C.M.C. Roque

Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method

In the present study the third-order theory of Reddy for composite laminated plates is discretized using a new type of meshless method, a finite point based on the multiquadric radial basis function method. The method allows a very accurate prediction of the field variables.

Analysis of Functionally Graded Plates by a Robust Meshless Method

The analysis of static deformations of functionally graded plates is performed by using the collocation method, the radial basis functions and a higher-order shear deformation theory. The collocation method is truly meshless, allowing a fast and simple domain and boundary discretization. We select the shape parameter in the radial basis functions by an optimization procedure based on the cross-validation technique, and use the Mori-Tanaka homogenization technique to deduce effective properties of functionally graded materials. Numerical tests show that the method is reliable, robust and produces accurate results.

Free Vibration Analysis of Composite and Sandwich Plates by a Trigonometric Layerwise Deformation Theory and Radial Basis Functions

In this study trigonometric layerwise deformation theory is used for the analysis of free vibration of symmetric composite plates. A meshless discretization method based on global multiquadric radial basis functions is used. The equations of motion and the boundary conditions are derived and interpolated by radial basis functions. This method is applied to the free vibration analysis of composite and sandwich plates. The results are then compared with analytical and numerical solutions. The results show that the use of trigonometric layerwise deformation theory discretized with multiquadrics provides very good solutions for the free vibration of composite and sandwich plates.

Two higher order Zig-Zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation

In this article, we combine the Carreras Unified Formulation, CUF (Carrera E. Theories and Finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng., 2003; 10: 215–297.) and a radial basis function collocation technique for predicting the static deformations, free vibrations and buckling behavior of thin and thick cross-ply laminated plates. We develop by the CUF two Zig-Zag theories according to Murakamis Zig-Zag function. Both theories account for through-the-thickness deformations, allowing the analysis of thick plates. The accuracy and efficiency of this collocation technique for static, vibration, and buckling problems are demonstrated through numerical examples.

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.

Analysis of sandwich plates by radial basis functions collocation, according to Murakami's Zig-Zag theory

In this article, the static analysis of sandwich plates is performed by radial basis functions collocation, according to the Murakamis Zig-Zag function theory. The Murakamis Zig-Zag function theory accounts for through-the-thickness deformation, by considering a Zig-Zag evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carreras unified formulation, and further interpolated by collocation with radial basis functions.

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.

Bending and vibration of laminated plates by a layerwise formulation and collocation with radial basis functions

This article addresses the static deformations and free vibration analysis of laminated composite and sandwich plates by collocation with radial basis functions, according to a layerwise formulation. The present layerwise approach accounts for through-the-thickness deformations. The equations of motion and the boundary conditions are obtained by the Carrera’s Unified Formulation, and further interpolated by collocation with 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.

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.