Radial basis functions–finite differences collocation and a Unified Formulation for bending, vibration and buckling analysis of laminated plates, according to Murakami’s zig-zag theory

2011 ◽  
Vol 93 (7) ◽  
pp. 1613-1620 ◽  
Author(s):  
J.D. Rodrigues ◽  
C.M.C. Roque ◽  
A.J.M. Ferreira ◽  
E. Carrera ◽  
M. Cinefra
Keyword(s):  
Radial Basis Functions ◽  
Finite Differences ◽  
Buckling Analysis ◽  
Laminated Plates ◽  
Basis Functions ◽  
Bending Vibration ◽  
Radial Basis

scholarly journals Free vibrations and buckling analysis of laminated plates by oscillatory radial basis functions

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
A. M. A. Neves ◽  
A. J. M. Ferreira
Keyword(s):  
Radial Basis Functions ◽  
Meshless Method ◽  
Free Vibrations ◽  
Buckling Analysis ◽  
Laminated Plates ◽  
Basis Functions ◽  
Numerical Examples ◽  
Transverse Normal Stress ◽  
Radial Basis ◽  
Refined Version

AbstractIn this paper the free vibrations and buckling analysis of laminated plates is performed using a global meshless method. A refined version of Kant’s theorie which accounts for transverse normal stress and through-the-thickness deformation is used. The innovation is the use of oscillatory radial basis functions. Numerical examples are performed and results are presented and compared to available references. Such functions proved to be an alternative to the tradicional nonoscillatory radial basis functions.

Solving PDEs with radial basis functions

Acta Numerica ◽  
2015 ◽  
Vol 24 ◽  
pp. 215-258 ◽  
Author(s):  
Bengt Fornberg ◽  
Natasha Flyer
Keyword(s):  
Radial Basis Functions ◽  
Finite Differences ◽  
Large Scale ◽  
Numerical Approach ◽  
Basis Functions ◽  
Integration Time ◽  
Small Scale ◽  
Major Step ◽  
Mesh Free ◽  
Radial Basis

Finite differences provided the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods. During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE ‘toy problems’ to becoming a major contender also for very large simulations on advanced distributed memory computer systems. Being entirely mesh-free, RBF-FD discretizations are also particularly easy to implement, even when local refinements are needed. This article gives some background to this development, and highlights some recent results.

Bending and Vibration of Laminated Plates by a Layerwise Formulation and Collocation with Radial Basis Functions

2013 ◽  
Vol 20 (8) ◽  
pp. 624-637 ◽  
Author(s):  
A. J.M. Ferreira ◽  
C. M. C. Roque ◽  
E. Carrera ◽  
M. Cinefra ◽  
O. Polit
Keyword(s):  
Radial Basis Functions ◽  
Laminated Plates ◽  
Basis Functions ◽  
Radial Basis
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