Discussion on Boote and Mascia: "On the Nonlinear Analysis Methodologies for Thin Spherical Shells Under External Pressure with Different Finite-Element Codes"

1991 ◽  
Vol 35 (04) ◽  
pp. 352-355
Author(s):  
G.D. Galletiy ◽  
J. Blachut
Keyword(s):  
Finite Element ◽  
Nonlinear Analysis ◽  
External Pressure ◽  
General Purpose ◽  
Spherical Shells ◽  
Geometric Imperfections ◽  
Buckling Resistance ◽  
The Subject ◽  
Initial Geometric Imperfections ◽  
Doubly Curved

The accurate prediction of the collapse pressures of thin, doubly curved elastic-plastic shells subjected to external pressure is important in many applications—not least to the occupants of submarines! As is well known, initial geometric imperfections can, in many shells, result in a substantial decrease in the shell's buckling resistance. In their paper, the authors (Boote and Mascia) discuss one imperfect hemispherical model which they analyzed with the help of two general purpose finite-element codes (MARC and ANSYS). The authors do not discuss the use of simpler programs for analyzing these shells [for example, BOSOR 5; Bushnell (1976)][Galletly etal (1987) or other work which has been published on the subject]. We have a number of comments on the subject paper, and these are given below.

Buckling Design of Imperfect Welded Hemispherical Shells Subjected to External Pressure

1991 ◽  
Vol 205 (3) ◽  
pp. 175-188 ◽  
Author(s):  
G D Galletly ◽  
J Blachut
Keyword(s):  
Experimental Information ◽  
External Pressure ◽  
Design Stage ◽  
Arc Length ◽  
Spherical Shells ◽  
Geometric Imperfections ◽  
Collapse Pressure ◽  
Buckling Resistance ◽  
Initial Geometric Imperfections ◽  
Hemispherical Shells

Welded hemispherical or spherical shells in practice have initial geometric imperfections in them that are random in nature. These imperfections determine the buckling resistance of a shell to external pressure but their magnitudes will not be known until after the shell has been built. If suitable simplified, but realistic, imperfection shapes can be found, then a reasonably accurate theoretical prediction of a spherical shell's buckling/collapse pressure should be possible at the design stage. The main aim of the present paper is to show that the test results obtained at the David Taylor Model Basin (DTMB) on 28 welded hemispherical shells (having diameters of 0.75 and 1.68 m) can be predicted quite well using such simplified shape imperfections. This was done in two ways. In the first, equations for determining the theoretical collapse pressures of externally pressurized imperfect spherical shells were utilized. The only imperfection parameter used in these equations is δ0, the amplitude of the inward radial deviation of the pole of the shell. Two values for δ0 were studied but the best overall agreement between test and theory was found using δ0 = 0.05 ✓ (Rt). This produced ratios of experimental to numerical collapse pressures in the range 0.98–1.30 (in most cases the test result was the higher). The second approach also used simplified imperfection shapes, but in conjunction with the shell buckling program BOSOR 5. The arc length of the imperfection was taken as simp = k ✓ (Rt) (with k = 3.0 or 3.5) and its amplitude as δ0 = 0.05√(Rt). Using this procedure on the 28 DTMB shells gave satisfactory agreement between the experimental and the computer predictions (in the range 0.92–1.20). These results are very encouraging. The foregoing method is, however, only a first step in the computerized buckling design of welded spherical shells and it needs to be checked against spherical shells having other values of R/t. In addition, more experimental information on the initial geometric imperfections in welded spherical shells (and how they vary with R/t) is desirable. A comparison is also given in the paper of the collapse pressures of spherical shells, as obtained from codes, with those predicted by computer analyses when the maximum shape deviations allowed by the codes are employed in the computer programs. The computed collapse pressures are frequently higher than the values given by the buckling strength curves in the codes. On the other hand, some amplitudes of imperfections studied in the paper give acceptable results. It would be helpful to designers if agreement could be reached on an imperfection shape (amplitude and arc length) that was generally acceptable. Residual stresses are not considered in this paper. They might be expected to decrease a spherical shell's buckling resistance to external pressure. However, experimentally, this does not always happen.

