Elliptical Deformation of a Floating Roof Pontoon Due to Radial Second Mode of Sloshing (Effect of the Geometry of Pontoon Cross-Section on the Hoop Membrane Stress)

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
M. Utsumi ◽  
K. Ishida
Keyword(s):  
Cross Section ◽  
Plane Deformation ◽  
Previous Method ◽  
Improved Method ◽  
Membrane Stress ◽  
Oil Storage ◽  
Second Mode ◽  
Out Of Plane ◽  
Bending Stresses ◽  
Circumferential Wave

The radial second mode of sloshing in a circular cylindrical oil storage tank induces an out-of-plane deformation of the floating roof deck. The radial contraction of the deck due to this out-of-plane deformation contains modal components with circumferential wave numbers 0 and 2, thereby causing an elliptical deformation of the pontoon, which encloses the deck. In a previous paper, the stress caused by this elliptical deformation was analyzed by regarding the radial contraction of the deck as an enforced displacement of the whole pontoon. This paper presents an improved method for this stress analysis by considering the radial contraction of the deck as an enforced displacement of the joint between the deck and the pontoon. First, the effectiveness of the previous method in estimating the hoop membrane stress at the joint with the deck is confirmed by comparing the results obtained from the previous and improved method. Next, the improved method is used to predict also the other stress components in each portion of the pontoon. Numerical results reveal that the bending stresses are magnified locally near the joint with the deck and that the hoop membrane stress in the outer portion of the pontoon sensitively depends on the geometry of the cross-section of the pontoon. It is found that the hoop membrane stress near the joint between the outer rim and the top (or bottom) of the pontoon can be significantly reduced by increasing the slope of the top (or bottom) of the pontoon.

Vibration Analysis of a Floating Roof Subjected to Radial Second Mode of Sloshing

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
M. Utsumi ◽  
K. Ishida
Keyword(s):  
Storage Tank ◽  
Plane Deformation ◽  
Analysis Method ◽  
Numerical Result ◽  
Oil Storage ◽  
Second Mode ◽  
Oil Storage Tank ◽  
Out Of Plane ◽  
Cost Efficient ◽  
Good Agreement

In a previous paper, a cost-efficient modal analysis method for the vibration of a floating roof coupled with nonlinear sloshing in a circular cylindrical oil storage tank is presented. This method is extended to the case in which the out-of-plane deformation of the roof-deck caused by the radial second mode of sloshing induces an elliptical deformation of the pontoon around the deck. First, the radial contraction of the deck is calculated from the slope of the out-of-plane deformation of the deck, and the following two points are confirmed: (i) the circumferential variation in this radial contraction results in the elliptical deformation of the pontoon, and (ii) the present theoretical prediction for the radial contraction is in good agreement with a numerical result obtained by LS-DYNA. Based on these points, the stresses arising in the pontoon are calculated by considering the contraction of the deck as an enforced displacement of the pontoon. Numerical results show that (a) the elliptical deformation of the pontoon causes a large circumferential in-plane stress, (b) reduction achieved by the increase in the thickness of the deck is larger for the radial contraction of the deck and the stresses in the pontoon than for the out-of-plane deformation of the deck, and (c) the radial contraction of the deck for a fixed value of the out-of-plane deformation of the deck increases with the decrease in the radius of the deck.

Global–Local-Distortional Vibration of Thin-Walled Rectangular Multi-Cell Beams

2015 ◽  
Vol 15 (08) ◽  
pp. 1540022 ◽  
Author(s):  
Rodrigo Gonçalves ◽  
Nuno Peres ◽  
Rui Bebiano ◽  
Dinar Camotim
Keyword(s):  
Cross Section ◽  
Plane Deformation ◽  
Beam Theory ◽  
Deformation Mode ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Computationally Efficient ◽  
Out Of Plane ◽  
Thin Walled ◽  
Deformation Modes

This paper presents the results of an investigation concerning the free vibration behavior (undamped natural frequencies and vibration mode shapes) of thin-walled beams with rectangular multi-cell cross-section (assemblies of parallel rectangular cells in a single direction). Besides local (plate-type) and global (flexural, torsional and extensional) vibration modes, attention is paid to the relatively less-known distortional vibration modes, which involve cross-section out-of-plane (warping) and in-plane deformation, including displacements of the wall intersections. A computationally efficient semi-analytical Generalized Beam Theory (GBT) approach is employed to obtain insight into the mechanics of the problem. In particular, the intrinsic modal decomposition features of GBT — the fact that the beam is described using a hierarchical set of relevant cross-section deformation modes — are exploited to identify and categorize the most relevant vibration modes and deformation mode couplings.

