scholarly journals First-Order Size Effects in the Mechanics of Miniaturized Components

2008 ◽  
Vol 13-14 ◽  
pp. 183-192 ◽  
Author(s):  
J.P.M. Hoefnagels ◽  
P.J.M. Janssen ◽  
T.H. de Keijser ◽  
M.G.D. Geers
Keyword(s):  
Free Surface ◽  
Grain Boundary ◽  
Cross Section ◽  
Stress Level ◽  
Size Effects ◽  
Uniaxial Tensile ◽  
Order Effects ◽  
First Order ◽  
Single Grain ◽  
The Cross

This work analyses those size effects that are encountered first upon downscaling, including grain boundary effects, free surface effects, grain statistics effects. The separate influence of first-order effects was carefully investigated from uniaxial tensile tests on high-purity aluminum specimens with a well-defined microstructure of through-thickness grains, whereby the total number of grains in the cross-section was reduced towards a single grain in a cross-section by, first, decreasing the film thickness and, second, for specimens with through-thickness grains decreasing the specimen width. In addition, 3D dislocation-field strain gradient plasticity simulations were employed to analyze the intrinsic size effects, using the grain size and texture as measured experimentally. The work shows that for miniaturized structures with a limited number of columnar grains a unique Hall-Petch relation does not exist, even though a grain boundary effect, i.e. a decrease in stress level (at a given strain) for decreasing grain boundary area per unit volume, is clearly present. When the microstructure is kept constant upon miniaturization, the free surface per unit area increases causing the stress level of the structure to decrease, the effect of which increases towards a single grain in the cross-section. In addition, the work shows that grain statistics effects also contribute to observed weakening, due to insufficient compensation of local (weaker) material properties by the surrounding material (i.e. grains). Finally, grain statistics also significantly increase the statistical variation in mechanical properties for small-sized structures, an effect that is especially important for the reliability of miniature components. The separate influence of these first-order effects as well as their interplay are explained in terms of the movement of the dislocations upon plastic flow.

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.

More on definable sets of p-adic numbers

1988 ◽  
Vol 53 (3) ◽  
pp. 912-920 ◽  
Author(s):  
Philip Scowcroft
Keyword(s):  
Cross Section ◽  
Quantifier Elimination ◽  
Order Theory ◽  
Model Completeness ◽  
First Order ◽  
First Order Theory ◽  
Ordered Fields ◽  
Definable Sets ◽  
The Cross ◽  
Primitive Recursive

To eliminate quantifiers in the first-order theory of the p-adic field Qp, Ax and Kochen use a language containing a symbol for a cross-section map n → pn from the value group Z into Qp [1, pp. 48–49]. The primitive-recursive quantifier eliminations given by Cohen [2] and Weispfenning [10] also apply to a language mentioning the cross-section, but none of these authors seems entirely happy with his results. As Cohen says, “all the operations… introduced for our simple functions seem natural, with the possible exception of the map n → pn” [2, p. 146]. So all three authors show that various consequences of quantifier elimination—completeness, decidability, model-completeness—also hold for a theory of Qp not employing the cross-section [1, p. 453; 2, p. 146; 10, §4]. Macintyre directs a more specific complaint against the cross-section [5, p. 605]. Elementary formulae which use it can define infinite discrete subsets of Qp; yet infinite discrete subsets of R are not definable in the language of ordered fields, and so certain analogies between Qp and R suggested by previous model-theoretic work seem to break down.To avoid this problem, Macintyre gives up the cross-section and eliminates quantifiers in a theory of Qp written just in the usual language of fields supplemented by a predicate V for Qp's valuation ring and by predicates Pn for the sets of nth powers in Qp (for all n ≥ 2).

scholarly journals An analysis of baffles designs for limiting impact on the directional response for a partially filled tank with agro-food liquids

2020 ◽  
Vol 180 ◽  
pp. 03024
Author(s):  
Gabriela Milian ◽  
Sorin-Ştefan Biriş ◽  
George Ipate ◽  
Alexandru Hristea ◽  
Cristian Sorica ◽  
...  
Keyword(s):  
Free Surface ◽  
Cross Section ◽  
Food Products ◽  
Tank Truck ◽  
Directional Response ◽  
Tank Model ◽  
Geometric Models ◽  
Ansys Cfx ◽  
The Cross ◽  
The Impact

