A PSO-Based Method for Tracing the Motion of Neutral Axis Plane of Asymmetric Hull Cross-Sections and its Application

2018 ◽  
Author(s):  
Chenfeng Li ◽  
Chao Gao ◽  
Xueqian Zhou ◽  
Sen Dong ◽  
Peng Fu ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
International Association ◽  
Random Search ◽  
Two Dimensions ◽  
Neutral Axis ◽  
Force Vector ◽  
Hull Girder ◽  
Vector Equilibrium ◽  
Force Equilibrium

The Smith’s method is stipulated by the International Association of Classification Societies in the Common Structure Rules as a standard method for estimating ultimate/residual strength of hull girder in both intact and damaged conditions. However, for the latter case where the effective hull cross-section is asymmetric and the neutral axis of damaged cross-section not only translates but also rotates, the additional force vector equilibrium also needs to be applied so as to determine the neutral axis plane. The commonly adopted iterative methods for the two-force-equilibrium problem do not always converge for the desired accuracy. This paper proposes a Particle Swarm Optimization based iteration method to trace the motion of the neutral axis plane of asymmetric cross sections. The translation and rotation of the neutral axis are taken as the two dimensions of particles in the model, and the force equilibrium error and the force vector equilibrium error are the objective functions. The neutral axis is determined by performing a random search within the entire range of possible position of neutral axis. The proposed method has been implemented and validated for the case of the DOW’s 1/3 frigate model, the analysis of efficiency and accuracy shows that the method performs in general better than traditional ones.

Ultimate Bearing Capacity Assessment of Hull Girder With Asymmetric Cross Section

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Chenfeng Li ◽  
Peng Fu ◽  
Huilong Ren ◽  
Weijun Xu ◽  
C. Guedes Soares
Keyword(s):  
Cross Section ◽  
Structural Integrity ◽  
Neutral Axis ◽  
Bending Moments ◽  
Hull Girder ◽  
Horizontal Wave ◽  
Asymmetric Load ◽  
Vector Equilibrium ◽  
Error Method ◽  
Force Equilibrium

The objective of this study is to investigate the variation of neutral axis of ship hull girder due to asymmetric geometry or asymmetric load, and its influence on the ultimate strength (ULS) of hull girder. In order to account for asymmetric geometries and loads of hull girders, the force equilibrium and force-vector equilibrium criteria together with a minimum convergence factors (error) method are employed to determine the translation and rotation of neutral axis plane (NAP) of symmetric or asymmetric hull cross section in the application of Smith's method at each step of curvature of the hull girder. The ULSs of Dow's 1/3 frigate model with three predefined structural integrity states, one intact and two damaged, respectively, is investigated by the improved Smith's method (ISM) for a range of variation of heeling angles. The influence of asymmetric geometry and load on the motion of NAP and on the ULS are analyzed and discussed. The results show that the improved iteration strategy together with the minimum convergence factors (error) method is efficient and more accurate in searching the translation and rotation of NAP. Finally, the envelope curves of the bending moments in the three predefined integrity states are obtained, which can be used for assessing ULS of hull girders under combined vertical and horizontal wave bending moments.

Ultimate Bearing Capacity Assessment of Hull Girder With Asymmetric Cross-Section

2017 ◽  
Author(s):  
ChenFeng Li ◽  
Peng Fu ◽  
HuiLong Ren ◽  
WeiJun Xu ◽  
C. Guedes Soares
Keyword(s):  
Ultimate Strength ◽  
Cross Section ◽  
Structural Integrity ◽  
Neutral Axis ◽  
Bending Moments ◽  
Hull Girder ◽  
Horizontal Wave ◽  
Asymmetric Load ◽  
Vector Equilibrium ◽  
Error Method

The objective of this study is to investigate the variation of neutral axis of ship hull girder due to asymmetric geometry or asymmetric load, and its influence on the ultimate strength of hull girder. In order to account for asymmetric geometries and loads of hull girders, the force equilibrium and force-vector equilibrium criteria together with a minimum convergence factors (error) method, are employed to determine the translation and rotation of neutral axis plane of symmetric or asymmetric hull cross-section in the application of Smith’s method at each step of curvature of the hull girder. The ultimate strengths of Dow’s 1/3 frigate model with three predefined structural integrity states, one intact and two damaged respectively, are investigated by the improved Smith’s method for a range of variation of heeling angles. The influence of asymmetric geometry and load on the motion of neutral axis plane and on the ultimate strength are analyzed and discussed. The results show that the improved iteration strategy together with the MCFM is self-adapting and more accurate in searching the translation and rotation of neutral axis plane. Finally, the envelope curves of the bending moments in the three predefined integrity states are obtained, which can be used for assessing ultimate strength of hull girders under combined vertical and horizontal wave bending moments.

