an:00571745
Zbl 0796.73077
Belytschko, T.; Lu, Y. Y.; Gu, L.
Element-free Galerkin methods
EN
Int. J. Numer. Methods Eng. 37, No. 2, 229-256 (1994).
00018154
1994
j
74S30 74P10 74S05 74B99 80A20
moving least-squares interpolants; variational principle; convergence; resolution of localized steep gradients; weight function
An 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. The numerical examples 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.