A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Shorya Awtar ◽  
Shiladitya Sen
Keyword(s):  
Two Dimensional ◽  
Finite Elements Analysis ◽  
Nonlinear Load ◽  
Beam Shape ◽  
Flexure Mechanism ◽  
Elastic Load ◽  
Nonlinear Finite Elements ◽  
Wide Range ◽  
Load Displacement ◽  
Constraint Model

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.

A Generalized Constraint Model for Two-Dimensional Beam Flexures

2009 ◽  
Author(s):  
Shorya Awtar ◽  
Shiladitya Sen
Keyword(s):  
Two Dimensional ◽  
Finite Elements Analysis ◽  
Beam Shape ◽  
Qualitative And Quantitative ◽  
Flexure Mechanism ◽  
Elastic Load ◽  
Quantitative Understanding ◽  
Constraint Model ◽  
Generalized Constraint ◽  
Displacement Model

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop a qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates any general loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified extensively by non-linear Finite Elements Analysis.

A Closed-Form Nonlinear Model for the Constraint Characteristics of Symmetric Spatial Beams

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Shiladitya Sen ◽  
Shorya Awtar
Keyword(s):  
Closed Form ◽  
Virtual Work ◽  
Practical Interest ◽  
Element Analysis ◽  
Nonlinear Load ◽  
Flexure Mechanism ◽  
Spatial Beams ◽  
Spatial Beam ◽  
Load Displacement ◽  
Constraint Model

The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a uniform and symmetric cross-section, slender, spatial beam—a basic flexure element commonly used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the nonlinear load–displacement relations at the beam end. Appropriate assumptions are made while formulating the strain and strain energy expressions for the spatial beam to retain relevant geometric nonlinearities. Using the principle of virtual work, nonlinear beam governing equations are derived and subsequently solved for general end loads. The resulting nonlinear load–displacement relations capture the constraint characteristics of the spatial beam in a compact, closed-form, and parametric manner. This constraint model is shown to be accurate using nonlinear finite element analysis, within a load and displacement range of practical interest. The utility of this model lies in the physical and analytical insight that it offers into the constraint behavior of a spatial beam flexure, its use in design and optimization of 3D flexure mechanism geometries, and its elucidation of fundamental performance tradeoffs in flexure mechanism design.

An XYZ Parallel-Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Finite Elements Analysis ◽  
Motion Direction ◽  
Flexure Mechanism ◽  
Nonlinear Finite Elements ◽  
Decoupled Motion ◽  
Motion Range ◽  
Stiffness Variation ◽  
Parallel Kinematic ◽  
Cross Axis

A novel parallel-kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz) is presented. Geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via nonlinear finite elements analysis (FEA). A proof-of-concept prototype is fabricated to validate the predicted large range and decoupled motion capabilities. The analysis and the hardware prototype demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the nonlinear FEA predicts cross-axis errors of less than 7.8%, parasitic rotations less than 10.8 mrad, less than 14.4% lost motion, actuator isolation better than 1.5%, and no perceptible motion direction stiffness variation.

A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Strain Energy Formulation

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Shorya Awtar ◽  
Shiladitya Sen
Keyword(s):  
Strain Energy ◽  
Virtual Work ◽  
Geometric Constraint ◽  
Element Analysis ◽  
Beam Shape ◽  
Nonlinear Strain ◽  
Energy Expression ◽  
Load Displacement ◽  
Constraint Model ◽  
Energy Formulation

The beam constraint model (BCM), presented previously, captures pertinent nonlinearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a nonlinear strain energy formulation for the beam flexure, consistent with the transverse-direction load-displacement and axial-direction geometric constraint relations in the BCM, is presented. An explicit strain energy expression, in terms of beam end displacements, that accommodates generalized loading conditions, boundary conditions, initial curvature, and beam shape, is derived. Using energy-based arguments, new insight into the BCM is elucidated by fundamental relations among its stiffness, constraint, and energy coefficients. The presence of axial load in the geometric constraint and strain energy expressions—a unique attribute of distributed compliance flexures that leads to the elastokinematic effect—is highlighted. Using the principle of virtual work, this strain energy expression for a generalized beam is employed in determining the load-displacement relations, and therefore constraint characteristics, of a flexure mechanism comprising multiple beams. The benefit of this approach is evident in its mathematical efficiency and succinctness, which is to be expected with the use of energy methods. All analytical results are validated to a high degree of accuracy via nonlinear finite element analysis.

