J. D. Rodrigues

An Improved Meshless Method for the Static and Vibration Analysis of Plates

An application of a meshless technique for the static and vibration analysis of plates is presented in this paper. The method is based on the radial basis functions-QR (RBF-QR) algorithm. Static deformations and free vibration analysis of plates are obtained by Gaussian RBF-QR technique, previously proposed by Fornberg and Piret (2007) for interpolation problems. Circular and square plates are analyzed considering free-edge, simply-supported, and fully-clamped boundary conditions. The presented technique can be applied to any geometry and node sets embedded in the 2D unitary disk. The RBF-QR approach is stable for decreasing values of the shape parameter, corresponding to flat RBFs and the conversion to polar coordinates brings an extra improvement in precision. The method produces highly accurate displacements, natural frequencies, and modes of vibrations.

Static Deformations and Vibration Analysis of Composite and Sandwich Plates Using a Layerwise Theory and a Local Radial Basis Functions-Finite Differences Discretization

A study of static deformations and free vibration of shear flexible isotropic and laminated composite plates is presented, using a layerwise theory. The analysis is based on a new numerical scheme based on a local collocation scheme with radial basis functions and finite differences to produce highly accurate results. Numerical results for symmetric laminated composite and sandwich plates are presented and discussed.