scholarly journals Buckling Capacity Curves for Steel Spherical Shells Loaded by the External Pressure

2015 ◽  
Vol 15 (4) ◽  
pp. 43-55 ◽  
Author(s):  
Paweł Błażejewski ◽  
Jakub Marcinowski
Keyword(s):  
Computer Software ◽  
External Pressure ◽  
Additional Parameter ◽  
Spherical Shells ◽  
Spherical Cap ◽  
Capacity Curve ◽  
Capacity Curves ◽  
Method Of Determination ◽  
Buckling Resistance

Abstract Assessment of buckling resistance of pressurised spherical cap is not an easy task. There exist two different approaches which allow to achieve this goal. The first approach involves performing advanced numerical analyses in which material and geometrical nonlinearities would be taken into account as well as considering the worst imperfections of the defined amplitude. This kind of analysis is customarily called GMNIA and is carried out by means of the computer software based on FEM. The other, comparatively easier approach, relies on the utilisation of earlier prepared procedures which enable determination of the critical resistance pRcr, the plastic resistance pRpl and buckling parameters a, b, h, l 0 needed to the definition of the standard buckling resistance curve. The determination of the buckling capacity curve for the particular class of spherical caps is the principal goal of this work. The method of determination of the critical pressure and the plastic resistance were described by the authors in [1] whereas the worst imperfection mode for the considered class of spherical shells was found in [2]. The determination of buckling parameters defining the buckling capacity curve for the whole class of shells is more complicated task. For this reason the authors focused their attention on spherical steel caps with the radius to thickness ratio of R/t = 500, the semi angle j = 30o and the boundary condition BC2 (the clamped supporting edge). Taking into account all imperfection forms considered in [2] and different amplitudes expressed by the multiple of the shell thickness, sets of buckling parameters defining the capacity curve were determined. These parameters were determined by the methods proposed by Rotter in [3] and [4] where the method of determination of the exponent h by means of additional parameter k was presented. As a result of the performed analyses the standard capacity curves for all considered imperfection modes and amplitudes 0.5t, 1.0t, 1.5t were obtained. Obtained capacity curves were compared with the recommendations for different fabrication quality classes formulated in [5].

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.

scholarly journals Development of a Procedure for the Determination of the Buckling Resistance of Steel Spherical Shells According to EC 1993-1-6

Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 25
Author(s):  
Paweł Błażejewski
Keyword(s):  
Spherical Shell ◽  
Simple Calculation ◽  
Difficult Problem ◽  
Calculation Algorithm ◽  
Spherical Shells ◽  
Engineering Approach ◽  
Low Degree ◽  
Buckling Resistance

This paper presents the process of developing a new procedure for estimating the buckling capacity of spherical shells. This procedure is based entirely on the assumptions included in the standard mentioned, EN-1993-1-6 and also becomes a complement of EDR5th by unifying provisions included in them. This procedure is characterized by clarity and its algorithm is characterized by a low degree of complexity. While developing the procedure, no attempt was made to change the main postulates accompanying the dimensions of the spherical shells. The result is a simple engineering approach to the difficult problem of determining the buckling capacity of a spherical shell. In spite of the simple calculation algorithm for estimating the buckling capacity of spherical shells, the results obtained reflect extremely accurately the behavior of real spherical shells, regardless of their geometry and the material used to manufacture them.

scholarly journals Comparisons of Buckling Capacity Curves of Pressurized Spheres with EDR Provisions and Experimental Results

2017 ◽  
Vol 25 (2) ◽  
pp. 59-76 ◽  
Author(s):  
Paweł Błażejewski ◽  
Jakub Marcinowski
Keyword(s):  
Nonlinear Analysis ◽  
General Procedure ◽  
Experimental Results ◽  
Spherical Shells ◽  
Geometrically Nonlinear Analysis ◽  
Design Recommendations ◽  
Capacity Curves ◽  
Buckling Resistance ◽  
The Stability ◽  
Linear Buckling Analysis

Abstract Existing provisions leading to the assessment of the buckling resistance of pressurised spherical shells were published in the European Design Recommendations (EDR) [1]. This book comprises rules which refer to the stability of steel shells of different shapes. In the first step of the general procedure they require calculation of two reference quantities: the elastic critical buckling reference pRcr and the plastic reference resistance pRpl. These quantities should be determined in the linear buckling analysis (LBA) and in the materially nonlinear analysis (MNA) respectively. Only in the case of spherical shells the existing procedure has exceptional character. It is based on the geometrically nonlinear analysis (GNA) and on the geometrically and materially nonlinear analysis (GMNA), respectively. From this reason, in this particular case there was a need to change the existing approach. The new procedure was presented in the work of Błażejewski & Marcinowski in 2016 (comp. [2]). All steps of the procedure leading to the assessment of buckling resistance of pressurized steel, spherical shells were presented in this work. The elaborated procedure is consistent with provisions of Eurocode EN1993-1-6 (comp. [3]) and with recommendations inserted in Europeans Design Recommendations [1]. The proposed capacity curves were compared with existing proposal published in [1] for three different fabrication quality classes predicted in [3]. In this work also comparisons of author’s proposals with experimental results obtained by other authors were presented.

