CAD-based collocation eigenanalysis of 2-D elastic structures

This paper investigates the performance of the global collocation method for the numerical eigenfrequency extraction of 2-D elastic structures. The method is applied to CAD-based macroelements, starting from the older blending function Coons-Gordon interpolation (based on Lagrange polynomials) and extending to tensor product Bézier and B-splines. Numerical findings show equivalence between Lagrangian and Bézierian macroelements, while a mass lumping procedure is proposed for the former ones. Concerning B-splines, the influence of multiplicity of inner knots and the position of collocation points is thoroughly investigated. The theory is supported by 2-D numerical examples on rectangular and curvilinear structures of simple shape under plane stress conditions, in which the approximate solution rapidly converges towards the exact solution faster than that of the conventional finite element of similar mesh density.