Discrete singular convolution methodology for free vibration and stability analyses of arbitrary straight‐sided quadrilateral plates

Abstract

SUMMARYA new discrete singular convolution (DSC) method is developed for vibration, buckling and static analyses of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for straight-sided quadrilateral thin plates such as rectangular, skew, trapezoidal and rhombic plates are presented. The results obtained by the DSC method were compared with those obtained by the other numerical and analytical methods.

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

“…The DQFEM solutions match with the DQM solutions [5,66] and the Ritz solutions [63], at least to four significant digits. In Table VIII, the DQFEM solutions for clamped and simply supported rhombic plates with diagonal line ratio a/b = 2.0 and 3.0 are compared with the DQM solutions [5], the DSC solutions [72] and the superposition solutions [76]. One can obtain the same conclusions as above.…”

“…The title problem or the free vibrations of isotropic thin plates with different planforms have been studied extensively due to a variety of applications by using the FEM [52][53][54][55][56], the Ritz method [57][58][59][60][61][62][63], the DQM [5,23,[64][65][66][67][68][69][70], the discrete singular convolution (DSC) method [71][72][73], the superposition method [74][75][76], the Green function method [77], the moving least-square Ritz method [78] and the Galerkin method [79]. In the above paragraph there are some comments on FEM and DQM.…”

On the Convergence of Laminated Composite Plates of Arbitrary Shape through Finite Element Models

“…The following triplets indicate the number of elements along a, b and the third digit stands for the number of elements on the external edge (correspondent to one-quarter of the plate). Thus, b/a = 1.5 has (2,3,5), (4,6,8), (8,12,14), (16,24,24), (32,48,50), (36,52,54), (40,56,58). b/a = 2 has (1,2,4), (2,4,6), (4,8,8), (8,16,16), (16,32,32), (24,48,48), (32,64,64).…”

“…The Straus7 mesh considers 20 × 20 decomposition of the starting 12 elements mesh for a total of 4800 elements and three different meshes are considered according to the shape for Abaqus: a/b = 1.5 (36,52,54), a/b = 2 (24,48,48), a/b = 2.5 (16,40,40) with the same meaning of the symbols discussed above. References models are made using 3D FE bricks for a/h = 10 by using Hexa20 in Straus7 and C3D20 in Abaqus.…”

Free Vibration Analysis of Carbon Nanotubes Based on Shear Deformable Beam Theory by Discrete Singular Convolution Technique

“…The method of discrete singular convolution (DSC) was proposed to solve linear and nonlinear differential equations by Wei [17], and later it was introduced to solid and fluid mechanics by Wei [18], Wei et al [19], Zhao et al [20,21], and Civalek [22][23][24][25][26][27][28][29]. For more details of the mathematical background and application of the DSC method in solving problems in engineering, the readers may refer to some recently published reference [21][22][23][24][25][26][27][28][29][30]. In the context of distribution theory, a singular convolution can be defined by [17] …”