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X. Zhang, X. Liu, M. W. Lu and Y. Chen, “Imposition of Essential Boundary Conditions by Displacement Constraint Equations in Meshless Methods,” Communications in Numerical Methods in Engineering, Vol. 17, No. 3, 2001, 165-178. Hdoi:10.1002/cnm.395

has been cited by the following article:

• TITLE: Elastoplastic Large Deformation Using Meshless Integral Method

  AUTHORS: Jianfeng Ma, X. J. Xin

  KEYWORDS: Meshless Method; Large Deformation; Local Boundary Integral Equation; Moving Least-Squares Approximation; Subtraction Method; Singularity Removal; Elastoplasticity; Green-Naghdi’s Theory

  JOURNAL NAME: World Journal of Mechanics, Vol.2 No.6, December 31, 2012

  ABSTRACT: In this paper, the meshless integral method based on the regularized boundary integral equation [1] has been extended to analyze the large deformation of elastoplastic materials. The updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity based on Green-Naghdi’s theory over a local sub-domain, and the moving least-squares approximation is used for meshless function approximation. Green-Naghdi’s theory starts with the additive decomposition of the Green-Lagrange strain into elastic and plastic parts and considers aJ2elastoplastic constitutive law that relates the Green-Lagrange strain to the second Piola-Kirchhoff stress. A simple, generalized collocation method is proposed to enforce essential boundary conditions straightforwardly and accurately, while natural boundary conditions are incorporated in the system governing equations and require no special handling. The solution algorithm for large deformation analysis is discussed in detail. Numerical examples show that meshless integral method with large deformation is accurate and robust.