A theoretical analysis of FGM doubly curved shallow thin shell based on physical neutral surface

Article type: Research Article

Authors: Zhang, Da-Guang^{a; *} | Zhou, You-He^a

Affiliations: [a] Key Laboratory of Mechanics on Western Disaster and Environment of the Ministry of Education, Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China

Correspondence: [*] Corresponding author. Tel.: +86 0931 8910340; Fax: +86 0931 8914561; E-mail: [email protected]

Abstract: In this paper, a new theory about functionally gradient materials (FGM) is constructed from the concept of physical neutral surface and classical double curved shallow thin shell theory (CDSST). In this theory, there is no stretching-bending coupling effect in constitutive equations, governing equations and boundary conditions have the simple forms as those of CDSST about homogeneous isotropic materials, so the solution procedure is as easy as homogeneous isotropic shell. Using this new theory, linear bending and vibration solutions are presented using analytical method and a nonlinear bending approximate solution is given out using Galerkin variational method. This new theory about FGM has more merits in engineering applications, because it is easier and simpler than any of geometric middle surface FGM double curved shallow shell theories.

Keywords: Physical neutral surface, functionally graded materials, double curved shallow thin shell, stretching-bending coupling, bending, vibration, nonlinear bending

DOI: 10.3233/JAE-2011-1322

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 35, no. 1, pp. 67-78, 2011