][20] were analyzed by using this method. Qin et al. developed the interpolating smoothed particle method [21]. ...

Reference:

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems
Analyzing nonlinear large deformation with an improved element-free Galerkin method via the interpolating moving least-squares method
  • Citing Article
  • November 2016

International Journal of Computational Materials ScieInternational Journal of Computational Materials Science and Engineeringnce and Engineering

... The method has some advantages, such as variable time frequency characteristics and multi-resolution characteristics. Therefore, the RKPM has been widely used in many practical engineering problems, such as large deformation analysis problems, structural dynamics problems, micro-electromechanical system analysis problems, nonlinear problem of hyperelastic rubber materials, high-speed impact problems and so on [45][46][47]. ...

The Interpolating Complex Variable Element-Free Galerkin Method for Temperature Field Problems
  • Citing Article
  • April 2015

International Journal of Applied Mechanics