Analysis of Functionally Graded Plates by a Robust Meshless Method

Ferreira, A.J.M.; Roque, C.M.C.; Jorge, R.M. Natal; Fasshauer, Gregory E.; Batra, R.C.

doi:10.1080/15376490701672732

Cited by 92 publications

(31 citation statements)

References 41 publications

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“…Wu [3] dealt with the thermal post-buckling behavior of simply supported models under uniform temperature rise based on first-order shear deformation plate theory. Ferreira et al [4] performed the static deformations of FG plates by using the robust meshless method, the radial basis functions and a higher-order shear deformation theory. Recently, Lee and Kim [5,6] investigated that the absorbed moisture and high temperature degrade the structural performance of FGMs.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of homogenized effective properties for FGM panels in aero-thermal environments

Lee

Kim

2015

Composite Structures

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Section: Introductionmentioning

confidence: 99%

Evaluation of homogenized effective properties for FGM panels in aero-thermal environments

Lee

Kim

2015

Composite Structures

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“…Note that (13) now is in the form of a standard interpolation system with system matrix n i=0 (I − A) i −1 , the same coefficient vector n i=0 (I − A) i f as above, and the usual right-hand side f given by the data.…”

Section: Direct Loocv For Iterated Amls Approximationmentioning

confidence: 98%

“…Of course, as mentioned earlier, Kansa's method has been popular since its introduction in [20] and countless papers exist in the literature dealing with all kinds of applications in science and engineering. An LOOCV algorithm for finding an "optimal" shape parameter similar to the one described in this paper was used with Kansa's method in [13].…”

Section: Remarks and Conclusionmentioning

confidence: 99%

On choosing “optimal” shape parameters for RBF approximation

2007

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Many radial basis function (RBF) methods contain a free shape parameter that plays an important role for the accuracy of the method. In most papers the authors end up choosing this shape parameter by trial and error or some other ad hoc means. The method of cross validation has long been used in the statistics literature, and the special case of leave-one-out cross validation forms the basis of the algorithm for choosing an optimal value of the shape parameter proposed by Rippa in the setting of scattered data interpolation with RBFs. We discuss extensions of this approach that can be applied in the setting of iterated approximate moving least squares approximation of function value data and for RBF pseudo-spectral methods for the solution of partial differential equations. The former method can be viewed as an efficient alternative to ridge regression or smoothing spline approximation, while the latter forms an extension of the classical polynomial pseudo-spectral approach. Numerical experiments illustrating the use of our algorithms are included.

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“…Then, the displacements generated in each layer may be written as: (7) where are displacement components in the and directions, respectively, are displacement components of a point on the mid-plane of the th layer.…”

Section: The Displacement and Strain Fieldsmentioning

confidence: 99%