A.M.A. Neves

Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects

In this paper, a variation of Murakamis Zig-Zag theory is proposed for the analysis of functionally graded plates. The new theory includes a hyperbolic sine term for the in-plane displacements expansion and accounts for through-the-thickness deformation, by considering a quadratic evolution of the transverse displacement with the thickness coordinate. The governing equations and the boundary conditions are obtained by a generalization of Carreras Unified Formulation, and further interpolated by collocation with radial basis functions. Numerical examples on the static analysis of functionally graded sandwich plates demonstrate the accuracy of the present approach. The thickness stretching effect on such problems is studied.

Dynamic Analysis of Functionally Graded Plates and Shells by Radial Basis Functions

A meshless numerical method with a first-order shear deformation theory is used to study the linear transient response of functionally graded plates and shells. The present meshless method is based on the combination of pseudospectral methods and a collocation method with radial basis functions. A Newmark algoritm is used to advance the analysis in time. Results obtained are compared with analytical solutions.

Influence of zig-zag and warping effects on buckling of functionally graded sandwich plates according to sinusoidal shear deformation theories

ABSTRACT In this article various sinusoidal shear deformation theories are used for the buckling analysis of functionally graded sandwich plates. The theories may account for through-the-thickness deformations and/or zig-zag effect. The governing equations and boundary conditions are derived using the Principle of Virtual Work under a generalization of Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions. A numerical investigation has been conducted on the buckling analysis of sandwich plates with functionally graded skins. The influence of the thickness stretching and the zig-zag effects on these problems is investigated. Numerical results demonstrate the accuracy of the present approach.

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

Abstract In 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.

Buckling behaviour of cross-ply laminated plates by a higher-order shear deformation theory

Abstract In this article, Carrera’s Unified Formulation (CUF) is combined with a radial basis function collocation technique. A higher-order theory that considers deformations in the thickness direction was developed under CUF to predict the buckling behaviour of laminated plates. The obtained governing equations and boundary conditions are then interpolated by collocation with radial basis functions. The accuracy and efficiency of the combination of the two techniques for buckling problems of laminated plates are demonstrated through numerical experiments.

Transient analysis of composite and sandwich plates by radial basis functions

This article presents a study of the linear transient response of composite plates using radial basis functions and collocation method. We use the Kansa method and radial basis functions in a pseudo-spectral framework. The first-order and a third-order shear deformation plate theories are used. It is shown that the present method produces highly accurate displacements and stresses when compared with the available results in the literature.

Adaptive Methods for Analysis of Composite Plates with Radial Basis Functions

Driscoll and Heryudono [1] developed an adaptive method for radial basis functions method. This article addresses the adaptive analysis of composite plates in bending with radial basis multiquadric functions using Driscoll and Heryudonos technique. In this article, various laminates, thickness to side length ratios, and boundary conditions are considered. The method allows for a more natural and automatic selection of the problem grid, where the user must only define the error tolerance. The results obtained show an interesting and promising approach to the static analysis of composite laminates.

Solving time-dependent problems by an RBF-PS method with an optimal shape parameter

An hybrid technique is used for the solutions of static and time-dependent problems. The idea is to combine the radial basis function (RBF) collocation method and the pseudospectal (PS) method getting to the RBF-PS method. The approach presented in this paper includes a shape parameter optimization and produces highly accurate results. Different examples of the procedure are presented and different radial basis functions are used. One and two-dimensional problems are considered with various boundary and initial conditions. We consider generic problems, but also results on beams and plates. The displacement and the stress analysis are conducted for static and transient dynamic situations. Results obtained are in good agreement with exact solutions or references considered.