Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation

D A Maturi,A M Zenkour,D S Mashat,A J M Ferreira

doi:10.1155/2013/123465

D A Maturi, A M Zenkour + Show 2 more

Open Access

https://doi.org/10.1155/2013/123465

Copy DOI

Abstract

The static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to Murakami’s zig-zag (ZZ) function (MZZF) theory . The MZZF theory accounts for through-the-thickness deformation, by considering a ZZ evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions.

Highlights

The efficient load-carrying capabilities of shell structures make them very useful in a variety of engineering applications
The most common mathematical models used to describe shell structures may be classified into two classes according to different physical assumptions: the Koiter model [1], based on the Kirchhoff hypothesis, and the Naghdi model [2], based on the Reissner-Mindlin assumptions that take into account the transverse shear deformation
In order to overcome the computational cost of the layerwise theories, Murakami [11] proposed a zig-zag function (ZZF) that is able to reproduce the slope discontinuity

Summary

Introduction

The efficient load-carrying capabilities of shell structures make them very useful in a variety of engineering applications. The most common mathematical models used to describe shell structures may be classified into two classes according to different physical assumptions: the Koiter model [1], based on the Kirchhoff hypothesis, and the Naghdi model [2], based on the Reissner-Mindlin assumptions that take into account the transverse shear deformation These theories are not adequate to describe the so-called zig-zag (ZZ) effect in sandwich structures or layered composites, due to the discontinuity of mechanical properties between faces and core at the interfaces; see Figure 1 (to trace accurate responses of sandwich structures, see the books by Zenkert [3] and Vinson [4]). The present paper, that performs the bending and free vibration analysis of laminated shells by collocation with radial basis functions, avoids the locking phenomenon. The quality of the present method in predicting static deformations and free vibrations of thin and thick laminated shells is compared and discussed with other methods in some numerical examples

Applying the Unified Formulation to MZZF

HβkRβk

The Radial Basis Function Method

Method

Numerical Examples

Concluding Remarks