A directional response for a partially filled tank with agro-food liquids incorporates the motion of the free surface due to roll and longitudinal accelerations into the dynamic tank model. This paper presents an analysis of efficaciousness of different designs of baffles for two different tank, to limit the impact of the response given by the liquid on the tank walls. In this paper modelling of the behaviour of the cross-section circular and ellipsoidal tank with baffles, partially filled with liquids agro-food, was developed, which performs a braking-in-a-turn manoeuver. Two different tank truck models have been used to simulate the sloshing effect of agro-food liquid cargo. Is also studied the two geometric models of the tank was done by using SolidWorks and simulating the behaviour of the tank ANSYS-CFX. In this study, there were simulated and modeled two models of tank-type “X”, respectively type “Y” used for the storage and transport of liquid agro-food products, namely water, for different speeds (v = 14m / s and v = 20m / s) and two filling levels of the tank trucks (40% and 80%). The results obtained were compared the behaviour of the tank partially filled into a braking-in-a-turn manoeuver, in which the total values of the deformations that appear as a result of the impact due to the movement of the liquid inside the tank trucks.

Dividend Yields, Dividend Growth, and Return Predictability in the Cross Section of Stocks

2015 ◽  
Vol 50 (1-2) ◽  
pp. 33-60 ◽  
Author(s):  
Paulo Maio ◽  
Pedro Santa-Clara
Keyword(s):  
Cross Section ◽  
Presidential Address ◽  
Variance Decomposition ◽  
Return Predictability ◽  
Expected Returns ◽  
First Order ◽  
Value Stocks ◽  
Econometric Methodology ◽  
The Cross ◽  
Dividend Growth

AbstractThere is a generalized conviction that variation in dividend yields is exclusively related to expected returns and not to expected dividend growth, for example, Cochrane’s (2011) presidential address. We show that this pattern, although valid for the aggregate stock market, is not true for portfolios of small and value stocks, where dividend yields are related mainly to future dividend changes. Thus, the variance decomposition associated with the aggregate dividend yield has important heterogeneity in the cross section of equities. Our results are robust to different forecasting horizons, econometric methodology (long-horizon regressions or first-order vector autoregression), and alternative decomposition based on excess returns.

scholarly journals Cálculo numérico de la matriz de flexibilidades de vigas de sección variable, con elementos finitos

2020 ◽  
pp. 22-31
Author(s):  
Jaime Retama Velasco ◽  
Ricardo Heras Cruz
Keyword(s):  
Finite Elements ◽  
Numerical Method ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Complementary Energy ◽  
First Order ◽  
Tapered Beam ◽  
Variable Section ◽  
The Cross

In this work, the flexibility properties of variable cross section beams are derived, through the application of the second theorem of Castigliano; considering the complementary energy by bending and share forces. To perform the integration of the flexibility coefficients, a numerical method, which considers the discretization of the beam domain with first order rectangular finite elements, in conjunction with the Gauss rule, is proposed. At the end of the work, the proposed method is applied to a tapered beam that has been discretized with a maximum of five finite elements. It is shown that the method is general, and that it can be applied to beams of variable section in which the cross section can be complex. The results shown that no more than 3 finite elements are needed to discretize the domain of beams in which, the ratio height-length is of the order of ten.

Numerical Investigation of the Physics of Higher Order Effects Generated by Wave Paddles

2020 ◽  
Author(s):  
Yun Zhi Law ◽  
Hui Liang ◽  
Harrif Santo ◽  
Kian Yew Lim ◽  
Eng Soon Chan
Keyword(s):  
Free Surface ◽  
Higher Order ◽  
The Other ◽  
Order Effects ◽  
Harmonic Waves ◽  
Regular Wave ◽  
Wave Tank ◽  
First Order ◽  
Higher Harmonic ◽  
Higher Order Effects