Beam Constraint Model: A Non-Linear Strain Energy Formulation for Generalized Two-Dimensional Beam Flexures

2010 ◽  
Author(s):  
Shorya Awtar ◽  
Shiladitya Sen
Keyword(s):  
Strain Energy ◽  
Virtual Work ◽  
Linear Strain ◽  
Element Analysis ◽  
Beam Shape ◽  
Energy Expression ◽  
Non Linear ◽  
Load Displacement ◽  
Constraint Model ◽  
Energy Formulation

In the past, we have introduced the Beam Constraint Model (BCM), which captures pertinent non-linearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a non-linear strain energy formulation for the beam flexure, consistent with the transverse-direction load-displacement and axial-direction geometric constraint relations in the BCM, is presented. An explicit strain energy expression, in terms of beam end-displacements, that accommodates generalized loading conditions, boundary conditions, initial curvature, and beam shape is derived. Using the Principle of Virtual Work, this strain energy expression for a generalized beam is employed in determining the load-displacement relations, and therefore constraint characteristics, for flexure mechanisms comprising multiple beams. The benefit of this approach is evident in its mathematical efficiency and succinctness, which is to be expected with the use of energy methods. All analytical results are validated to a high degree of accuracy via non-linear Finite Element Analysis. Furthermore, the proposed energy formulation leads to new insights into the nature of the BCM.

Aromatic Volatile Composition of Celery and Celeriac Cultivars

HortScience ◽  
1990 ◽  
Vol 25 (5) ◽  
pp. 556-559 ◽  
Author(s):  
Fredy Van Wassenhove ◽  
Patrick Dirinck ◽  
Georges Vulsteke ◽  
Niceas Schamp
Keyword(s):  
Volatile Compounds ◽  
Chromatographic Method ◽  
Apium Graveolens ◽  
Volatile Components ◽  
Two Dimensional ◽  
Qualitative Composition ◽  
Volatile Composition ◽  
Wide Range ◽  
Gas Chromatographic Method ◽  
Identification And Quantification

A two-dimensional capillary gas chromatographic method was developed to separate and quantify aromatic volatiles of celery in one analysis. The isolation, identification, and quantification of the volatile compounds of four cultivars of blanching celery (Apium graveolens L. var. dulce) and six cultivars of celeriac (Apium graveolens L. var. rapaceum) are described. The qualitative composition of Likens-Nickerson extracts of both cultivars is similar. The concentration of terpenes and phthalides, the key volatile components, found in various cultivars of both celery and celeriac varied over a wide range.

scholarly journals Prediction of Wide Range Two-Dimensional Refractivity Using an IDW Interpolation Method from High-Altitude Refractivity Data of Multiple Meteorological Observatories

2021 ◽  
Vol 11 (4) ◽  
pp. 1431
Author(s):  
Sungsik Wang ◽  
Tae Heung Lim ◽  
Kyoungsoo Oh ◽  
Chulhun Seo ◽  
Hosung Choo
Keyword(s):  
High Altitude ◽  
Korean Peninsula ◽  
Interpolation Method ◽  
Atmospheric Condition ◽  
Propagation Path ◽  
Two Dimensional ◽  
Data Set ◽  
Wide Range ◽  
Atmospheric Data ◽  
Terrain Surface

