Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method

Abstract

SUMMARYA new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi-boundary conditions in twodimensional problems. Since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi-degree-of-freedom at the boundary points, the method is easier to extend to two-or three-dimensional problems. A new version of the differential quadrature plate element has been established for demonstration. The essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined. The methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method.

Free vibration of generally supported rectangular Kirchhoff plates: State‐space‐based differential quadrature method

“…The lowest eight frequency parameters of the second case for different are predicted and listed in Table VII. It is seen that the present results agree well with those obtained by using DQEM [33]. For cases of = 0 and 1.0, the present results are identical to the exact solution reported by Leissa [5].…”

New approaches in application of differential quadrature method to fourth‐order differential equations

“…(F) Built-in method (3) [16,17]: The built-in method (3) [16] is also an extension of the built-in method (1) [8], similar to the built-in method (2) described above. The essential di erence from the built-in method (2) [15] is that w …”

“…As can be seen, the symbolic expressions are exactly the same as the ones for DQEM or GDQR, thus, all boundary conditions can be conveniently applied. It is noted that this method is readily extended to the DQEM by using w N as independent variables [16,17]. The only di erence from the existing DQEM is the way to compute the weighting coe cients.…”

“…Various methods to apply multiple boundary conditions are available in the literature [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and will be summarized in this section. Two new approaches are also presented.…”

“…In the formulation of the weighting coe cients of third-and fourth-order derivatives, the second derivatives at the boundary points are viewed as an additional independent variable. Wang et al [16,17] extended the method in Reference [8] to all boundary conditions by viewing the ÿrst derivatives at boundary points as an additional independent variable. Both methods introduce an additional degree of freedom at boundary points, but compute the weighting coe cients of the ÿrst-order derivative as in the ordinary DQ methods by using explicit formulae [4,18].…”