The Application of Combined Buckling Mode Imperfections on Shell Structures

2013 ◽  
Author(s):  
Sean Laird ◽  
Robert Frith
Keyword(s):  
Plastic Material ◽  
Initial Imperfection ◽  
External Pressure ◽  
Mode Shapes ◽  
Buckling Mode ◽  
Linear Elastic ◽  
Higher Order Modes ◽  
Fabrication Tolerances ◽  
Critical Buckling Pressure ◽  
Shell Geometry

This paper presents the results of a numerical investigation for applying a combination of buckling mode shapes as an initial imperfection to shell geometries under external pressure. The effect that imposed imperfections had on the critical buckling pressure was found to be dependent upon both the shell geometry and the characteristics of the imposed imperfection. Imperfections were generated via linear combinations of the linear elastic buckling mode shapes, with the fundamental mode having the greatest influence. For a number of tests, inclusion of higher order modes into the initial imperfection caused an increase in the critical buckling pressure. This behaviour was observed for both elastic and plastic material models. For the purpose of limiting the extent of the analysis, the magnitudes of imposed imperfections were maintained within the industry required fabrication tolerances and in particular, acceptable out-of-roundness. The purpose of this paper is to present the methodology and results from this imperfection investigation. Additional testing and discussion may allow a design methodology to be developed that addresses the application of initial imperfections in shells under external pressure.

Elastic buckling of imperfect circular toroidal shells under external pressure

1998 ◽  
Vol 212 (3) ◽  
pp. 197-209 ◽  
Author(s):  
G D Galletly
Keyword(s):  
External Pressure ◽  
Mode Shapes ◽  
Buckling Mode ◽  
Geometric Imperfections ◽  
Buckling Modes ◽  
The North ◽  
Buckling Resistance ◽  
Maximum Decrease ◽  
Initial Geometric Imperfections ◽  
Toroidal Shells

When perfect, externally pressurized complete circular toroidal shells buckle, the minimum buckling pressure pcr usually occurs in the axisymmetric n = 0 mode, with pcr for n = 2 being only slightly larger. In the present paper, the effects of axisymmetric initial geometric imperfections on reducing pcr for the perfect shell are investigated. Various types of imperfection are studied, i.e. localized flat spots, smooth dimples, sinusoids and buckling mode shapes. The principal geometry investigated was R/b = 10, b/t = 100, although other geometries were also considered. The maximum decrease in buckling resistance, Δ pcr, was found to be about 16 per cent at δ 0/t = 1 and it occurred with smooth dimples at the north (φ = 180°) and south (φ=0°) poles. This value of Δ pcr is not large. Circular toroidal shells thus do not appear to be very sensitive to axisymmetric initial geometric imperfections. The reductions in the buckling pressure of the above shell, arising because of initial imperfections having the shape of the n = 0 and the n = 2 buckling modes, were 12 and 9 per cent respectively for wo/t = 1. These decreases in the buckling resistance are smaller than that for the ‘two smooth dimple’ case mentioned above.

The Influence of Stochastic Imperfection Field on the Bearing Capacity of Hyperbolic Cooling Towers

2011 ◽  
Vol 374-377 ◽  
pp. 2297-2300
Author(s):  
Hai Zhao ◽  
Ya Zhou Xu ◽  
Guo Liang Bai
Keyword(s):  
Bearing Capacity ◽  
Large Scale ◽  
Initial Imperfection ◽  
Orthogonal Basis ◽  
Imperfection Sensitivity ◽  
Stochastic Field ◽  
Buckling Mode ◽  
Material Inhomogeneity ◽  
Initial Imperfections ◽  
Distribution Form

The uncontrollable factors such as construction errors, material inhomogeneity, etc. will inevitably lead to a certain initial imperfections. It is generally known that the stochastic initial imperfection of the structure is an important factor for affecting structural stability and bearing capacity. Since these imperfections are random in nature, this paper proposes the method mainly based on the standard orthogonal basis to expand the stochastic field, taking into account the decomposition of the stochastic initial imperfections related to structures, which is projected in the buckling mode orthogonal basis. In the end, the article by the stability analysis example shows that this method can use less random variables effectively describing the original stochastic imperfection field, and efficiently search for the most unfavorable initial imperfection distribution form in order to ensure the imperfection sensitivity structures have a higher reliability, so it can be applied to large-scale engineering structure stochastic imperfection analysis.

