Plastic Analysis of Circular Conical Shells

1960 ◽  
Vol 27 (4) ◽  
pp. 696-700 ◽  
Author(s):  
P. G. Hodge
Keyword(s):  
Conical Shell ◽  
Collapse Load ◽  
Finite Area ◽  
Concentrated Load ◽  
Conical Shells ◽  
Edge Angle ◽  
Rotationally Symmetric ◽  
Plastic Analysis ◽  
Circular Conical Shells ◽  
Support Conditions

A right circular conical shell of edge angle α is subjected to a concentrated load Q directed along the axis. The collapse load is found to be Q = 2πM0 cos2 α, independently of the size or support conditions of the shell. Some solutions are also obtained for the case where the load is distributed over a finite area. Bounds are found on the collapse load of a general rotationally symmetric shell under a concentrated load.

Thin Circular Conical Shells Under Arbitrary Loads

1955 ◽  
Vol 22 (4) ◽  
pp. 557-562
Author(s):  
N. J. Hoff
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conical Shell ◽  
Strain Energy ◽  
Variational Calculus ◽  
Radius Of Curvature ◽  
Median Surface ◽  
Conical Shells ◽  
Arbitrary Loading ◽  
Circular Conical Shells

Abstract Equations defining the displacements of the median surface of a conical shell under arbitrary loads are developed. In their derivation only the essential parts of the strain energy are considered and three simultaneous partial differential equations are obtained through the use of the variational calculus. When the minimum radius of curvature of the median surface of the cone is made to approach a constant value, the cone goes over into a cylinder. At the same time the equations here developed for the cone are transformed into the Donnell equations of the theory of cylindrical shells. It is shown how eigenfunctions of the homogeneous equations can be constructed and how particular solutions can be found for any arbitrary loading.

Stability and vibration analysis of an axially moving thin walled conical shell

2021 ◽  
pp. 107754632199760
Author(s):  
Hossein Abolhassanpour ◽  
Faramarz Ashenai Ghasemi ◽  
Majid Shahgholi ◽  
Arash Mohamadi
Keyword(s):  
Natural Frequency ◽  
Conical Shell ◽  
Shell Theory ◽  
Cone Angle ◽  
Theory Of Elasticity ◽  
Lower Velocity ◽  
Motion Equations ◽  
Conical Shells ◽  
Divergence Instability ◽  
Axially Moving

This article deals with the analysis of free vibration of an axially moving truncated conical shell. Based on the classical linear theory of elasticity, Donnell shell theory assumptions, Hamilton principle, and Galerkin method, the motion equations of axially moving truncated conical shells are derived. Then, the perturbation method is used to obtain the natural frequency of the system. One of the most important and controversial results in studies of axially moving structures is the velocity detection of critical points. Therefore, the effect of velocity on the creation of divergence instability is investigated. The other important goal in this study is to investigate the effect of the cone angle. As a novelty, our study found that increasing or decreasing the cone angle also affects the critical velocity of the structure in addition to changing the natural frequency, meaning that with increasing the cone angle, the instability occurs at a lower velocity. Also, the effect of other parameters such as aspect ratio and mechanical properties on the frequency and instability points is investigated.

scholarly journals Natural Vibrations of the Reinforced Tapered Shell with Taking Into Account the Viscoelastic Properties of the Material

2021 ◽  
Vol 264 ◽  
pp. 01011
Author(s):  
Matlab Ishmamatov ◽  
Nurillo Kulmuratov ◽  
Nasriddin Ахmedov ◽  
Shaxob Хаlilov ◽  
Sherzod Ablakulov
Keyword(s):  
Conical Shell ◽  
Variational Principles ◽  
Variational Equation ◽  
Frequency Equation ◽  
Main Element ◽  
Algebraic Equations ◽  
Natural Vibrations ◽  
Natural Oscillations ◽  
Conical Shells ◽  
Truncated Conical Shell

In this paper, the integro-differential equations of natural oscillations of a viscoelastic ribbed truncated conical shell are obtained based on the Lagrange variational equation. The general research methodology is based on the variational principles of mechanics and variational methods. Geometrically nonlinear mathematical models of the deformation of ribbed conical shells are obtained, considering such factors as the discrete introduction of edges. Based on the finite element method, a method for solving and an algorithm for the equations of natural oscillations of a viscoelastic ribbed truncated conical shell with articulated and freely supported edges is developed. The problem is reduced to solving homogeneous algebraic equations with complex coefficients of large order. For a solution to exist, the main determinant of a system of algebraic equations must be zero. From this condition, we obtain a frequency equation with complex output parameters. The study of natural vibrations of viscoelastic panels of truncated conical shells is carried out, and some characteristic features are revealed. The complex roots of the frequency equation are determined by the Muller method. At each iteration of the Muller method, the Gauss method is used with the main element selection. As the number of edges increases, the real and imaginary parts of the eigenfrequencies increase, respectively.

The Nonlinear Internal Resonance Analysis of a Rotary Truncated Conical Shell

2006 ◽  
Author(s):  
Changping Chen ◽  
Liming Dai
Keyword(s):  
Conical Shell ◽  
Dynamic Properties ◽  
Harmonic Balance Method ◽  
Multiple Scale ◽  
High Order ◽  
Internal Dynamic ◽  
Conical Shells ◽  
System A ◽  
Truncated Conical Shell ◽  
Low Order

Truncated conical shell is an important structure that has been widely applied in many engineering fields. The present paper studies the internal dynamic properties of a truncated rotary conical shell with considerations of intercoupling the high and low order modals by utilizing Harmonic Balance Method. To disclosure the detailed intercoupling characteristics of high order modal and low order modal of the system, a truncated shallow shell is studied and the internal response properties of the system is investigated by using the Multiple Scale Method. Abundant dynamic characteristics are found in the research of this paper. It is found in the research of the paper that the high-order modals of rotating conical shells have significant effects to the amplitude and frequency of the shells.

A Numerical Solution for Vibration Analysis of the Stiffened Variable-Thickness Conical Shells

2015 ◽  
Vol 757 ◽  
pp. 121-125
Author(s):  
Wei Ning ◽  
Feng Sheng Peng ◽  
Nan Wang ◽  
Dong Sheng Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variable Thickness ◽  
Conical Shell ◽  
Thickness Distribution ◽  
Ritz Method ◽  
Free Vibrations ◽  
Conical Shells ◽  
Linear Eigenvalue Problem ◽  
Element Method

The free vibrations of the stiffened hollow conical shells with different variable thickness distribution modes are investigated in detail in the context of Donnel-Mushtari conical shell theory. Two sets of boundary conditions have been considered. The algebraic energy equations of the conical shell and the stiffeners are established separately. The Rayleigh-Ritz method is used to equate maximum strain energy to maximum kinetic energy which leads to a standard linear eigenvalue problem. Numerical results are presented graphically for different geometric parameters. The parametric study reveals the characteristic behavior which is useful in selecting the shell thickness distribution modes and the stiffener type. The comparison between the present results and those of finite element method shows that the present results agree well with those of finite element method.

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