2015
DOI: 10.1115/1.4028859
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Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

Abstract: A survey of several methods under the heading of strong formulation finite element method (SFEM) is presented. These approaches are distinguished from classical one, termed weak formulation finite element method (WFEM). The main advantage of the SFEM is that it uses differential quadrature method (DQM) for the discretization of the equations and the mapping technique for the coordinate transformation from the Cartesian to the computational domain. Moreover, the element connectivity is performed by using kinema… Show more

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Cited by 394 publications
(196 citation statements)
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“…GDQ technique, as an efficient numerical technique, is implemented for solving partial differential equations, especially in the field of solid mechanics [37][38][39][40][41]. Here, this method is utilized to obtain the natural frequencies of non-uniform CNTFPC beam.…”
Section: Gdq Methodsmentioning
confidence: 99%
“…GDQ technique, as an efficient numerical technique, is implemented for solving partial differential equations, especially in the field of solid mechanics [37][38][39][40][41]. Here, this method is utilized to obtain the natural frequencies of non-uniform CNTFPC beam.…”
Section: Gdq Methodsmentioning
confidence: 99%
“…Thus, the unknown functional values f (x i ) at each grid point are found by solving the system of equations with the appropriate boundary conditions. The DQM is a versatile numerical discretisation technique that can be used to develop strong-form finite elements [43]. Using this technique, the relatively simple geometry of a square, flat plate investigated here can be extended to the analysis of more complex geometries.…”
Section: Model Implementationmentioning
confidence: 99%
“…Second, the matrix inversion is not computed using the backslash operator in MATLAB, but rather with the Moore-Penrose pseudoinverse as detailed in reference [48]. One possible solution is to discretise the plate into multiple DQM elements using the method proposed by Tornabene et al [43]. Such an approach is equivalent to a strong-form FEM and considerably reduces the bandwidth of the matrices to improve the conditioning of the stiffness matrix.…”
Section: Model Implementationmentioning
confidence: 99%
“…The DQ method approximates a derivative at a point as a linear weighted sum of all the functional values on the domain. How to evaluate the weighting coefficients is one of the key points of this technique [Tornabene et al (2015)]. However, DQM is not always stable increasing the number of collocation points.…”
Section: Free Vibration Analysis Of Reinforced Composite Functionallymentioning
confidence: 99%