Solid circular plate unilaterally supported along two antipodal edge arcs and deflected by a central transverse concentrated force

2020 ◽  
pp. 095440622092444
Author(s):  
Antonio Strozzi
Keyword(s):  
Circular Plate ◽  
Mechanical Response ◽  
Central Zone ◽  
Angular Width ◽  
Concentrated Force ◽  
Mechanical Responses ◽  
Angular Extent ◽  
Kirchhoff Model ◽  
High Support ◽  
Plate Deflection

A solid circular plate unilaterally supported along two antipodal edge arcs and deflected by a static central transverse concentrated force is considered. It is clarified that two distinct mechanical responses are possible, depending on the angular extent of the supports; in the first kind of response, valid for small support angular widths, the plate rotates about the support lateral sides, lifting from the supports along their central zone. The second response is valid for high support angular extents, and according to this response the plate additionally beds over the central portion of the support upper faces. Only the first kind of response is examined in this paper. This plate contact problem is classifiable as receding, and the plate deflection is described in terms of a plate Kirchhoff model. The plate deflection is analytically expressed together with the transitional value of the support angular width that describes the passage from the first to the second mechanical response.

Płyty kołowe Hencky’ego–Bolle’a spoczywające na podłożu sprężystym Własowa

2020 ◽  
Vol 29 (4) ◽  
pp. 444-453
Author(s):  
Mykola Nagirniak
Keyword(s):  
Differential Equation ◽  
Circular Plate ◽  
Significant Influence ◽  
Single Layer ◽  
Medium Thickness ◽  
Cross Sectional ◽  
Equation Solution ◽  
Integral Characteristics ◽  
Two Parameter ◽  
Plate Deflection

The work presents the equations of the theory of symmetrical plates, resting on one-way, single-layer, two-parameter Vlasov’s subsoil. Two cases of differential equation solution of the plate deflection of thin and medium thickness on the ground substrate were analyzed depending on the size of the integral characteristics UÖD and 6ÖD. The example of loading the circular plate with a Pk load evenly distributed over the edge was considered and shows dimensionless graphs of deflection, bending torques and transverse forces in the plate and in the ground subsoil. The effect of the Poisson’s coefficient of the plate on deflection values and cross-sectional forces was investigated. The Poisson’s number has been shown to have a significant influence on deflection values and bending torque, however shown negligible effect on transverse forces values.

The Method of Finite Differences in Solutions Concerning Circular Plate

2011 ◽  
Vol 490 ◽  
pp. 305-311
Author(s):  
Henryk G. Sabiniak
Keyword(s):  
Circular Plate ◽  
Finite Differences ◽  
Machine Building ◽  
Polar Coordinates ◽  
Circular Plates ◽  
Technical Problems ◽  
Theory Of Plates ◽  
Worm Gearing ◽  
Mixed Derivatives ◽  
Plate Deflection

Finite difference method in solving classic problems in theory of plates is considered a standard one [1], [2], [3], [4]. The above refers mainly to solutions in right-angle coordinates. For circular plates, for which the use of polar coordinates is the best option, the question of classic plate deflection gets complicated. In accordance with mathematical rules the passage from partial differentials to final differences seems firm. Still final formulas both for the equation (1), as well as for border conditions of circular plate obtained in this study and in the study [3] differ considerably. The paper describes in detail necessary mathematical calculations. The final results are presented in identical form as in the study [3]. Difference of results as well as the length of arm in passage from partial differentials to finite differences for mixed derivatives are discussed. Generalizations resulting from these discussions are presented. This preliminary proceeding has the purpose of searching for solutions to technical problems in machine building and construction, in particular finding a solution to the question of distribution of load along contact line in worm gearing.

scholarly journals Understanding the effects of beetroot juice intake on CrossFit performance by assessing hormonal, metabolic and mechanical response: a randomized, double-blind, crossover design

2020 ◽  
Author(s):  
Manuel V. Garnacho-Castaño ◽  
Guillem Palau-Salvà ◽  
Noemí Serra-Payá ◽  
Mario Ruiz-Hermosel ◽  
Marina Berbell ◽  
...  
Keyword(s):  
Oxygen Saturation ◽  
Interaction Effect ◽  
Mechanical Response ◽  
Crossover Design ◽  
Muscular Fatigue ◽  
Anaerobic Performance ◽  
Beetroot Juice ◽  
Double Blind ◽  
Mechanical Responses ◽  
Bonferroni Test

