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Development of MLS Difference Method for Material Nonlinear Problem

MLS차분법을 이용한 재료비선형 문제 해석

  • Received : 2016.03.14
  • Accepted : 2016.04.29
  • Published : 2016.06.30

Abstract

This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.

Keywords

material nonlinearity;MLS difference method;strong formulation;double derivative approximation;Newton method

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Cited by

  1. Dynamic Analysis of MLS Difference Method using First Order Differential Approximation vol.31, pp.6, 2018, https://doi.org/10.7734/COSEIK.2018.31.6.331

Acknowledgement

Supported by : 한국연구재단