scholarly journals 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

2014 ◽  
Vol 36 (4) ◽  
pp. 255-265 ◽  
Author(s):  
Dao Van Dung ◽  
Vu Hoai Nam
Keyword(s):  
Axial Compression ◽  
Nonlinear Dynamic ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
External Pressure ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Numerical Results ◽  
Time Dependent ◽  
Circular Cylindrical Shells

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.

scholarly journals 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

2014 ◽  
Vol 36 (3) ◽  
pp. 201-214
Author(s):  
Dao Van Dung ◽  
Vu Hoai Nam
Keyword(s):  
Axial Compression ◽  
Nonlinear Dynamic ◽  
Analytical Approach ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
External Pressure ◽  
Functionally Graded ◽  
Time Dependent ◽  
Nonlinear Buckling ◽  
Circular Cylindrical Shells

Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Galerkin method, this paper deals with the nonlinear dynamic problem of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure by analytical approach. The present novelty is that an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the nonlinear dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form.

scholarly journals Solving nonlinear stability problem of imperfect functionally graded circular cylindrical shells under axial compression by Galerkin's method

2012 ◽  
Vol 34 (3) ◽  
pp. 139-156 ◽  
Author(s):  
Dao Van Dung ◽  
Le Kha Hoa
Keyword(s):  
Axial Compression ◽  
Nonlinear Stability ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Method Effects ◽  
Circular Cylindrical Shells

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection.  Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper  [13] which were solved by Ritz energy method.

Nonlinear Thermo-Mechanical Stability Analysis of Eccentrically Spiral Stiffened Sandwich Functionally Graded Cylindrical Shells Subjected to External Pressure

2019 ◽  
Vol 11 (05) ◽  
pp. 1950045 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Cao Van Doan ◽  
Nguyen Thoi Trung
Keyword(s):  
Mechanical Stability ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
External Pressure ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Nonlinear Buckling ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

A new analytical approach to investigate the nonlinear buckling and postbuckling of the sandwich functionally graded circular cylindrical shells reinforced by ring and stringer or spiral stiffeners subjected to external pressure is presented in this paper. By employing the Donnell shell theory, the geometrical nonlinearity in Von Kármán sense and developed Lekhnitskii’s smeared stiffener technique, the governing equations of sandwich functionally graded circular cylindrical shells are derived. Resulting equations are solved by applying the Galerkin method to obtain the explicit expression of critical buckling external pressure load and postbuckling load–deflection curve. Effects of spiral stiffeners, thermal environment, external pressure, and geometrical parameters on nonlinear buckling behavior of sandwich functionally graded circular cylindrical shells are shown in numerical results.

scholarly journals Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation

2014 ◽  
Vol 36 (1) ◽  
pp. 27-47 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dao Huy Bich ◽  
Dao Van Dung
Keyword(s):  
Elastic Foundation ◽  
Axial Compression ◽  
Nonlinear Dynamic ◽  
Linear Time ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Buckling Load ◽  
Dynamic Responses ◽  
Nonlinear Buckling

This paper presents an analytical approach to investigate the nonlinear buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression and surrounded by an elastic foundation. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, initial geometrical imperfection, the smeared stiffeners technique and Pasternak’s two-parameter elastic foundation, the governing equations of eccentrically stiffened functionally graded cylindrical shells are derived. The functionally graded cylindrical shells are reinforced by homogeneous ring and stringer stiffener system on internal and (or) external surface. The resulting equations are solved by the Galerkin method to obtain the explicit expression of static critical buckling load, post-buckling load-deflection curve and nonlinear dynamic motion equation. The nonlinear dynamic responses are found by using fourth order Runge-Kutta method. The dynamic critical buckling loads of shells are considered for step loading of infinite duration and linear-time compression. The obtained results show the effects of foundation, stiffeners and input factors on the nonlinear buckling behavior of these structures. 

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

Nonlinear thermal vibration and dynamic buckling of eccentrically stiffened sandwich-FGM cylindrical shells containing fluid

2018 ◽  
Vol 38 (6) ◽  
pp. 253-266
Author(s):  
Khuc Van Phu ◽  
Dao Huy Bich ◽  
Le Xuan Doan
Keyword(s):  
Thermal Environment ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Fluid Pressure ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Thermal Vibration ◽  
Foundation Model ◽  
Classical Shell Theory

The governing equations for analysing thermal vibration and dynamic buckling of eccentrically stiffened sandwich functionally graded cylindrical shells full filled with fluid and surrounded by elastic foundations in thermal environment are derived by using the classical shell theory, the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Pasternak’s foundation model. Solutions of the problem are established according to the Galerkin’s method and Runge–Kutta method. The effects of fluid pressure, stiffeners, geometrical ratios, temperature and elastic foundation on the dynamic responses of shells are investigated.

Nonlinear Static and Dynamic Buckling Analyses of Imperfect FGP Cylindrical Shells Resting on Nonlinear Elastic Foundation Under Axial Compression

2020 ◽  
Vol 20 (07) ◽  
pp. 2050074
Author(s):  
Kamran Foroutan ◽  
Habib Ahmadi
Keyword(s):  
Elastic Foundation ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Porosity Distribution ◽  
Nonlinear Elastic Foundation ◽  
Special Cases ◽  
Nonlinear Static ◽  
Nonlinear Elastic

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

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