Nonlinear postbuckling of eccentrically stiffened functionally graded plates and shallow shells

Abstract

The paper deals with the formulation of governing equations of eccentrically stiffened functionally graded plates and shallow shells based upon the classical shell theory and the smeared stiffeners technique taking into account geometrical nonlinearity in Von Karman-Donnell sense. Material properties are assumed to be temperature-independent and graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of constituents. The shells are reinforced by eccentrically longitudinal and transversal stiffeners made of full metal or full ceramic depending on situation of stiffeners at metal-rich side or ceramic-rich side of the shell respectively. Obtained governing equations can be used in research on nonlinear postbuckling of mentioned above structures. By use of the Galerkin method an approximated analytical solution to the nonlinear stability problem of reinforced FGM plates and shallow shells is performed. The postbuckling load-deflection curves of the shells are investigated and analytical expressions of the upper and lower buckling loads are presented. A comparison of the effectiveness of stiffeners in enhancing the stability of FGM plates and shallow shells is given.

Nonlinear thermal stability of eccentrically stiffened functionally graded truncated conical shells surrounded on elastic foundations

“…The effective properties of the FGM truncated conical shell (the elastic modulus E , the Poisson ratioν , the thermal expansion coefficient α ) can be written as follows (Bich et al, 2011;Dung et al, 2013;Duc and Quan, 2013;Duc and Cong, 2014): …”

“…To guarantee the continuity between the stiffener and shell, the stiffener is taken to be pure-metal if it is located at metal-rich side and is pure-ceramic if it is located at ceramic-rich side (this assumption was proposed by Bich in (Bich et al, 2011)). In order to investigate the FGM truncated conical shell with stiffeners in thermal environment, we have not only taken into account the materials muduli with temperature-dependent properties but also assumed that all elastic moduli of FGM truncated conical shell and stiffener are temperature dependence and they are deformed in the presence of temperature.…”

Semi-analytical approach for analyzing the nonlinear dynamic torsional buckling of stiffened functionally graded material circular cylindrical shells surrounded by an elastic medium

“…(23,24,26) by Runge-Kutta method and based on Budiansky-Roth criterion, Table 4 shows effects of step size on dynamic critical torsional load. It can be seen that the error reduces with the increase of step number.…”

“…the τ ψ − relation of shells will be studied.For dynamic buckling analysis, consider a cylindrical shell subjected to torsional load linearly varying on time τ=Ct in which C is a loading speed (MPa/s). By using the Runge-Kutta method, the responses of ES-FGM cylindrical shells surrounded by elastic foundation can be determined from coupling governing equations (23),(24) and(26). The dynamic critical time t cr can be obtained according to BudianskyRoth criterion[14,30,35]: Under the action of dynamic load, the deflection of structure increases progressively with the increase of time.…”

“…(30), the static upper critical torsional load is found. The dynamic critical torsional load and dynamic responses are obtained by solving Eqs (23,24,26). by Runge-Kutta method and based on Budiansky-Roth criterion.…”