Smooth Mixed Geometry Profiles of Nozzles and Transition Ducts

2005 ◽  
Vol 127 (6) ◽  
pp. 1211-1213 ◽  
Author(s):  
James F. Wilson
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Smooth Surface ◽  
Axial Flow ◽  
Plane Flow ◽  
Out Of Plane ◽  
Surface Profiles

Parametric equations are derived that characterize smooth surface profiles for two general classes of nozzles and nonbranching transition ducts: straight sections for axial flow and curved sections (elbows) for in-plane or out-of-plane flow. For each profile, the terminal cross sections are specified as rectangular, elliptical, circular, or a combination of those shapes. At each terminal and in line with the flow, the displacement, slope, and curvature with its respective intersecting uniform section is maintained. Included is a design example of a 90deg elbow duct whose cross section remains constant between terminals of elliptical and circular cross sections.

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.

scholarly journals Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

2020 ◽  
Vol 10 (21) ◽  
pp. 7802
Author(s):  
Jarosław Latalski ◽  
Daniele Zulli
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Beam Theory ◽  
Middle Surface ◽  
Fem Model ◽  
Out Of Plane ◽  
Thin Walled ◽  
Generalized Beam Theory ◽  
Load Conditions

The use of the Generalized Beam Theory (GBT) is extended to thin-walled beams with curvilinear cross-sections. After defining the kinematic features of the walls, where their curvature is consistently accounted for, the displacement of the points is assumed as linear combination of unknown amplitudes and pre-established trial functions. The latter, and specifically their in-plane components, are chosen as dynamic modes of a curved beam in the shape of the member cross-section. Moreover, the out-of-plane components come from the imposition of the Vlasov internal constraint of shear indeformable middle surface. For a case study of semi-annular cross-section, i.e., constant curvature, the modes are analytically evaluated and the procedure is implemented for two different load conditions. Outcomes are compared to those of a FEM model.

Out-of-plane buckling of arches with rectangular cross-sections and curved webs

2021 ◽  
Author(s):  
Gilles Van Staen ◽  
Philippe Van Bogaert ◽  
Hans De Backer
Keyword(s):  
Sectional Curvature ◽  
Cross Section ◽  
Cross Sections ◽  
Plate Thickness ◽  
Cross Sectional ◽  
Fem Model ◽  
Out Of Plane ◽  
Arch Bridges ◽  
The Relationship ◽  
The Web

<p>Contemporary arch bridges are mostly designed as slender structures. Due to the presence of mainly compressive forces in the arches, the bridge may become prone to out-of-plane buckling. The main purpose of this research is to examine the influence of the geometric properties of a cross-section of the arch on this behaviour. To this end, a detailed FEM model of an arch bridge is built and validated by the results of a measurement programme. Thereafter, the critical buckling load is examined by numerical and analytical analyses. Furthermore, the influence of the plate thickness and the introduction of a cross-sectional curvature in the web on the buckling behaviour is evaluated. From that, it can be concluded that the relationship between the critical load and moment of inertia around the weak axis of the arch is linear, and in addition independent of the shape of the cross-section. Nevertheless, a cross-sectional curvature in the web shows the most potential in terms of structural efficiency.</p>

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.

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

Cross Section Analysis of Cu Filled TSVs Based on High Throughput Plasma-FIB Milling

2012 ◽  
Author(s):  
Frank Altmann ◽  
Jens Beyersdorfer ◽  
Jan Schischka ◽  
Michael Krause ◽  
German Franz ◽  
...  
Keyword(s):  
High Resolution ◽  
Cross Section ◽  
High Throughput ◽  
Cross Sections ◽  
Electron Backscatter Diffraction ◽  
Grain Structure ◽  
Electron Backscatter ◽  
Section Surface ◽  
Backscatter Diffraction ◽  
Section Analysis

Abstract In this paper the new Vion™ Plasma-FIB system, developed by FEI, is evaluated for cross sectioning of Cu filled Through Silicon Via (TSV) interconnects. The aim of the study presented in this paper is to evaluate and optimise different Plasma-FIB (P-FIB) milling strategies in terms of performance and cross section surface quality. The sufficient preservation of microstructures within cross sections is crucial for subsequent Electron Backscatter Diffraction (EBSD) grain structure analyses and a high resolution interface characterisation by TEM.

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