Element‐free Galerkin methods

International Journal for Numerical Methods in Engineering - Tập 37 Số 2 - Trang 229-256 - 1994
Ted Belytschko1, Ye Lu1, Linxia Gu1
1Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, The Technological Institute, Northwestern University, Evanston, IL 60208‐3109, U.S.A.

Tóm tắt

AbstractAn element‐free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least‐squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least‐squares interpolants and the choices of the weight function are also discussed in this paper.

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International Journal for Numerical Methods in Engineering

Tập 37 Số 2

229-256

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