Free vibration analysis of two-dimensional structures using Coons-patch macroelements

Recently, Coons’ interpolation was used for the construction of large finite elements with degrees of freedom appearing mostly along the boundaries of a structure. In the regime of elasticity problems, these so-called “Coons-patch macroelements” were successfully applied to the static analysis of plane structures [C.G. Provatidis, Analysis of axisymmetric structures using Coons’ interpolation, Finite Elem. Anal. Des. 39 (2003) 535–558.] while this paper continues the research by investigating their performance in the extraction of natural frequencies and mode shapes. Apart from the piecewise-linear and cubic B-splines interpolation previously used, the performance of Lagrange polynomials and the role of additional internal nodes is studied here. Relationships with classical Serendipity and Lagrangian type elements are discussed. Moreover, the capability of Coons-patch macroelements to couple with conventional finite elements is investigated. The proposed method was applied to three illustrative examples and it was successfully compared with conventional bilinear finite elements.