Abstract Background: Acute beetroot juice (BJ) intake has shown to enhance aerobic and anaerobic performance. However, no studies have evaluated the effects of BJ intake on CrossFit (CF) performance by linking hormonal, metabolic, and mechanical responses. The purpose of this study was to determine the causal physiological association between hormonal, metabolic and mechanical responses, and CF workouts performance after acute BJ intake. Methods: Twelve well-trained male practitioners undertook a CF workout after drinking 140 mL of BJ (~ 12.8 mmol NO3−) or placebo. The two experimental conditions (BJ or placebo) were administered using a randomized, double-blind, crossover design. The CF workout consisted of repeating the same exercise routine twice: Wall ball (WB) shots plus full back squat (FBS) with 3-min rest (1st routine) or without rest (2nd routine) between the two exercises. A 3-min rest was established between the two exercise routines.Results: An interaction effect was observed in the number of repetitions performed (p = 0.04). The Bonferroni test determined a higher number of repetitions after BJ than placebo intake when a 3-min rest between WB and FBS (1st routine) was established (p = 0.007). An interaction effect was detected in cortisol response (p = 0.04). Cortisol showed a higher increase after BJ compared to placebo intake (76% vs. 36%, respectively). No interaction effect was observed in the testosterone and testosterone/cortisol ratio (p > 0.05). A significant interaction effect was found in oxygen saturation (p = 0.01). A greater oxygen saturation drop was observed in BJ compared to placebo (p < 0.05). An interaction effect was verified in muscular fatigue (p = 0.03) with a higher muscular fatigue being observed with BJ than placebo (p = 0.02). Conclusions: BJ intake improved anaerobic performance only after the recovery time between exercises. This increase in performance in the first routine probably generated greater hypoxia in the muscle mass involved, possibly conditioning post-exercise performance. This was observed with a fall in oxygen saturation and in muscle fatigue measured at the end of the CF workout. The greatest perceived changes in cortisol levels after BJ intake could be attributed to the nitrate-nitrite-nitric oxide pathway

scholarly journals INELASTIC RESPONSES OF SWOLLEN NITRILE RUBBER UNDER CYCLIC LOADING

2018 ◽  
Vol 91 (1) ◽  
pp. 136-150 ◽  
Author(s):  
Mei Sze Loo ◽  
Jean Benoît Le Cam ◽  
Andri Andriyana ◽  
Eric Robin
Keyword(s):  
Cyclic Loading ◽  
Mechanical Response ◽  
Mechanical Responses ◽  
Material Compatibility ◽  
Durability Analysis ◽  
Inelastic Responses ◽  
Nitrile Rubbers ◽  
Loading Tests ◽  
Cyclic Loading Tests ◽  
Conventional Diesel Fuel

ABSTRACT Palm biodiesel is deemed a promising future fuel substitute for conventional diesel fuel. In line with this perspective, necessary changes in the existing diesel engine system are expected in order to address the issue of material compatibility. One typical degradation observed in rubber components exposed to aggressive solvent such as palm biodiesel during the service is swelling. Thus, the investigation of the effect of swelling on the mechanical response under cyclic loading is prerequisite for durability analysis of such components. In this study, filled and unfilled swollen nitrile rubbers are immersed in conventional diesel and palm biodiesel baths until a 5% swelling level is achieved. Both dry and swollen rubbers are subjected to uniaxial cyclic loading tests. The analysis of the mechanical responses has shown that swelling decreases inelastic effects such as hysteresis, stress softening, and permanent set. For both dry and swollen rubbers, fillers are found to have significant effects in the inelastic responses, whereas the effects of solvent and loading rate are comparable.

