Stable Postbuckling Equilibria of Axially Compressed, Elastic Circular Cylindrical Shells: A Finite-Element Analysis and Comparison With Experiments

1977 ◽  
Vol 44 (3) ◽  
pp. 475-481 ◽  
Author(s):  
A. Maewal ◽  
W. Nachbar
Keyword(s):  
Finite Element ◽  
Bifurcation Point ◽  
Cylindrical Shells ◽  
Special Technique ◽  
Equilibrium Path ◽  
Postbuckling Behavior ◽  
Element Analysis ◽  
Bifurcation Points ◽  
Contour Maps ◽  
Circular Cylindrical Shells

Postbuckling behavior of clamped circular cylindrical shells of finite length under uniform axial compression is analyzed using a potential-energy-based, displacement finite-element method. Contour maps of equal radial deflection computed from this analysis for one-tier and two-tier postbuckled, stable equilibrium patterns show very good agreement with experimentally measured contour maps for a polyester shell with L/R = 0.7 and R/h = 405. Developed for these computations, and essential for them, are: (a) A 48 DOF shell element; (b) A method to calculate accurately for the perfect shell the nonlinear fundamental path and its bifurcation points. The lowest such bifurcation point does not correspond to the first observed postbuckle pattern, which is reproduced by calculating the continuous equilibrium path from the sixth bifurcation point. Patterns of successive postbuckling shapes that are formed under additional end-shortening are determined by using a special technique to calculate equilibrium paths extending continuously from still higher bifurcation points on the fundamental path.

Stresses around large circular holes in uniform circular cylindrical shells

1982 ◽  
Vol 17 (1) ◽  
pp. 9-12 ◽  
Author(s):  
J W Bull
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Element Analysis ◽  
Three Point Bending ◽  
Circular Holes ◽  
Circular Cylindrical Shells ◽  
Good Agreement

An experimental and finite element analysis of a uniform cylindrical shell with a large circular cut-out is presented. In this analysis three hole sizes are considered, namely μ = 2.037, 4.084, and 6.344 (where μ = {[12(1 - y2)]1/4/2} × [ a/( Rt)1/2]), for loadings of axial compression, torsion and three point bending. The experimental results are the only ones available for cylindrical shells with large values of μ (except for one graph by Savin (1)†), while for three point bending there is no previously published theoretical or analytical results. Good agreement is found between the calculated and experimental stresses around the holes.

Structural Optimization and Form-Finding of Cylindrical Shells for Targeted Elastic Postbuckling Response

2014 ◽  
Author(s):  
Nan Hu ◽  
Rigoberto Burgueño ◽  
Nizar Lajnef
Keyword(s):  
Finite Element ◽  
Multiple Scales ◽  
Optimization Problems ◽  
Numerical Study ◽  
Cylindrical Shells ◽  
Mode Shapes ◽  
Optimization Approach ◽  
Postbuckling Behavior ◽  
Element Analysis ◽  
Thin Walled

This paper presents a finite element based numerical study on controlling the postbuckling behavior of thin-walled cylindrical shells under axial compression. With the increasing interest of various disciplines for harnessing elastic instabilities in materials and mechanical systems, the postbuckling behavior of thin-walled cylindrical shells may have a new role to design materials and structures at multiple scales with switchable functionalities, morphogenesis, etc. In the design optimization approach presented herein, the mode shapes and their amplitudes are linearly combined to generate initial geometrical designs with predefined imperfections. A nonlinear postbuckling finite element analysis evaluates the design objective function, i.e., the desired postbuckling force-displacement path. Single and multi-objective optimization problems are formulated with design variables consisting of shape parameters that scale base eigenvalue shapes. A gradient-based algorithm and numerical sensitivity evaluations are used. Results suggest that an optimized shape for a cylindrical shell can achieve a targeted response in the elastic postbuckling regime with multiple mode transitions and energy dissipation characteristics. The optimization process and the obtained geometry can be potentially used for energy harvesting and other sensing and actuation applications.

