A partition of unity-based 'FE-meshfree' QUAD4 element for geometric non-linear analysis

The recently published 'FE-Meshfree' QUAD4 element is extended to geometrical non-linear analysis. The shape functions for this element are obtained by combining meshfree and finite element shape functions. The concept of partition of unity (PU) is employed for the purpose. The new shape functions inherit their higher order completeness properties from the meshfree shape functions and the mesh-distortion tolerant compatibility properties from the finite element (FE) shape functions. Updated Lagrangian formulation is adopted for the non-linear solution. Several numerical example problems are solved and the performance of the element is compared with that of the well-known Q4, QM6 and Q8 elements. The results show that, for regular meshes, the performance of the element is comparable to that of QM6 and Q8 elements, and superior to that of Q4 element. For distorted meshes, the present element has better mesh-distortion tolerance than Q4, QM6 and Q8 elements. Copyright (C) 2009 John Wiley & Sons, Ltd.