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.

scholarly journals Nonlinear dynamics of spherical shells buckling under step pressure

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180884 ◽  
Author(s):  
Jan Sieber ◽  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Nonlinear Dynamics ◽  
External Pressure ◽  
Dynamic Buckling ◽  
Spherically Symmetric ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Buckling Mode ◽  
Geometric Imperfections ◽  
Pressure Threshold ◽  
Initial Geometric Imperfections

Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric ‘breathing’ mode and the buckling mode. In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead, there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections, the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure.

Evaluation of Compressive Strengths of HPS Plate Systems Stiffened with Trapezoidal Stiffeners

2013 ◽  
Vol 671-674 ◽  
pp. 1025-1028
Author(s):  
Dong Ku Shin ◽  
Kyungsik Kim
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
High Performance ◽  
Nonlinear Finite Element ◽  
Linear Strain ◽  
Element Analysis ◽  
Geometric Imperfections ◽  
Eurocode 3 ◽  
Initial Geometric Imperfections ◽  
Plate System

The ultimate compressive strengths of high performance steel (HPS) plate system stiffened longitudinally by closed stiffeners have been investigated by the nonlinear finite element analysis. Both conventional and high performance steels were considered in models following multi-linear strain hardening constitutive relationships. Initial geometric imperfections and residual stresses were also incorporated in the analysis. Numerical results have been compared to compressive strengths from Eurocode 3 EN 1993-1-5 and FHWA-TS-80-205. It has been found that although use of Eurocode 3 EN 1993-1-5 and FHWA-TS-80-205 may lead to highly conservative design strengths when very large column slenderness parameters are encountered

scholarly journals ANÁLISE NUMÉRICA DE PERFIS DE AÇO FORMADOS A FRIO EM SEÇÃO “I” CONSTITUÍDA POR DUPLO “U” SUBMETIDOS À COMPRESSÃO

2020 ◽  
Vol 12 (1) ◽  
pp. 95-110
Author(s):  
Gabriel Cintra Macedo ◽  
Wanderson Fernando Maia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plate Thickness ◽  
Experimental Studies ◽  
Structural Behavior ◽  
The Finite Element Method ◽  
Geometric Imperfections ◽  
Initial Geometric Imperfections ◽  
Normal Strength ◽  
Double Channel

Although the section “I”, in double channel, is widely used, there are few studies on its behavior. Therefore, this work aims to contribute to a greater mastery over the structural behavior of this built-up sections. A nonlinear numerical analysis was performed using the Finite Element Method in the Ansys program, using existing experimental studies as a comparative database. The effect of length, number of connections, plate thickness and the presence of geometric and material imperfections on the normal strength of the columns. For this analysis, it was essential to consider the initial geometric imperfections, because there was a considerable reduction in the normal strength of the columns, thus getting closer to the values obtained experimentally. With regard to normative procedures, values against security were found in most cases, showing the need to conduct further studies in the area for the development of more appropriate formulations.

Clamped torispherical shells under external pressure — some new results

1988 ◽  
Vol 23 (1) ◽  
pp. 9-24 ◽  
Author(s):  
J Blachut ◽  
G D Galletly
Keyword(s):  
Failure Mode ◽  
External Pressure ◽  
Spherical Cap ◽  
Geometric Imperfections ◽  
Collapse Pressure ◽  
Modes Of Failure ◽  
Shell Buckling ◽  
Bifurcation Buckling ◽  
Initial Geometric Imperfections ◽  
The One