Abstract When free-surface waves are generated using wave paddles to produce the desired waves, higher order effects might be inevitable for some cases. These can be due to the mismatch in the wave paddle displacement and non-linear free-surface wave kinematics, as well as the moving boundary of wave paddles. Such higher order effects are often manifested as higher harmonic waves, which can propagate independently (or free waves). The presence of such waves will contaminate the quality of the tank test, and together with effects due to scaling and finite size of tank, it is important to reduce or mitigate such effects as much as possible in a wave tank in order to simulate a more realistic scenario. This study investigates the above problem in a systematic manner by using a fully-nonlinear numerical wave tank based on the three-dimensional time-domain Harmonic Polynomial Cell (HPC) method. Wave is generated by flap-type wave paddles on one end of the tank, and is damped on the other end. The paddle boundary conditions are satisfied on the instantaneous paddles surfaces, and the free surface is tracked by the generalized semi-Lagrangian scheme. In this study, first order paddle signal is used to generate regular waves, and the focus is on characterising the behaviour of the generated free higher harmonic waves. We first look into a rectangular wave tank where the paddles are distributed at one side of the tank. Upon the generation of an oblique regular wave (primary wave), it is observed that the generated free waves propagate at a different angle/direction. An explicit analytical expression is derived for the direction of the free waves, which agrees with the numerical observation. Besides propagating at a different direction, the free waves also interact with the primary waves resulting in additional bound waves of the first and third harmonics. Next, we consider a circular wave tank, where paddles along half of the circumference are used to generate planar regular wave, while paddles at the other half are assumed to be able to fully absorb the wave. The generated free waves are observed to focus at a particular region in the tank due to constructive interference. To eliminate or at least mitigate such undesired waves, correction to first order paddle signal is required. Second order correction scheme based on Schaffer (1996) is implemented for such purpose. Preliminary results seem to suggest that second order correction to the paddle signal can only mitigate but cannot completely eliminate the existence of free higher harmonic waves.

The Heterogeneity of Composition and Microstructure in Cast Large Sized 3104 Alloy Slab

2012 ◽  
Vol 217-219 ◽  
pp. 349-353
Author(s):  
Rui Yin Huang ◽  
Zhi Min Yin ◽  
Yuan Zhi Zhu
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Aluminium Alloy ◽  
Cooling Rate ◽  
Surface Area ◽  
Cross Section ◽  
Chemical Compositions ◽  
The Cross

Heterogeneity of composition and microstructure in cast large sized 3104 aluminium alloy slab were studied using AES-ICP, OM, SEM, etc. The results show that the cooling rate on the cross section of 3104 slab is different, macro-segregation is found in the different section in the slab .The content of Ti decreases gradually from the surface to about 1/4 thickness of the slab, then increases rapidly to the center of slab; other elements content increases gradually from the surface to the about 1/4 thickness and then decreases rapidly to the center; the grain size on the surface area is fine, and the grain size at the center is coarse , segregation of Mg is found within the grains; great amount compound is found to be of presence on the grain boundary, with chemical compositions of Al 87（FeMn）13 and Al83（FeMn）12Si5; The compound size at the surface area is comparatively smaller, and coarser at the centre of slab.

The shape of free jets of water under gravity

1976 ◽  
Vol 76 (4) ◽  
pp. 625-640 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Flow Velocity ◽  
Cross Section ◽  
Cross Sections ◽  
Cross Flow ◽  
Free Jets ◽  
Elliptic Cross ◽  
Cross Flow Velocity ◽  
The Cross

A study is made of the form taken by a slender jet of water whose only boundary is a free surface. The only forces acting are inertial and gravitational. Attention is paid to the cross-flow velocity components and to the development of the shape of the cross-section of the jet as it progresses. It is established that a jet with initially elliptic cross-sections can remain elliptical, and the variation in the aspect ratio along the jet is determined.

The scattering of short surface waves by a cylinder

1977 ◽  
Vol 82 (4) ◽  
pp. 673-686 ◽  
Author(s):  
G. Alker
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Fixed Points ◽  
Cross Section ◽  
Asymptotic Expansions ◽  
Matched Asymptotic Expansions ◽  
The Cross ◽  
Pass Through

The scattering of short surface waves by a partially immersed cylinder is considered. The cylinder is taken to be circular and to pass through two fixed points on the free surface with its centre on or above the free surface. Of particular interest is the behaviour of the solution as the cross-section of the immersed part of the cylinder approaches a semicircle. The method of matched asymptotic expansions is used.

The effect of non-linearity at the free surface on flow past a submerged cylinder

1965 ◽  
Vol 22 (2) ◽  
pp. 401-414 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Second Order ◽  
Order Effects ◽  
Surface Boundary ◽  
First Order ◽  
Flow Past ◽  
Free Surface Boundary Condition ◽  
Non Linear ◽  
Wave Induced

Plane potential flow past a circular cylinder beneath a free surface under gravity is investigated in order to determine the importance or otherwise of non-linear effects from the free-surface boundary condition. It is shown that non-linear second-order corrections to the first-order linearized expressions for the wave-induced forces on the cylinder are considerably larger than second-order effects which are present even with a linear free-surface condition. Further evidence for the importance of non-linearity is presented in the form of streamline plots of the first-order solution showing strange behaviour at wave crests.

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