Transmission of Elastic Stress Through Circular and Elliptic Cross Sections of Microstructural Elements Embedded in a Matrix Material

2004 ◽  
Vol 72 (4) ◽  
pp. 558-563 ◽  
Author(s):  
C. M. Kennefick
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Matrix Material ◽  
Circular Cross Section ◽  
Tensile Load ◽  
Two Dimensions ◽  
Radial Coordinate ◽  
Infinite Plane ◽  
Material Particle ◽  
Elliptic Cross

With the use of contact stress theory and complex variable methods in two dimensions, the transmission of a compressive stress through a circular cross section of a small material particle is calculated in the infinite plane of material below the circular cross section. The circular cross section of the particle is embedded in and completely bonded to an infinite plane of matrix material. It is shown that part of the stress is transmitted with a dependence of 1∕r, where r is a radial coordinate. Additionally, the stress is calculated in two dimensions for the interior of an ellipse that could model a cross section of a grain or particle. The boundary of the ellipse is loaded with the stress holding an elliptic kernel in place in an elastic matrix material after the kernel has undergone a small rotation under an applied tensile load. The resulting stresses are shown in contour plots for elliptic cross sections of varying shapes and orientations.

scholarly journals Cortical Thickness Adaptive Response to Mechanical Loading Depends on Periosteal Position and Varies Linearly With Loading Magnitude

2021 ◽  
Vol 9 ◽  
Author(s):  
Corey J. Miller ◽  
Silvia Trichilo ◽  
Edmund Pickering ◽  
Saulo Martelli ◽  
Peter Delisser ◽  
...  
Keyword(s):  
Bone Formation ◽  
Cross Section ◽  
Mechanical Loading ◽  
Cortical Thickness ◽  
Cross Sections ◽  
Peak Load ◽  
Neutral Axis ◽  
Cross Sectional ◽  
Periosteal Surface ◽  
Tensile Strains

The aim of the current study was to quantify the local effect of mechanical loading on cortical bone formation response at the periosteal surface using previously obtained μCT data from a mouse tibia mechanical loading study. A novel image analysis algorithm was developed to quantify local cortical thickness changes (ΔCt.Th) along the periosteal surface due to different peak loads (0N ≤ F ≤ 12N) applied to right-neurectomised mature female C57BL/6 mice. Furthermore, beam analysis was performed to analyse the local strain distribution including regions of tensile, compressive, and low strain magnitudes. Student’s paired t-test showed that ΔCt.Th in the proximal (25%), proximal/middle (37%), and middle (50%) cross-sections (along the z-axis of tibia) is strongly associated with the peak applied loads. These changes are significant in a majority of periosteal positions, in particular those experiencing high compressive or tensile strains. No association between F and ΔCt.Th was found in regions around the neutral axis. For the most distal cross-section (75%), the association of loading magnitude and ΔCt.Th was not as pronounced as the more proximal cross-sections. Also, bone formation responses along the periosteum did not occur in regions of highest compressive and tensile strains predicted by beam theory. This could be due to complex experimental loading conditions which were not explicitly accounted for in the mechanical analysis. Our results show that the bone formation response depends on the load magnitude and the periosteal position. Bone resorption due to the neurectomy of the loaded tibia occurs throughout the entire cross-sectional region for all investigated cortical sections 25, 37, 50, and 75%. For peak applied loads higher than 4 N, compressive and tensile regions show bone formation; however, regions around the neutral axis show constant resorption. The 50% cross-section showed the most regular ΔCt.Th response with increased loading when compared to 25 and 37% cross-sections. Relative thickness gains of approximately 70, 60, and 55% were observed for F = 12 N in the 25, 37, and 50% cross-sections. ΔCt.Th at selected points of the periosteum follow a linear response with increased peak load; no lazy zone was observed at these positions.

A New Unified Strength of Materials Solution for Stresses in Curved Beams and Rings

1992 ◽  
Vol 114 (2) ◽  
pp. 231-237 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Cross Sections ◽  
Solution Method ◽  
Normal Force ◽  
Neutral Axis ◽  
Curved Beams ◽  
Strength Of Materials ◽  
Special Cases ◽  
Elasticity Solutions ◽  
Simplified Solution ◽  
Force Equilibrium

Presently existing strength of materials solutions for stresses in curved beams use an incorrect normal force equilibrium condition to define neutral axis location, and to reach a simplified solution, which neglects the curvature effect on stresses due to normal force. This article presents a new but a most general form of the strength of materials solution for determining tangential normal stresses in curved beams, including reductions to special cases. The neutral axis phenomenon is clarified and experimentally verified. Several numerical examples are included, some of which offer photoelastic experimental results, where results predicted by the exact elasticity solution, method of the article, Winkler’s theory, and the conventional simplified method are compared. The hook, diametrically loaded cut, and full ring applications are included. It is shown that simplified theory leads to very large errors. Results by the method offered are very reliable with small errors which are comparable with those of exact elasticity solutions. Stress and deflection analyses of curved beams with varying thicknesses of cross-sections by exact elasticity solutions are given in a separate article [6].