Distortional buckling of compressed cold‐formed lipped C channels via buckling mode shapes

ce/papers ◽  
2021 ◽  
Vol 4 (2-4) ◽  
pp. 2535-2541
Author(s):  
Bálint Vaszilievits‐Sömjén
Keyword(s):  
Mode Shapes ◽  
Distortional Buckling ◽  
Buckling Mode

CLASSIFICATION OF BUCKLING MODES IN STIFFENED FUNCTIONALLY GRADED COMPOSITE TUBES SUBJECT TO BENDING

2021 ◽  
Author(s):  
LUAN TRINH ◽  
PAUL WEAVER
Keyword(s):  
Wall Thickness ◽  
Functionally Graded ◽  
Geometric Parameters ◽  
Mode Shapes ◽  
Local Mode ◽  
Buckling Mode ◽  
Global Mode ◽  
Local Modes ◽  
Linear Discriminant ◽  
Finite Element Software

Bamboo poles, and other one-dimensional thin-walled structures are usually loaded under compression, which may also be subject to bending arising from eccentric loading. Many of these structures contain diaphragms or circumferential stiffeners to prevent cross-sectional distortions and so enhance overall load-carrying response. Such hierarchical structures can compartmentalize buckling to local regions in addition to withstanding global buckling phenomena. Predicting the buckling mode shapes of such structures for a range of geometric parameters is challenging due to the interaction of these global and local modes. Abaqus finite element software is used to model thousands of circular hollow tubes with random geometric parameters such that the ratios of radius to periodic length range from 1/3-1/7, the ratio of wall thickness to radius varies from 1/4-1/10. The material used in this study is a type of bamboo, where the Young’s and shear moduli are point-wise orthotropic and gradually increase in magnitude in the radial direction. Under eccentric loads with varying eccentricity, the structures can buckle into a global mode or local modes within an internode, i.e. periodic unit. Moreover, the local modes may contain only one wave or multiple waves in the circumferential direction. As expected, numerical results show that the global mode is more likely to occur in small and thick tubes, whereas the local modes are observed in larger tubes with a smaller number of circumferential waves present in thicker walls. Also, greater eccentricity pushes the local mode domains towards smaller tubes. An efficient classification method is developed herein to identify the domains of each mode shape in terms of radius, wall thickness and eccentricity. Based on linear discriminant analysis, explicit boundary surfaces for the three domains are defined for the obtained data, which can help designers in predicting the mode shapes of tubular structures under axial bending.

scholarly journals NUMERICAL MODELLING OF THE SOIL BEHAVIOUR BY USING NEWLY DEVELOPED ADVANCED MATERIAL MODEL

2017 ◽  
Vol 57 (1) ◽  
pp. 58-70 ◽  
Author(s):  
Jan Veselý
Keyword(s):  
Numerical Modelling ◽  
Plastic Material ◽  
Material Model ◽  
Small Strain ◽  
Theoretical Background ◽  
Linear Elastic ◽  
In Situ Data ◽  
Modified Cam Clay ◽  
Soil Behaviour

This paper describes a theoretical background, implementation and validation of the newly developed Jardine plastic hardening-softening model (JPHS model), which can be used for numerical modelling of the soils behaviour. Although the JPHS model is based on the elasto-plastic theory, like the Mohr-Coulomb model that is widely used in geotechnics, it contains some improvements, which removes the main disadvantages of the MC model. The presented model is coupled with an isotopically hardening and softening law, non-linear elastic stress-strain law, non-associated elasto-plastic material description and a cap yield surface. The validation of the model is done by comparing the numerical results with real measured data from the laboratory tests and by testing of the model on the real project of the tunnel excavation. The 3D numerical analysis is performed and the comparison between the JPHS, Mohr-Coulomb, Modified Cam-Clay, Hardening small strain model and monitoring in-situ data is done.

Ruga mechanics of soft-orifice closure under external pressure

2021 ◽  
Vol 477 (2249) ◽  
Author(s):  
Hanxun Jin ◽  
Alexander K. Landauer ◽  
Kyung-Suk Kim
Keyword(s):  
Surface Layer ◽  
Limit Load ◽  
Phase Evolution ◽  
External Pressure ◽  
Soft Material ◽  
Buckling Mode ◽  
Cross Sectional ◽  
Threefold Symmetry ◽  
Instability Modes ◽  
Symmetry Mode

Here, we report the closure resistance of a soft-material bilayer orifice increases against external pressure, along with ruga-phase evolution, in contrast to the conventional predictions of the matrix-free cylindrical-shell buckling pressure. Experiments demonstrate that the generic soft-material orifice creases in a threefold symmetry at a limit-load pressure of p / μ  ≈ 1.20, where μ is the shear modulus. Once the creasing initiates, the triple crease wings gradually grow as the pressure increases until the orifice completely closes at p / μ  ≈ 3.0. By contrast, a stiff-surface bilayer orifice initially wrinkles with a multifold symmetry mode and subsequently develops ruga-phase evolution, progressively reducing the orifice cross-sectional area as pressure increases. The buckling-initiation mode is determined by the layer's thickness and stiffness, and the pressure by two types of the layer's instability modes—the surface-layer-wrinkling mode for a compliant and the ring-buckling mode for a stiff layer. The ring-buckling mode tends to set the twofold symmetry for the entire post-buckling closure process, while the high-frequency surface-layer-wrinkling mode evolves with successive symmetry breaking to a final closure configuration of two- or threefold symmetry. Finally, we found that the threefold symmetry mode for the entire closure process provides the orifice's strongest closure resistance, and human saphenous veins remarkably follow this threefold symmetry ruga evolution pathway.

