Bounds on the Maximum Thermoelastic Stress and Deflection in a Beam and Plate

1966 ◽  
Vol 33 (4) ◽  
pp. 881-887 ◽  
Author(s):  
Bruno A. Boley
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Thermoelastic Stress ◽  
Cross Sectional ◽  
Special Cases ◽  
End Conditions ◽  
Instantaneous Temperature ◽  
The Cross ◽  
Sectional Shape

It is shown in this paper that the thermal stress in a beam or plate cannot exceed the value kαEΔT, where ΔT is the maximum instantaneous temperature excursion in a cross section, and k is a coefficient dependent on the shape of the cross section. A simple general formula for k is found, and results for several special cases of practical interest are given. For rectangular beams (suitably oriented) and for plates, for example, k = 4/3. For any section, k = 1 if the thermal moment is zero; simplifications also occur if the thermal force is zero. The corresponding results for beam deflections are also carried out: The maximum deflection cannot exceed the value kδ kδ′αLΔT, where kδ and kδ′ are coefficients depending respectively on the cross-sectional shape and on the end conditions. For example, for rectangular cross sections, kδ = 3/4; and for a simply supported beam, kδ′ = 1/8.

Design of C-Frames Using Real-Coded Genetic Optimization Algorithms and NURBS

1999 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Cross Section ◽  
Cross Sections ◽  
Design Parameters ◽  
Binary Representation ◽  
Cross Sectional ◽  
Search Spaces ◽  
The Cross ◽  
Sectional Shape ◽  
Real Coded Genetic Algorithms

Abstract C-frames constitute a large portion of machine tools that are currently used in industry. Examples of these frames include drilling machines, presses, punching and stamping machines, clamps, hooks, etc. The design parameters of these frames include the dimensions of their cross-sections, which should be chosen to withstand the applied loads and minimize the element’s overall weight. Traditionally, the cross-section of C-frame belonged to a set of primitive shapes, which included I, T, trapezoidal and rectangular sections. This paper introduces a new methodology for designing the frame’s cross-section. The cross-sectional shape is represented using non-uniform rational B-Spline (NURBS) in order to give it a form of shape flexibility. A special form of genetic algorithms known as real-coded genetic algorithms is used to conduct the search for the design objectives. Real-coded genetic algorithms are known to outperform the simple binary representation genetic algorithms when dealing with continuous search spaces. The results showed that the optimal shape was a semi I/T-section with the material bulk related to the applied load.

Automated 3D measurement of fiber cross section morphology in handsheets

2012 ◽  
Vol 27 (2) ◽  
pp. 264-269 ◽  
Author(s):  
Christian Lorbach ◽  
Ulrich Hirn ◽  
Johannes Kritzinger ◽  
Wolfgang Bauer
Keyword(s):  
Image Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Image Plane ◽  
3D Measurement ◽  
Cross Sectional ◽  
Fiber Cross Section ◽  
Fiber Wall ◽  
Sectional Shape ◽  
Cross Section Geometry

Abstract We present a method for 3D measurement of fiber cross sectional morphology from handsheets. An automated procedure is used to acquire 3D datasets of fiber cross sectional images using an automated microtome and light microscopy. The fiber cross section geometry is extracted using digital image analysis. Simple sample preparation and highly automated image acquisition and image analysis are providing an efficient tool to analyze large samples. It is demonstrated that if fibers are tilted towards the image plane the images of fiber cross sections are always larger than the true fiber cross section geometry. In our analysis the tilting angles of the fibers to the image plane are measured. The resulting fiber cross sectional images are distorted to compensate the error due to fiber tilt, restoring the true fiber cross sectional shape. We use an approximated correction, the paper provides error estimates of the approximation. Measurement results for fiber wall thickness, fiber coarseness and fiber collapse are presented for one hardwood and one softwood pulp.

scholarly journals Supplemental Material: Plate boundary trench retreat and dextral shear drive intracontinental fault-slip histories: Neogene dextral faulting across the Gabbs Valley and Gillis Ranges, Central Walker Lane, Nevada

2020 ◽  
Author(s):  
J. Lee ◽  
et al.
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Plate Boundary ◽  
Fault Slip ◽  
Cross Sectional ◽  
Walker Lane ◽  
Dextral Shear ◽  
The Cross

<div>Figure 6. Interpretative cross sections illustrating the cross-sectional geometry of several paleovalleys. See Figure 3 for location of all cross sections and Figure 8 for location of cross section CCʹ. Cross sections AAʹ and BBʹ are plotted at the same scale, and cross section CCʹ is plotted at a smaller scale. Figure 6 is intended to be viewed at a width of 45.1 cm.</div>

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

Numerical study for the improvement of bead spreading architecture with modified nozzle geometries in additive manufacturing of polymers