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Oxygen K near edge structures studied with multiple scattering calculations

1988 ◽  
Vol 46 ◽  
pp. 504-505
Author(s):  
Xudong Weng ◽  
Peter Rez
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Partial Cross Section ◽  
Energy Window ◽  
Edge Structure ◽  
Fine Structures ◽  
Hydrogenic Model ◽  
Electron Energy Loss ◽  
Quantitative Chemical

In electron energy loss spectroscopy, quantitative chemical microanalysis is performed by comparison of the intensity under a specific inner shell edge with the corresponding partial cross section. There are two commonly used models for calculations of atomic partial cross sections, the hydrogenic model and the Hartree-Slater model. Partial cross sections could also be measured from standards of known compositions. These partial cross sections are complicated by variations in the edge shapes, such as the near edge structure (ELNES) and extended fine structures (ELEXFS). The role of these solid state effects in the partial cross sections, and the transferability of the partial cross sections from material to material, has yet to be fully explored. In this work, we consider the oxygen K edge in several oxides as oxygen is present in many materials. Since the energy window of interest is in the range of 20-100 eV, we limit ourselves to the near edge structures.

Absolute inner-shell cross section determination for EELS analysis

1988 ◽  
Vol 46 ◽  
pp. 534-535
Author(s):  
P.A. Crozier
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Absolute Cross Section ◽  
Specimen Thickness ◽  
Mass Thickness ◽  
Scattering Cross ◽  
Before And After ◽  
Estimated Error ◽  
Scattering Cross Sections ◽  
Electron Microscopist

Absolute inelastic scattering cross sections or mean free paths are often used in EELS analysis for determining elemental concentrations and specimen thickness. In most instances, theoretical values must be used because there have been few attempts to determine experimental scattering cross sections from solids under the conditions of interest to electron microscopist. In addition to providing data for spectral quantitation, absolute cross section measurements yields useful information on many of the approximations which are frequently involved in EELS analysis procedures. In this paper, experimental cross sections are presented for some inner-shell edges of Al, Cu, Ag and Au.Uniform thin films of the previously mentioned materials were prepared by vacuum evaporation onto microscope cover slips. The cover slips were weighed before and after evaporation to determine the mass thickness of the films. The estimated error in this method of determining mass thickness was ±7 x 107g/cm2. The films were floated off in water and mounted on Cu grids.

A technique for preparing semiconductor cross sections for both TEM and SEM analysis

1989 ◽  
Vol 47 ◽  
pp. 712-713
Author(s):  
Stanley J. Klepeis ◽  
J.P. Benedict ◽  
R.M Anderson
Keyword(s):  
Sample Preparation ◽  
Cross Section ◽  
Cross Sections ◽  
Sem Analysis ◽  
Preparation Technique ◽  
Ion Milling ◽  
Tem Analysis ◽  
Polished Cross Section ◽  
Area Of Interest ◽  
Polished Side

The ability to prepare a cross-section of a specific semiconductor structure for both SEM and TEM analysis is vital in characterizing the smaller, more complex devices that are now being designed and manufactured. In the past, a unique sample was prepared for either SEM or TEM analysis of a structure. In choosing to do SEM, valuable and unique information was lost to TEM analysis. An alternative, the SEM examination of thinned TEM samples, was frequently made difficult by topographical artifacts introduced by mechanical polishing and lengthy ion-milling. Thus, the need to produce a TEM sample from a unique,cross-sectioned SEM sample has produced this sample preparation technique.The technique is divided into an SEM and a TEM sample preparation phase. The first four steps in the SEM phase: bulk reduction, cleaning, gluing and trimming produces a reinforced sample with the area of interest in the center of the sample. This sample is then mounted on a special SEM stud. The stud is inserted into an L-shaped holder and this holder is attached to the Klepeis polisher (see figs. 1 and 2). An SEM cross-section of the sample is then prepared by mechanically polishing the sample to the area of interest using the Klepeis polisher. The polished cross-section is cleaned and the SEM stud with the attached sample, is removed from the L-shaped holder. The stud is then inserted into the ion-miller and the sample is briefly milled (less than 2 minutes) on the polished side. The sample on the stud may then be carbon coated and placed in the SEM for analysis.

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