scholarly journals Elastic Stability Analysis of a Two-Layered Functionally Graded Cylindrical Shell under Axial Compression with the use of Energy Approach

2009 ◽  
Vol 18 (6) ◽  
pp. 096369350901800 ◽  
Author(s):  
H. Sepiani ◽  
A. Rastgoo ◽  
M. Ahmadi ◽  
A.Ghorbanpour Arani ◽  
K. Sepanloo
Keyword(s):  
Cylindrical Shell ◽  
Potential Energy ◽  
Axial Compression ◽  
Elastic Layer ◽  
Elastic Stability ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Minimum Potential Energy ◽  
Equilibrium Equations ◽  
Minimum Potential

This paper investigates the elastic axisymmetric buckling of a thin, simply supported functionally graded (FG) cylindrical shell embedded with an elastic layer under axial compression. The analysis is based on energy method and simplified nonlinear strain-displacement relations for axial compression. Material properties of functionally graded cylindrical shell are considered graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Using minimum potential energy together with Euler equations, equilibrium equations are obtained. Consequently, stability equation of functionally graded cylindrical shell with an elastic layer is acquired by means of minimum potential energy theory and Trefftz criteria. Another analysis is made using the equivalent properties of FG material. Numerical results for stainless steel-ceramic cylindrical shell and aluminum layer are obtained and critical load curves are analyzed for a cylindrical shell with an elastic layer. A comparison is made to the results in the literature. The results show that the elastic stability of functionally graded cylindrical shell with an elastic layer is dependent on the material composition and FGM index factor, and the shell geometry parameters and it is concluded that the application of an elastic layer increases elastic stability and significantly reduces the weight of cylindrical shells.

Buckling Analysis of a Bi-Directional Strain-Gradient Euler–Bernoulli Nano-Beams

2020 ◽  
Vol 20 (11) ◽  
pp. 2050114
Author(s):  
Murat Çelik ◽  
Reha Artan
Keyword(s):  
Potential Energy ◽  
Gradient Elasticity ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Minimum Potential Energy ◽  
End Conditions ◽  
Graded Material ◽  
Minimum Potential ◽  
Gradient Elasticity Theory ◽  
Basic Equations

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed.

A vibration and buckling investigation of two-layered functionally graded cylindrical structures

2010 ◽  
Vol 224 (9) ◽  
pp. 1905-1913 ◽  
Author(s):  
H A Sepiani ◽  
A Rastgoo ◽  
H Karimipour ◽  
M H Naei
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Transverse Shear ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Elastic Stability ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Axial Forces ◽  
Classical Shell Theory

This work investigates the free vibration and buckling of a two-layered cylindrical shell structure made of an elastic embedded functionally graded (FG) shell subjected to combined static and periodic axial forces. Such structures are widely used in chemical and nuclear reactors, space and aerial industries, and so on. Material properties of an FG cylindrical shell are considered to be temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Theoretical formulations are presented based on two different methods of the first-order shear deformation theory considering the transverse shear strains and the rotary inertias and the classical shell theory. The results obtained show that the effect of transverse shear and rotary inertias on free vibration of an FG cylindrical shell is dependent on the material composition, deformation mode, and geometry parameters of the shells. It is concluded that the application of an outer elastic layer increases elastic stability.

The Flexure of a Uniformly Pressurized, Circular, Cylindrical Shell

1958 ◽  
Vol 25 (4) ◽  
pp. 453-458
Author(s):  
J. D. Wood
Keyword(s):  
Cylindrical Shell ◽  
Potential Energy ◽  
Cross Section ◽  
Circular Cylindrical Shell ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
The Cross ◽  
The Moment

Abstract This paper presents the moment-curvature relationship and the components of displacement in the cross section of a uniformly pressurized, long, closed, circular, cylindrical shell. The shell is loaded in one of its principal planes by two equal and opposite terminal couples: First, the shell undergoes small initial displacements. These are formed by superimposing pressurization displacements upon Saint Venant displacements. Second, from this deformed position the shell is perturbed into a system of additional small displacements. A Rayleigh-Ritz technique is used to find the latter displacements from the theorem of minimum potential energy. The point at which the moment-curvature relationship becomes nonlinear is shown by several curves in this paper.

On the Inflation of a Plane Nonlinear Membrane

1974 ◽  
Vol 41 (3) ◽  
pp. 767-771 ◽  
Author(s):  
W. W. Feng ◽  
P. Huang
Keyword(s):  
Potential Energy ◽  
Minimum Potential Energy ◽  
Equilibrium Equations ◽  
Energy Principle ◽  
Strain Energy Density Function ◽  
Total Potential ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle ◽  
Admissible Functions ◽  
Nonlinear Membrane

The deformed configurations of an inflated flat nonlinear membrane are obtained by the minimum potential energy principle. The deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy of the deformed membrane are determined by Fletcher and Powell’s [1] method. The strain-energy-density function for the numerical calculations is assumed to have the Mooney form. The results for a particular case when the Mooney membrane reduces to the neo-Hookean membrane, agree with the previous results obtained by numerical integration of the corresponding equilibrium equations.

Principles of minimum potential energy and complementary energy

2020 ◽  
pp. 228-248
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Boundary Condition ◽  
Potential Energy ◽  
Displacement Field ◽  
Mixed Boundary ◽  
Energy Functional ◽  
The Body ◽  
Minimum Potential Energy ◽  
Complementary Energy ◽  
Minimum Potential ◽  
Potential Energy Functional

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.

Optimization for Minimum Potential Energy, Maximum Rigidity and Minimum Deformability

1984 ◽  
pp. 9-87
Author(s):  
Andrej M. Brandt ◽  
Wojciech Dzieniszewski ◽  
Stefan Jendo ◽  
Wojciech Marks ◽  
Stefan Owczarek ◽  
...  
Keyword(s):  
Potential Energy ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
Energy Maximum
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