Perfect clamped torispherical shells subjected to external pressure are analysed in the paper using the BOSOR 5 shell buckling program. Various values of the knuckle radius-to-diameter ratio ( r/D) and the spherical cap radius-to-thickness ratio ( Rs/ t) were studied, as well as four values of σyp, the yield point of the material. Buckling/collapse pressures, modes of failure and the development of plastic zones in the shell wall were determined. A simple diagram is presented which enables the failure mode in these shells to be predicted. The collapse pressures, pc, were also plotted against the parameter Λs (√( pyp/ pcr)). When the controlling failure mode was axisymmetric yielding in the knuckle, the collapse pressure curves depended on the value of σyp, which is unusual. However, when the controlling failure mode was bifurcation buckling (at the crown/knuckle junction), the collapse pressure curves for the various values of σyp all merged, i.e., they were independent of σyp. This latter situation is the one which normally occurs with the buckling of cylindrical and hemispherical shells. A limited investigation was also made into the effects of axisymmetric initial geometric imperfections on the strength of externally-pressurised torispherical shells. When the failure mode was axisymmetric yielding in the knuckle, initial imperfections of moderate size did not affect the collapse pressures. In the cases where bifurcation buckling at the crown/knuckle junction occurred, small initial geometric imperfections at the apex did not affect the buckling pressure, but axisymmetric imperfections at the buckle location did influence it. With the other failure mode (i.e., axisymmetric yielding collapse at the crown of the shell), initial geometric imperfections caused a reduction in the torisphere's strength.

On the Nonlinear Analysis Methodologies for Thin Spherical Shells Under External Pressure with Different Finite-Element Codes

1989 ◽  
Vol 33 (04) ◽  
pp. 318-325
Author(s):  
Dario Boote ◽  
Donatella Mascia
Keyword(s):  
Finite Element ◽  
Numerical Procedure ◽  
External Pressure ◽  
Experimental Investigations ◽  
Nonlinear Analyses ◽  
Spherical Shells ◽  
Double Curvature ◽  
Load Carrying ◽  
Material Load ◽  
Structure Collapse

Submersible structures consist merely of simple and double curvature thin-walled shells. For this kind of structure, collapse occurs due to the combined nonlinear action of buckling and plasticity of material. Load-carrying capacity may then be assessed mainly by two approaches: experimental investigations and step-by-step numerical procedures. In nonlinear analyses, the results obtained are influenced by the magnitude of the load increment adopted. Solution procedures are then required in order to choose adequate parameters for material failure description as well as elastic nonlinearity. The aim of this paper is to carry out a suitable numerical procedure whose reliability does not depend on the finite-element code adopted.

Penetrations in Shells Under External Pressure

1970 ◽  
Vol 92 (2) ◽  
pp. 269-274
Author(s):  
R. C. DeHart ◽  
L. F. Greimann
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Stress Condition ◽  
External Pressure ◽  
Experimental Stress ◽  
Spherical Shells ◽  
Premature Failure ◽  
Resistant Structure ◽  
Theoretical Results ◽  
Stress Analyses

Penetrations, in the pressure-resistant structure of a submersible, disturb the stress condition in the shell and may cause a premature failure. In this paper, two types of finite-element solutions are used to predict the stress distribution near view port openings in spherical shells under external pressure. Results of experimental stress analyses are also given and compared to the theoretical results.

A Data-Driven Framework for Buckling Analysis of Near-Spherical Composite Shells under External Pressure

2021 ◽  
pp. 1-27
Author(s):  
Mitansh Doshi ◽  
Xin Ning
Keyword(s):  
Machine Learning ◽  
Finite Element ◽  
Learning Model ◽  
External Pressure ◽  
Finite Element Simulations ◽  
Data Driven ◽  
Composite Shells ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Machine Learning Model

Abstract This paper presents a data-driven framework that can accurately predict the buckling loads of composite near-spherical shells (i.e. variants of regular icosahedral shells) under external pressure. This framework utilizes finite element simulations to generate data to train a machine learning regression model based on open-source algorithm Extreme Gradient Boosting (XGBoost). The trained XGBoost machine learning model can then predict buckling loads of new designs with small margin of error without time-consuming finite element simulations. Examples of near-spherical composite shells with various geometries and material layups demonstrate the efficiency and accuracy of the framework. The machine learning model removes the demanding hardware and software requirements on computing buckling loads of near-spherical shells, making it particularly suitable to users without access to those computational resources.

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