Buckling Analysis of Tapered Continuous Columns by Using Modified Buckling Mode Shapes

2019 ◽  
Vol 18 (2) ◽  
pp. 160-166
Author(s):  
Sina Toosi ◽  
Akbar Esfandiari ◽  
Ahmad Rahbar Ranji
Keyword(s):  
Buckling Analysis ◽  
Mode Shapes ◽  
Buckling Mode

GBT Analysis of Steel-Concrete Composite Beams: Recent Developments

2020 ◽  
Vol 20 (13) ◽  
pp. 2041007
Author(s):  
Rodrigo Gonçalves ◽  
Dinar Camotim ◽  
David Henriques
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Composite Beams ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Shear Lag ◽  
Buckling Mode ◽  
Concrete Cracking ◽  
Lag Effects ◽  
Recent Developments

This paper reports the most recent developments concerning Generalized Beam Theory (GBT) formulations, and corresponding finite element implementations, for steel-concrete composite beams. These formulations are able to perform the following types of analysis: (i) materially nonlinear analysis, to calculate the beam load-displacement response, up to collapse, including steel plasticity, concrete cracking/crushing and shear lag effects, (ii) bifurcation (linear stability) analysis, to obtain local/distortional bifurcation loads and buckling mode shapes of beams subjected to negative (hogging) bending, accounting for shear lag and concrete cracking effects and (iii) long-term service analysis including creep, cracking and arbitrary cross-section deformation (which includes shear lag) effects. The potential (computational efficiency and accuracy) of the proposed GBT-based finite elements is illustrated through several numerical examples. For comparison purposes, results obtained with standard finite strip and shell/brick finite element models are provided.

A Global Energy Approach for Analysis of a Propagating Buckle in Submarine Pipelines

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Mingqiao Tang ◽  
Jianghong Xue ◽  
Renhuai Liu
Keyword(s):  
Steady State ◽  
Transition Zone ◽  
Plastic Material ◽  
External Pressure ◽  
Thick Wall ◽  
Yield Coefficient ◽  
Rigid Plastic ◽  
Stretching Factor ◽  
Buckle Propagation ◽  
Membrane Stretching

This paper presents a unique approach to analyze the steady-state buckle propagation phenomenon in underwater pipelines. In previous work, we restudied the buckling of a very long pipeline subjected to external pressure and found that buckling happens only over a certain length of the pipeline. In this paper, the collapse mode of the pipeline obtained in previous studies is taken as the transition zone during steady-state buckle propagation. Kinematics in the transition zone is analyzed based on von Kármán–Donnell type of nonlinearity. Assuming linear elastic rigid plastic material properties, the mechanical responses in the transition zone are examined using the deformation theory. Two parameters, the yield coefficient and the membrane stretching factor, are introduced to depict the effects of transversal bending and the membrane stretching, respectively. Analytical solution of buckle propagation pressure is derived by considering the energy conversation calculated from shell theory. It is found that the buckle propagation performance is governed by the transversal bending, including the circumferential bending and longitudinal bending. The membrane stretching is significant only for thick wall pipeline, in particular when the ratio of radius-to thickness is small than ten. The analysis is in effect by comparing the obtained solutions with the well-established predictions and the experimental results.

scholarly journals Snap-Through of the Very Shallow Shell with Initial Imperfection

2016 ◽  
Vol 16 (2) ◽  
pp. 43-48
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Analysis ◽  
Shallow Shell ◽  
Initial Imperfection ◽  
Limit Load ◽  
External Pressure ◽  
Load Level ◽  
Nonlinear Equilibrium ◽  
Load Displacement ◽  
Ansys System

Abstract Elastic shallow shell of translation subjected to the external pressure is analysed in the paper numerically by FEM. Nonlinear equilibrium paths are calculated for the different boundary conditions. Special attention is paid to the influence of initial imperfection on the limit load level of fundamental load-displacement path of nonlinear analysis. ANSYS system was used for analysis, arclength method was chosen for obtain fundamental load-displacement path of solution.

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