Improvement of Numerical Manifold Method Using Nine-node Quadrilateral and Ten-node Triangular ...

In this paper, the numerical manifold method (NMM) with a 9-node quadrilateral element and a 10-node triangular element is developed. Furthermore, complex Fourier shape functions are used to improve the 9-node quadrilateral NMM. This paper also compares the two approaches of higher-order NMM construction, increasing the order of weight functions or local approximation ones; for this purpose, 6-node triangular and 3-node triangular using 2nd-order and 3rd order NMM are used. For validation of the suggested method, one free vibration and two forced vibration numerical examples are assessed. The results show that the proposed methods are more accurate than the conventional NMM. In addition, the superiority of complex Fourier shape functions compared to classical Lagrange ones in improving accuracy are perceived.