This article proposes a method for the prediction of wide range two-dimensional refractivity for synthetic aperture radar (SAR) applications, using an inverse distance weighted (IDW) interpolation of high-altitude radio refractivity data from multiple meteorological observatories. The radio refractivity is extracted from an atmospheric data set of twenty meteorological observatories around the Korean Peninsula along a given altitude. Then, from the sparse refractive data, the two-dimensional regional radio refractivity of the entire Korean Peninsula is derived using the IDW interpolation, in consideration of the curvature of the Earth. The refractivities of the four seasons in 2019 are derived at the locations of seven meteorological observatories within the Korean Peninsula, using the refractivity data from the other nineteen observatories. The atmospheric refractivities on 15 February 2019 are then evaluated across the entire Korean Peninsula, using the atmospheric data collected from the twenty meteorological observatories. We found that the proposed IDW interpolation has the lowest average, the lowest average root-mean-square error (RMSE) of ∇M (gradient of M), and more continuous results than other methods. To compare the resulting IDW refractivity interpolation for airborne SAR applications, all the propagation path losses across Pohang and Heuksando are obtained using the standard atmospheric condition of ∇M = 118 and the observation-based interpolated atmospheric conditions on 15 February 2019. On the terrain surface ranging from 90 km to 190 km, the average path losses in the standard and derived conditions are 179.7 dB and 182.1 dB, respectively. Finally, based on the air-to-ground scenario in the SAR application, two-dimensional illuminated field intensities on the terrain surface are illustrated.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

scholarly journals Robust anomalous metallic states and vestiges of self-duality in two-dimensional granular In-InOx composites

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Xinyang Zhang ◽  
Bar Hen ◽  
Alexander Palevski ◽  
Aharon Kapitulnik
Keyword(s):  
Magnetic Field ◽  
Metallic Phase ◽  
Broadband Noise ◽  
Two Dimensional ◽  
Conventional Theory ◽  
Logarithmic Divergence ◽  
Self Duality ◽  
Low Field ◽  
Wide Range ◽  
Low Temperature Resistance

AbstractMany experiments investigating magnetic-field tuned superconductor-insulator transition (H-SIT) often exhibit low-temperature resistance saturation, which is interpreted as an anomalous metallic phase emerging from a ‘failed superconductor’, thus challenging conventional theory. Here we study a random granular array of indium islands grown on a gateable layer of indium-oxide. By tuning the intergrain couplings, we reveal a wide range of magnetic fields where resistance saturation is observed, under conditions of careful electromagnetic filtering and within a wide range of linear response. Exposure to external broadband noise or microwave radiation is shown to strengthen the tendency of superconductivity, where at low field a global superconducting phase is restored. Increasing magnetic field unveils an ‘avoided H-SIT’ that exhibits granularity-induced logarithmic divergence of the resistance/conductance above/below that transition, pointing to possible vestiges of the original emergent duality observed in a true H-SIT. We conclude that anomalous metallic phase is intimately associated with inherent inhomogeneities, exhibiting robust behavior at attainable temperatures for strongly granular two-dimensional systems.

scholarly journals Energetics of mesoscale cell turbulence in two-dimensional monolayers

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Shao-Zhen Lin ◽  
Wu-Yang Zhang ◽  
Dapeng Bi ◽  
Bo Li ◽  
Xi-Qiao Feng
Keyword(s):  
Kinetic Energy ◽  
Tumor Metastasis ◽  
Cell Types ◽  
Boltzmann Distribution ◽  
Scaling Exponent ◽  
Biological Processes ◽  
Two Dimensional ◽  
Cell Monolayers ◽  
Wide Range ◽  
Epithelial Cell Monolayers

AbstractInvestigation of energy mechanisms at the collective cell scale is a challenge for understanding various biological processes, such as embryonic development and tumor metastasis. Here we investigate the energetics of self-sustained mesoscale turbulence in confluent two-dimensional (2D) cell monolayers. We find that the kinetic energy and enstrophy of collective cell flows in both epithelial and non-epithelial cell monolayers collapse to a family of probability density functions, which follow the q-Gaussian distribution rather than the Maxwell–Boltzmann distribution. The enstrophy scales linearly with the kinetic energy as the monolayer matures. The energy spectra exhibit a power-decaying law at large wavenumbers, with a scaling exponent markedly different from that in the classical 2D Kolmogorov–Kraichnan turbulence. These energetic features are demonstrated to be common for all cell types on various substrates with a wide range of stiffness. This study provides unique clues to understand active natures of cell population and tissues.

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