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In this paper, we present a meshless method belonging to the family ofelement-free Galerkin (EFG) methods. The distinguishing feature of thepresented meshless method is that it allows accurate enforcement of essentialboundary conditions. The method uses total Lagrangian formulation with explicittime integration to facilitate code simplicity and robust computations inapplications that involve large deformations and non-linear materials. We use aregularized weight function, which closely approximates the Kronecker delta, togenerate interpolating shape functions. The imposition of the prescribeddisplacements on the boundary becomes as straightforward as in the finiteelement (FE) method. The effectiveness and accuracy of the proposed method isdemonstrated using 3D numerical examples that include cylinder indentation by70% of its initial height, and indentation of the brain.

Simple and robust element-free Galerkin method with interpolating shape functions for finite deformation elasticity