NURBS-Augmented Finite Element Method (NAFEM) for bending of thin arbitrary plates

Abstract eng:
In the Isogeometric Analysis (IGA) the Non-Uniform Rational B-Spline (NURBS) basis functions are engaged to represent the geometry and the field variables. In NURBS-Enhanced Finite Element Method (NEFEM), a standard FE interpolation and numerical integration are used for the elements which do not intersect the boundary and a specifically designed piecewise polynomial interpolation and numerical integration are used for elements intersecting the NURBS boundary. The NURBS basis functions are efficient in representing the geometry accurately; but fail to satisfy the Kronecker-Delta property as they are non-interpolating in nature. As a result it becomes difficult to enforce the essential boundary conditions at the control variables. Though IGA and NEFEM are efficient in integrating CAD and FEA, its inherent problem with the imposition of boundary conditions makes it a poor choice for the finite element analysis. To circumvent this problem, a new method NAFEM (NURBS-Augmented Finite Element Method) is proposed in the present work. Here the NURBS basis functions are used to represent the geometry accurately and the usual finite element basis functions are adopted for the field variables. As the finite element basis functions satisfy the Kronecker-Delta property, the imposition of boundary conditions is now simplified. Plates having different geometries, loadings and boundary conditions have been analysed for bending and the results are found to be in excellent agreement with the existing ones.

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