SUMMARYAn 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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Element free Galerkin (EX) methods are methods for solving p a differential equations that require only nodal data and a description of the gwmeuy; no element connectivity data are needed. This makes the method very atmctive for the modeling of lhe propagation of cracks. as the number of data changes required is small and easily developed. The method is based on the use of moving least-squares interpolants with a Galerkin method, and it provides highly accurate solutions for elliptic problem. The implementation of the EFC method for problems of frachlre and static crack growth is described. Numerical examples show that accurate stress intensity factors can be obtained without any enrichment of the displacement field by a near-crack-tip singularity and that crack growth can be easily modeled since it requires hardly any remeshing.

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