Abstract
This paper presents a fast treatment of essential boundary conditions in three-dimensional (3D) meshfree computation for computational efficiency. Due to the loss of Kronecker delta properties in the meshfree shape functions, the imposition of essential boundary conditions is tedious, especially in 3D applications. The proposed boundary singular kernel (BSK) method introduces singularities to the kernel functions associated with the essential and kinematically constrained boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values, and consequently constraints can be imposed directly. In this work, the recovery of nodal value properties on essential boundary nodes is proved for general n-dimensional geometries. The extension of previously proposed two-dimensional BSK method to 3D formulation thus becomes straightforward, and essential boundary treatment consumes almost no additional cost to meshfree computation and makes the method affordable for industrial applications. The effectiveness of the proposed method is demonstrated in 3D metal forming examples.
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