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Easir Arafat Papon ◽  
Anwarul Haque ◽  
Muhammad Ali Rob Sharif
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
3D Printing ◽  
Cross Section ◽  
Nozzle Exit ◽  
Cross Sectional ◽  
Content Type ◽  
The Cross ◽  
Viscous Polymer ◽  
Sectional Shape

Purpose This paper aims to develop a numerical model of bead spreading architecture of a viscous polymer in fused filament fabrication (FFF) process with different nozzle geometry. This paper also focuses on the manufacturing feasibility of the nozzles and 3D printing of the molten beads using the developed nozzles. Design/methodology/approach The flow of a highly viscous polymer from a nozzle, the melt expansion in free space and the deposition of the melt on a moving platform are captured using the FLUENT volume of fluid (VOF) method based computational fluid dynamics code. The free surface motion of the material is captured in VOF, which is governed by the hydrodynamics of the two-phase flow. The phases involved in the numerical model are liquid polymer and air. A laminar, non-Newtonian and non-isothermal flow is assumed. Under such assumptions, the spreading characteristic of the polymer is simulated with different nozzle-exit geometries. The governing equations are solved on a regular stationary grid following a transient algorithm, where the boundary between the polymer and the air is tracked by piecewise linear interface construction (PLIC) to reconstruct the free surface. The prototype nozzles were also manufactured, and the deposition of the molten beads on a flatbed was performed using a commercial 3D printer. The deposited bead cross-sections were examined through optical microscopic examination, and the cross-sectional profiles were compared with those obtained in the numerical simulations. Findings The numerical model successfully predicted the spreading characteristics and the cross-sectional shape of the extruded bead. The cross-sectional shape of the bead varied from elliptical (with circular nozzle) to trapezoidal (with square and star nozzles) where the top and bottom surfaces are significantly flattened (which is desirable to reduce the void spaces in the cross-section). The numerical model yielded a good approximation of the bead cross-section, capturing most of the geometric features of the bead with a reasonable qualitative agreement compared to the experiment. The quantitative comparison of the cross-sectional profiles against experimental observation also indicated a favorable agreement. The significant improvement observed in the bead cross-section with the square and star nozzles is the flattening of the surfaces. Originality/value The developed numerical algorithm attempts to address the fundamental challenge of voids and bonding in the FFF process. It presents a new approach to increase the inter-bead bonding and reduce the inter-bead voids in 3D printing of polymers by modifying the bead cross-sectional shape through the modification of nozzle exit-geometry. The change in bead cross-sectional shape from elliptical (circular) to trapezoidal (square and star) cross-section is supposed to increase the contact surface area and inter-bead bonding while in contact with adjacent beads.

scholarly journals Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 316 ◽  
Author(s):  
Yongquan Zhang ◽  
Hong Lu ◽  
He Ling ◽  
Yang Lian ◽  
Mingtian Ma
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Predictive Accuracy ◽  
Neutral Axis ◽  
Longitudinal Stress ◽  
Linear Superposition ◽  
Element Analysis ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape

The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Erythrocyte Sedimentation Rates in Inclined Vessels

1973 ◽  
Vol 51 (9) ◽  
pp. 685-690 ◽  
Author(s):  
R. N. O'Brien ◽  
M. B. Hocking ◽  
P. McOrmond ◽  
K. R. Thornton
Keyword(s):  
Cross Section ◽  
Sedimentation Rates ◽  
Settling Rate ◽  
Cross Sectional ◽  
Erythrocyte Sedimentation ◽  
The Cross ◽  
Sectional Shape ◽  
Erythrocyte Sedimentation Rates ◽  
Test Rack ◽  
Settling Rates

The rates of erythrocyte settling have been investigated in round and square cross-section tubes, vertically; and at nine different angles; and with the square tubes flat and on edge, to a minimum of 15° from the horizontal. Apparent settling rates increased as the angle from the horizontal decreased. Real settling rates (vertical settling rates) increased sharply on decreasing the angle from the horizontal, to a maximum at about 60°, and then decreased less abruptly for the shallower angles. The cross-sectional shape of the tube did not significantly affect the settling rates of erythrocytes. Settling in inclined tubes proceeds fast enough to permit clinical erythrocyte settling rate (E.S.R.) tests to be carried out in 10 min in place of the usual 60 min. If the standard E.S.R. test rack deviates as little as 5° from the vertical it can cause the observed settling rates to double relative to readings obtained on a vertical rack.

