Dao Van Dung

Analytical investigation on the free vibration behavior of rotating FGM truncated conical shells reinforced by orthogonal eccentric stiffeners

ABSTRACT This article presents an analytical investigation on the free vibration behavior of rotating functionally graded truncated conical shells reinforced by stringers and rings with the change of spacing between stringers. Using the Donnell shell theory, smeared stiffeners technique, and taking into account the influences of centrifugal force and Coriolis acceleration, the governing equations are derived. These variable coefficient partial differential equations are studied by the Galerkin method. The sixth-order polynomial equation of natural frequency is obtained. Numerical results show effects of stiffener and input parameters on the frequency of shell.

NONLINEAR BUCKLING AND POST-BUCKLING OF ECCENTRICALLY STIFFENED FUNCTIONALLY GRADED CYLINDRICAL SHELLS SURROUNDED BY AN ELASTIC MEDIUM BASED ON THE FIRST ORDER SHEAR DEFORMATION THEORY

In this paper, the nonlinear buckling and post-buckling of an eccentrically stiffened cylindrical shell made of functionally graded materials, surrounded by an elastic medium and subjected to mechanical compressive loads and external pressures are investigated by an analytical approach. The cylindrical shells are reinforced by longitudinal and circumferential stiffeners. The material properties of cylindrical shells are graded in the thickness direction according to a volume fraction power-law distribution. The nonlinear stability equations for stiffened cylindrical shells are derived by using the first order shear deformation theory and smeared stiffeners technique. Closed-form expressions for determining the buckling load and load-deflection curves are obtained. The effectiveness of stiffeners in enhancing the stability of cylindrical shells is shown. The effects of volume fraction indexes, material properties, geometrical parameters and foundation parameters are analyzed in detail.

Thermomechanical postbuckling analysis of eccentrically stiffened FGM sandwich plates with general Sigmoid and power laws based on TSDT

The buckling and postbuckling behaviors of eccentrically stiffened sandwich plates on elastic foundations subjected to in-plane compressive loads, thermal loads, or thermomechanical loads are presented analytically by using the Reddy’s third-order shear deformation plate theory with von Karman geometrical nonlinearity. Four cases of general Sigmoid and power laws are considered. The material properties of the facesheets, the core layer, and stiffeners are assumed to be temperature-dependent. Theoretical formulations based on the smeared stiffeners technique and third-order shear deformation plate theory are derived. The expressions of thermal parameters are found in the analytical form. Applying the Galerkin method, the expressions for determination of the critical buckling load and analysis of the postbuckling mechanical and thermal load–deflection curves are obtained. The iterative algorithm is presented for the case of temperature-dependent plate material properties. In addition, the influences of thermal element, functionally graded material stiffeners, the facesheet thickness to total thickness ratio, initial imperfection, and foundations are clarified in detail.

Nonlinear stability analysis of stiffened functionally graded material sandwich cylindrical shells with general Sigmoid law and power law in thermal environment using third-order shear deformation theory

This paper investigates analytically nonlinear buckling and postbuckling of functionally graded sandwich circular thick cylindrical shells filled inside by Pasternak two-parameter elastic foundations under thermal loads and axial compression loads. Shells are reinforced by closely spaced functionally graded material (FGM) rings and stringers. The temperature field is taken into account. Two general Sigmoid law and general power law, with four models of stiffened FGM sandwich cylindrical shell, are proposed. Using the Reddy’s third-order shear deformation shell theory (TSDT), stress function, and Lekhnitsky’s smeared stiffeners technique, the governing equations are derived. The closed form to determine critical axial load and postbuckling load-deflection curves are obtained by the Galerkin method. The effects of the face sheet thickness to total thickness ratio, stiffener, foundation, material, and dimensional parameters on critical thermal loads, critical mechanical loads and postbuckling behavior of shells are analyzed. In addition, this paper shows that for thin shells we can use the classical shell theory to investigate stability behavior of shell, but for thicker shells the use of TSDT for analyzing nonlinear stability of shell is necessary and suitable.

Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 1: Governing equations establishment

In this paper, the buckling and post-buckling behaviors of eccentricallyxa0 stiffened functionally graded material (ES-FGM) plates on elasticxa0 foundations subjected to in-plane compressive loads or thermal loads arexa0 investigated by an analytical solution. The novelty of this work is that FGMxa0 plates are reinforced by FGM stiffeners and the temperature, stiffener,xa0 foundation are considered. The first-order shear deformationxa0 plate theory is used. The thermal elements of plate and stiffeners inxa0 fundamental equations are introduced. Theoretical formulations based on thexa0 smeared stiffeners technique and the first-order shear deformation platexa0 theory, are derived. The analytical expressions to determine the staticxa0 critical buckling load and post-buckling load-deflection curves arexa0 obtained.

Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 2: Numerical results and discussions

Based on the first-order shear deformation plate theory (FSDT), the smearedxa0stiffeners technique and Galerkin method, the analytical expressions toxa0determine the static critical buckling load and analyze the post-bucklingxa0load-deflection curves of FGM plates reinforced by FGM stiffeners resting onxa0elastic foundations and subjected to in-plane compressive loads or thermalxa0loads are established in part 1. In this part, we will use them to study thexa0effects of temperature, stiffener, volume fraction index, geometricalxa0parameters, elastic foundations on the buckling and post-buckling behaviorxa0of plates. In addition, the results in comparisons between the classicalxa0plate theory (CPT) and the first order shear deformation theory (FSDT) alsoxa0are carried out and shown that the buckling and post-buckling behavior ofxa0more thick plate should be studied by FSDT.

An analytical approach to analyze nonlinear dynamic response of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure. Part 1: Governing equations establishment

Based on the classical thin shell theory with the geometrical nonlinearityxa0in von Karman-Donnell sense, the smeared stiffener technique and Galerkinxa0method, this paper deals with the nonlinear dynamic problem of eccentricallyxa0stiffened functionally graded circular cylindrical shells subjected to timexa0dependent axial compression and external pressure by analytical approach.xa0The present novelty is that an approximate three-term solution of deflectionxa0taking into account the nonlinear buckling shape is chosen, the nonlinearxa0dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained inxa0explicit form.

An analytical approach to analyze nonlinear dynamic response of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure. Part 2: Numerical results and discussion

Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique, Galerkin method and an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the governing nonlinear dynamic equations of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure is established in part 1. In this study, the nonlinear dynamic responses are obtained by fourth order Runge-Kutta method and the nonlinear dynamic buckling behavior of stiffened functionally graded shells under linear-time loading is determined by according to Budiansky-Roth criterion. Numerical results are investigated to reveal effects of stiffener, input factors on the vibration and nonlinear dynamic buckling loads of stiffened functionally graded circular cylindrical shells.