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.

Computer-Assisted High-Re Solution TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 162-163
Author(s):  
F.A. Ponce ◽  
H. Hikashi
Keyword(s):  
Signal To Noise Ratio ◽  
Accurate Determination ◽  
Computer Software ◽  
Video Camera ◽  
Image Contrast ◽  
Objective Lens ◽  
Computer Assisted ◽  
Optical Parameters ◽  
Astigmatism Correction

The determination of the atomic positions from HRTEM micrographs is only possible if the optical parameters are known to a certain accuracy, and reliable through-focus series are available to match the experimental images with calculated images of possible atomic models. The main limitation in interpreting images at the atomic level is the knowledge of the optical parameters such as beam alignment, astigmatism correction and defocus value. Under ordinary conditions, the uncertainty in these values is sufficiently large to prevent the accurate determination of the atomic positions. Therefore, in order to achieve the resolution power of the microscope (under 0.2nm) it is necessary to take extraordinary measures. The use of on line computers has been proposed [e.g.: 2-5] and used with certain amount of success.We have built a system that can perform operations in the range of one frame stored and analyzed per second. A schematic diagram of the system is shown in figure 1. A JEOL 4000EX microscope equipped with an external computer interface is directly linked to a SUN-3 computer. All electrical parameters in the microscope can be changed via this interface by the use of a set of commands. The image is received from a video camera. A commercial image processor improves the signal-to-noise ratio by recursively averaging with a time constant, usually set at 0.25 sec. The computer software is based on a multi-window system and is entirely mouse-driven. All operations can be performed by clicking the mouse on the appropiate windows and buttons. This capability leads to extreme friendliness, ease of operation, and high operator speeds. Image analysis can be done in various ways. Here, we have measured the image contrast and used it to optimize certain parameters. The system is designed to have instant access to: (a) x- and y- alignment coils, (b) x- and y- astigmatism correction coils, and (c) objective lens current. The algorithm is shown in figure 2. Figure 3 shows an example taken from a thin CdTe crystal. The image contrast is displayed for changing objective lens current (defocus value). The display is calibrated in angstroms. Images are stored on the disk and are accessible by clicking the data points in the graph. Some of the frame-store images are displayed in Fig. 4.

Development of a method for multielemental determination in water by EDXRF with radioisotopic source of 238Pu.

2019 ◽  
Vol 7 (2A) ◽  
Author(s):  
Camilo Fuentes Serrano ◽  
Juan Reinaldo Estevez Alvares ◽  
Alfredo Montero Alvarez ◽  
Ivan Pupo Gonzales ◽  
Zahily Herrero Fernandez ◽  
...  
Keyword(s):  
Thin Layer ◽  
Expanded Uncertainty ◽  
Considerable Decrease ◽  
X Ray ◽  
Precipitation Efficiency ◽  
Method Of Determination ◽  
Sensitivity Curves ◽  
Order Of Magnitude ◽  
Metrological Parameters

A method for determination of Cr, Fe, Co, Ni, Cu, Zn, Hg and Pb in waters by Energy Dispersive X Ray Fluorescence (EDXRF) was implemented, using a radioisotopic source of 238Pu. For previous concentration was employed a procedure including a coprecipitation step with ammonium pyrrolidinedithiocarbamate (APDC) as quelant agent, the separation of the phases by filtration, the measurement of filter by EDXRF and quantification by a thin layer absolute method. Sensitivity curves for K and L lines were obtained respectively. The sensitivity for most elements was greater by an order of magnitude in the case of measurement with a source of 238Pu instead of 109Cd, which means a considerable decrease in measurement times. The influence of the concentration in the precipitation efficiency was evaluated for each element. In all cases the recoveries are close to 100%, for this reason it can be affirmed that the method of determination of the studied elements is quantitative. Metrological parameters of the method such as trueness, precision, detection limit and uncertainty were calculated. A procedure to calculate the uncertainty of the method was elaborated; the most significant source of uncertainty for the thin layer EDXRF method is associated with the determination of instrumental sensitivities. The error associated with the determination, expressed as expanded uncertainty (in %), varied from 15.4% for low element concentrations (2.5-5 μg/L) to 5.4% for the higher concentration range (20-25 μg/L).

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