Seismic Behavior of a Single Deck Floating Roof Due to Second Sloshing Mode

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Mohammad Ali Goudarzi
Keyword(s):  
Numerical Analysis ◽  
Seismic Behavior ◽  
Plane Deformation ◽  
Vertical Deformation ◽  
Radial Shrinkage ◽  
Deck Plate ◽  
Second Mode ◽  
Out Of Plane ◽  
Sloshing Mode ◽  
Seismic Stress

Second mode sloshing motion induces the vertical out-of-plane deformation of deck plate in single deck floating roof (FR) cylindrical storage tanks. This vertical deformation tends to shrink the deck plate in horizontal direction, causing elliptical deformation of pontoon. In order to evaluate seismic stress caused by the second sloshing mode, the relation between out-of-plane vertical deformation of deck plate and the radial shrinkage of pontoon is required. In this study, a simple analytical approach is proposed for calculating the shrinkage of the pontoon. The numerical analysis is also performed for five tanks with various dimensions to assess the effectiveness of introduced new method. The accuracy of proposed formulation is confirmed by comparing its results with the results of both numerical analysis and available experimental measurements. Despite existing empirical formula, geometric characteristics of considered tanks are involved in proposed formulation and it is shown that final relationship could be utilized for various ranges of tank dimensions without scaling or unit limitation. It is also found from the results of numerical analysis that the dynamic characteristics of sloshing modes are not considerably affected by the presence of floating roof.

scholarly journals Characterization and ballistic performance of thin pre-damaged resin-starved aramid-fiber composite panels

2021 ◽  
pp. 004051752110134
Author(s):  
Cerise A Edwards ◽  
Stephen L Ogin ◽  
David A Jesson ◽  
Matthew Oldfield ◽  
Rebecca L Livesey ◽  
...  
Keyword(s):  
Fiber Composite ◽  
Plane Deformation ◽  
Ballistic Impact ◽  
Image Correlation ◽  
Composite Panel ◽  
Composite Panels ◽  
Micro Computed Tomography ◽  
Ballistic Performance ◽  
Low Level ◽  
Out Of Plane

Military personnel use protective armor systems that are frequently exposed to low-level damage, such as non-ballistic impact, wear-and-tear from everyday use, and damage during storage of equipment. The extent to which such low-level pre-damage could affect the performance of an armor system is unknown. In this work, low-level pre-damage has been introduced into a Kevlar/phenolic resin-starved composite panel using tensile loading. The tensile stress–strain behavior of this eight-layer material has been investigated and has been found to have two distinct regions; these have been understood in terms of the microstructure and damage within the composite panels investigated using micro-computed tomography and digital image correlation. Ballistic testing carried out on pristine (control) and pre-damaged panels did not indicate any difference in the V50 ballistic performance. However, an indication of a difference in response to ballistic impact was observed; the area of maximal local out-of-plane deformation for the pre-damaged panels was found to be twice that of the control panels, and the global out-of-plane deformation across the panel was also larger.

scholarly journals In-Process Measurement of Three-Dimensional Deformations Based on Speckle Photography

2021 ◽  
Vol 11 (11) ◽  
pp. 4981
Author(s):  
Andreas Tausendfreund ◽  
Dirk Stöbener ◽  
Andreas Fischer
Keyword(s):  
Evaluation Method ◽  
Process Analysis ◽  
Plane Deformation ◽  
Three Dimensional ◽  
Machining Process ◽  
Image Correlation ◽  
Speckle Photography ◽  
Process Measurement ◽  
Out Of Plane ◽  
Plane Deformations

In the concept of the process signature, the relationship between a material load and the modification remaining in the workpiece is used to better understand and optimize manufacturing processes. The basic prerequisite for this is to be able to measure the loads occurring during the machining process in the form of mechanical deformations. Speckle photography is suitable for this in-process measurement task and is already used in a variety of ways for in-plane deformation measurements. The shortcoming of this fast and robust measurement technique based on image correlation techniques is that out-of-plane deformations in the direction of the measurement system cannot be detected and increases the measurement error of in-plane deformations. In this paper, we investigate a method that infers local out-of-plane motions of the workpiece surface from the decorrelation of speckle patterns and is thus able to reconstruct three-dimensional deformation fields. The implementation of the evaluation method enables a fast reconstruction of 3D deformation fields, so that the in-process capability remains given. First measurements in a deep rolling process show that dynamic deformations underneath the die can be captured and demonstrate the suitability of the speckle method for manufacturing process analysis.

Inverse algorithm for out-of-plane deformation in shearography

2021 ◽  
Vol 53 (1) ◽  
Author(s):  
Shuangle Wu ◽  
Fangyuan Sun ◽  
Haotian Xie ◽  
Qihan Zhao ◽  
Peizheng Yan ◽  
...  
Keyword(s):  
Plane Deformation ◽  
Inverse Algorithm ◽  
Out Of Plane

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

The Allocating Point Solution for the Out-of-Plane Stability of Arches with the Double Symmetry Axis Section

2010 ◽  
Vol 29-32 ◽  
pp. 1313-1316
Author(s):  
Yu Ji Chen
Keyword(s):  
Governing Equation ◽  
Spline Function ◽  
Symmetry Axis ◽  
Plane Deformation ◽  
Point Method ◽  
Out Of Plane ◽  
Point Solution ◽  
Double Symmetry ◽  
Paper Method

In order to study the buckling mechanics behaviour of the out-of-plane stability of arches with the double symmetry axis section, by mean of potential variational theories, considering the out-of-plane deformation of arches, the out-of-plane stability governing equation of arches was obtained. The problem was solved by the spline function allocating point method. An example was calculated with this paper method. It is shown by comparing the result of this paper with the others that the paper method is reliable and accurate.

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