Reduced-Order Nonlinear Modal Equations of Circular Cylindrical Shells Based on the Finite-Element Method

2004 ◽  
Author(s):  
Yukinori Kobayashi ◽  
Tomoaki Furukawa ◽  
Gen Yamada
Keyword(s):  
Finite Element ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Nonlinear Finite Element ◽  
Element Analysis ◽  
Reduced Order ◽  
Finite Element Equation ◽  
Displacement Vectors ◽  
Circular Cylindrical Shells

This paper presents a procedure to derive reduced-order nonlinear modal equations of circular cylindrical shells. Modal analysis is applied to the nonlinear finite element equation by using base vectors obtained by the finite element analysis. Reduced-order modal equations are derived by transforming the equations of motion from the physical coordinates to the modal coordinates. Base vectors for the transformation consist of dominant linear eigenmodes and nonlinear displacement vectors derived approximately from the nonlinear finite element equation. Asymmetry of the deformation of the circular cylindrical shell with respect to its neutral surface is taken into consideration to determine the base vectors. Numerical results show good agreement with those presented in other papers.

Finite Element Analysis of Composite Cylindrical Shells with and without Cutouts

2012 ◽  
Vol 1 (1) ◽  
pp. 34-38
Author(s):  
B. Siva Konda Reddy ◽  
◽  
CH. Srikanth ◽  
G. Sandeep Kumar ◽  
◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cylindrical Shells ◽  
Element Analysis ◽  
Composite Cylindrical Shells

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

On A Formulation of the Elastic Stability Equations of Circular Cylindrical Shells Under Variable Internal Pressure

1985 ◽  
Vol 9 (2) ◽  
pp. 64-69
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Mathematical Model ◽  
Internal Pressure ◽  
Cylindrical Shells ◽  
Direct Analysis ◽  
Elastic Stability ◽  
Equilibrium Path ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Variable Internal Pressure ◽  
The Mathematical Model

The mathematical model of the stability analysis of circular cylindrical shells under arbitrary internal pressure is presented. The paper consists of a direct analysis of the equilibrium modes in the neighbourhood of the unperturbed principal equilibrium path. The final stability condition results in a completely symmetric differential operator which is then compared with current theories found in the literature.

Postbuckling Analyses of Elastic Cylindrical Shells Under Axial Compression

2009 ◽  
Author(s):  
Takaya Kobayashi ◽  
Yasuko Mihara
Keyword(s):  
Critical Load ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
General Purpose ◽  
Experimental Results ◽  
Ideal Condition ◽  
Postbuckling Behavior ◽  
Mode Shift ◽  
Applied Loading ◽  
Circular Cylindrical Shells

In designing a modern lightweight structure, it is of technical importance to assure its safety against buckling under the applied loading conditions. For this issue, the determination of the critical load in an ideal condition is not sufficient, but it is further required to clarify the postbuckling behavior, that is, the behavior of the structure after passing through the critical load. One of the reasons is to estimate the effect of practically unavoidable imperfections on the critical load, and the second reason is to evaluate the ultimate strength to exploit the load-carrying capacity of the structure. For the buckling problem of circular cylindrical shells under axial compression, a number of experimental and theoretical studies have been made by many researchers. In the case of the very thin shell that exhibits elastic buckling, experimental results show that after the primary buckling, secondary buckling takes place accompanying successive reductions in the number of circumferential waves at every mode shift on systematic (one-by-one) basis. In this paper, we traced this successive buckling of circular cylindrical shells using the latest in general-purpose FEM technology. We carried out our studies with three approaches: the arc-length method (the modified Riks method); the static stabilizing method with the aid of (artificial) damping especially, for the local instability; and the explicit dynamic procedure. The studies accomplished the simulation of successive buckling following unstable paths, and showed agreement with the experimental results.

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