Variational finite difference method for free vibration of sector plates

Finite-difference time-domain analysis of the vibration characteristics of a beam-plate structure using a dimension-reduced model

“…On the other hand, in order to treat the one-plate model in the figure, A = 1 and B = 0 should be applied and the continuity equations of Eqs. (18) and (19) are neglected. In the latter case, the number of unknown parameters is reduced to four and comprise w n;P1 1;j ; w n;P1 2;j ; w n;B j , and h n;B j .…”

“…In order to decrease these costs, the application of dimension-reduced models using one-or two-dimensional elements is effective. Computational methods applying finite-difference schemes to a two-dimensional plate with a beam structure have been proposed [16][17][18][19][20], but these methods basically use energy-based schemes whereby the time dependence is eliminated by assuming harmonic motion. As such, these methods cannot directly describe the http://dx.doi.org/10.1016/j.apacoust.2014.12.011 0003-682X/Ó 2015 Elsevier Ltd. All rights reserved.…”

A weak form quadrature element method for plane elasticity problems

“…As the approach is based on the minimum potential energy principle, it was named as the finite difference energy method (FDEM). The limited ensuing publications in the eighties and the nineties of the last century were virtually all related to the analysis of plates [5][6][7]. As reported by Bushnell [3], the finite difference energy method tended to exhibit superior performance normally and required less computational time to form the global matrices than the finite element models.…”

Analysis of Thin Walled Wavy Shell of Monge Type Surface with Parabola and Sinusoid Curves by Variational-Difference Method

“…In paper, the variational-difference method (VDM) [2,4,[7][8][9][10][11][12][13] is used for analysis of the stress-strain state of the shell. The variational-difference method is based on the Lagrange principle, the principle of minimum total potential energy [14][15][16][17][18][19][20][21][22].…”