Dynamic analysis of functionally graded material bars by using novel weak form quadrature element method

This paper presents an efficient approach to simulate frequency and wave propagations in functionally graded material (FGM) bars by using novel weak form quadrature element method (WQEM). Based on Mindlin-Herrmann rod theory, a time domain N-node quadrature bar element is proposed. Detailed formulations are given. Dynamic problems of FGM bars are investigated by using the proposed weak form quadrature bar element. Comparisons are made with results obtained by using frequency domain spectral element method (SEM) and by using strong form differential quadrature method (DQM) to verify the developed quadrature bar element. It is shown that one 21-node bar element can yield very accurate frequencies and that the proposed element can efficiently simulate the wave propagation in FGM bars. Compared to results based on the simple rod theory, the results based on Mindlin-Herrmann rod theory should be more reliable, especially for the wave forms and group velocity.