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.

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 of a Cylindrical Shell Subjected to Nonuniform External Pressure

1962 ◽  
Vol 29 (4) ◽  
pp. 675-682 ◽  
Author(s):  
B. O. Almroth
Keyword(s):  
Cylindrical Shell ◽  
Lateral Pressure ◽  
Circular Cylindrical Shell ◽  
External Pressure ◽  
Buckling Analysis ◽  
Graphical Form ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
Ritz Procedure ◽  
The Stability

A buckling analysis is presented for a circular cylindrical shell subjected to nonuniform external pressure. The general approach is not restricted with respect to the distribution of the lateral pressure. However, the final formulation is specialized for the case in which the pressure distribution is of the form p = p0 + p1 cos φ within a centrally located circumferential band. In the buckling analysis the stability criterion is based on the principle of minimum potential energy, and the Rayleigh-Ritz procedure is used to expand the displacement components in trigonometric series. Buckling pressures are computed in terms of nondimensional parameters and are presented in graphical form.

Carrying Capacity of an Elastic-Plastic Cylindrical Shell With Linear Strain-Hardening

1958 ◽  
Vol 25 (1) ◽  
pp. 79-85
Author(s):  
P. G. Hodge ◽  
S. V. Nardo
Keyword(s):  
Cylindrical Shell ◽  
Carrying Capacity ◽  
Circular Cylindrical Shell ◽  
Maximum Load ◽  
Isotropic Hardening ◽  
Linear Strain ◽  
Minimum Potential Energy ◽  
Rigid Plastic ◽  
Plastic Cylindrical Shell ◽  
Minimum Potential

Abstract The approximate capacity of a thin-walled closed circular cylindrical shell, simply supported at each end and subjected to a uniform hydrostatic pressure, is determined. Elastic and plastic strains are considered, and the latter are assumed to follow a linear law of isotropic hardening. The principle of minimum potential energy is used to determine an approximate solution for the stress resultants, displacements, and maximum load. In an example, it is found that the carrying capacity is considerably lower than that predicted by either rigid-plastic theory or elasticity theory.

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

A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)

1994 ◽  
Vol 61 (4) ◽  
pp. 914-918 ◽  
Author(s):  
J. E. Taylor
Keyword(s):  
Potential Energy ◽  
Problem Formulation ◽  
Extremum Problem ◽  
Equilibrium Analysis ◽  
Minimum Potential Energy ◽  
Problem Statement ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

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