Semicrystalline Structure and Mechanical Properties of Polyolefin-Based Materials

2012 ◽  
Vol 441 ◽  
pp. 713-716
Author(s):  
Mizue Kuriyagawa ◽  
Koh Hei Nitta
Keyword(s):  
Mechanical Properties ◽  
Cross Section ◽  
Draw Ratio ◽  
Structural Model ◽  
Point Of View ◽  
Cross Sectional ◽  
Molecular Weights ◽  
The Cross ◽  
Sectional Shape ◽  
Structural Point

The mechanical yielding and necking behaviors of metallocene-catalyzed high density polyethylenes were investigated from a structural point of view. In particular the natural draw ratio was investigated with different crosshead speeds, molecular weights, and the cross-section shapes of sample specimens. We proposed a structural model for explaining the necking formation in addition to the molecular weight and the cross-sectional shape dependences of the natural draw ratio.

scholarly journals ЩОДО ПИТАННЯ ПРО РАЦІОНАЛЬНУ ФОРМУ ПРЕСОВАНОГО БУЛЬБОКОСИНЦЯ

2020 ◽  
pp. 165-172
Author(s):  
А. Г. Дибир ◽  
А. А. Кирпикин ◽  
Н. И. Пекельный
Keyword(s):  
Service Life ◽  
Residual Stresses ◽  
Cross Section ◽  
Transverse Load ◽  
Shear Stresses ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape ◽  
Aircraft Panels ◽  
Better Than

In airplane building and helicopter engineering a bulb angle bar  an angle bar with a bulb at the end of a wall are widespread. They are better than a simple angle bar, since they have higher critical stresses under compression more than the proportionality limit. They are better than T bar, as T bar are fastened with two rows of rivets, which impairs tightness. Bulb angle bar are better than Z bar. The latter are higher, which reduces the structural height of the cross section and increases the load on the panel and usually have an excess cross-sectional area. Bulb angle bars are widely used in the structure of metal fuselages of airplanes and helicopters, in the tail boom of helicopters, in the wing and tail unit of light aircraft, in flaps, ailerons and rudders. However, modern the bulb angle bar have a significant drawback.When a bulb angle bar is loaded by a transverse load from the skin in the wing structure, tail unit, fuselage, except of normal stresses from bending of the stringer with attached skin, supported by ribs or frames, additional normal and shear torsional stresses arise. This torsion is caused by the fact that the lateral load is not applied at the center of the bend. Additional stresses reduce the service life and tightness of the structure in this place. An altered cross-sectional shape of the bulb is proposed for use in light aircraft panels to increase their strength and service life. The change in shape had a significant impact on the location of the center of the bend in the cross section. The determination of the position of the center of the bend in the balloncube was carried out using the Wagner model with walls not working for shear stresses. The modified cross-sectional shape of the bulbogon allowed to reduce the level of residual stresses after the panels were assembled, to rationally transfer the load from the casing to the stringer and to improve the technology of their assembly in the panels. It is recommended to drill holes for rivets in the stringer in the middle of the entire width of its shelf, taking into account the wall.A modified cross-sectional shape of a corner with bulb is proposed for use in light aircraft panels. The change in shape had a significant impact on the location of the center of the bend in the cross section. This made it possible to reduce the level of residual stresses after the assembly of the panels, to rationally transfer the load from the casing to the stringer and to improve the technology of their assembly.

scholarly journals Analytical description of nanowires. I. Regular cross sections for zincblende and diamond structures

2019 ◽  
Vol 75 (5) ◽  
pp. 788-802 ◽  
Author(s):  
Dirk König ◽  
Sean C. Smith
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Analytical Description ◽  
Data Interpretation ◽  
High Symmetry ◽  
Cross Sectional ◽  
Impurity Atoms ◽  
Si Nanocrystals ◽  
Impurity Doping ◽  
The Cross

Semiconductor nanowires (NWires) experience stress and charge transfer from their environment and impurity atoms. In response, the environment of a NWire experiences a NWire stress response which may lead to propagated strain and a change in the shape and size of the NWire cross section. Here, geometric number series are deduced for zincblende- (zb-) and diamond-structured NWires of diameter d Wire to obtain the numbers of NWire atoms N Wire(d Wire[i]), bonds between NWire atoms N bnd(d Wire[i]) and interface bonds N IF(d Wire[i]) for six high-symmetry zb NWires with the low-index faceting that occurs frequently in both bottom-up and top-down approaches of NWire processing. Along with these primary parameters, the specific lengths of interface facets, the cross-sectional widths and heights and the cross-sectional areas are presented. The fundamental insights into NWire structures revealed here offer a universal gauge and thus could enable major advancements in data interpretation and understanding of all zb- and diamond-structure-based NWires. This statement is underpinned with results from the literature on cross-section images from III–V core–shell NWire growth and on Si NWires undergoing self-limiting oxidation and etching. The massive breakdown of impurity doping due to self-purification is shown to occur for both Si NWires and Si nanocrystals (NCs) for a ratio of N bnd/N Wire = N bnd/N NC = 1.94 ± 0.01 using published experimental data.

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