A Study of the Strain Response of Stainless Steel 304 to Extreme Uniform Instantaneous Explosion Pressure Loads

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Geraint O. Thomas ◽  
Gwyn L. Oakley
Keyword(s):  
Stainless Steel ◽  
Mechanical Response ◽  
Gaseous Detonation ◽  
Explosion Pressure ◽  
Mechanical Responses ◽  
Physical Measurements ◽  
Linear Relationships ◽  
Stainless Steel 304 ◽  
Series Of Experiments ◽  
Universal Correlation

Abstract The paper describes a new configuration using a gaseous detonation explosive blast source suitable for the studies of the instantaneous uniform pressure loading and mechanical response of materials. The capabilities of the configuration are illustrated by a preliminary series of experiments of the dynamic loading of clamped circular plates of 304 grade stainless steel with thicknesses ranging from 9.5 mm to 0.5 mm. The mechanical responses of the plates were monitored using strain gauges placed across the plate radius together with physical measurements of any permanent residual displacement of the center of the plate. The residual central deformations were analyzed using a well-established correlation involving nondimensional pressure load impulse. No universal correlation for the present data was found, but linear relationships for changes in two experimental parameters were identified, suggesting that the existing correlations have some deficiencies when applied to stainless steel 304.

Structure, Process, and Material Influences for 3D Printed Lattices Designed With Mixed Unit Cells

2020 ◽  
Author(s):  
Gabriel Briguiet ◽  
Paul F. Egan
Keyword(s):  
Elastic Modulus ◽  
Mechanical Testing ◽  
Mechanical Response ◽  
Cell Types ◽  
Unit Cell ◽  
Ultraviolet Curing ◽  
Mechanical Responses ◽  
Lattice Design ◽  
Unit Cells ◽  
3D Printed

Abstract Emerging 3D printing technologies are enabling the design and fabrication of novel architected structures with advantageous mechanical responses. Designing complex structures, such as lattices, with a targeted response is challenging because build materials, fabrication process, and topological design have unique influences on the structure’s mechanical response. Changing any factor may have unanticipated consequences, even for simpler lattice structures. Here, we conduct mechanical compression experiments to investigate varied lattice design, fabrication, and material combinations using stereolithography printing with a biocompatible polymer. Mechanical testing demonstrates that a higher ultraviolet curing time increases elastic modulus. Material testing demonstrated that anisotropy does not strongly influence lattice mechanics. Designs were altered by comparing homogenous lattices of single unit cell types and heterogeneous lattices that combine two types of unit cells. Unit cells for heterogeneous structures include a Cube design for a high elastic modulus and Cross design for improved shear response. Mechanical testing of three heterogeneous layouts demonstrated how unit cell organization influences mechanical outcomes, therefore enabling the tuning of an elastic modulus that surpasses the law of averages designed for application-dependent mechanical needs. These findings provide a foundation for linking design, process, and material for engineering 3D printed structures with preferred properties, while also facilitating new directions in design automation and optimization.

Experimental and Numerical Assessment of Both Slug and Vortex Induced Vibrations on a Spool Model

2020 ◽  
Author(s):  
Matthieu Minguez ◽  
Kevin Le Prin ◽  
Alain Liné ◽  
Vincent Lafon ◽  
François Pétrié ◽  
...  
Keyword(s):  
Slug Flow ◽  
Mechanical Response ◽  
Numerical Models ◽  
Induced Response ◽  
Flow Properties ◽  
External Excitation ◽  
Mechanical Responses ◽  
Vortex Induced Vibrations ◽  
Numerical Assessment ◽  
Slug Flows

Abstract The paper addresses the flow-induced response of a rigid spool/jumper. It mainly focuses on its mechanical response resulting from internal intermittent slug flows but also addresses potential coupling with an external excitation due to vortex shedding. These works provide quantitative experimental data that match quite well with existing empirical correlations in terms of slug flow properties. The repeatability of the measurement system has been experienced and underlines promising capabilities. The tests provide exhaustive complementary data regarding the slug flow properties (e.g. pocket length) which will be reused for numerical modelling purpose. The mechanical response of the spool is exhaustively addressed for different regular slug flows. Some correlations are proposed aiming at describing the mechanical responses. The coupling with an additional external current solicitation and Vortex Induced Vibrations (VIV) is discussed and characterized for some conditions. Finally, a discussion on the current Industry Best Practices is introduced in order to challenge the capability of the proposed approaches to described and recover such complex phenomenon. The comparisons underline the weak agreement between experiments and numerical models, opening discussion on the best way to address this physics and the next developments.

scholarly journals Geomechanical characterisation of organic-rich calcareous shale using AFM and nanoindentation

2020 ◽  
Author(s):  
S. P. Graham ◽  
M. Rouainia ◽  
A. C. Aplin ◽  
P. Cubillas ◽  
T. D. Fender ◽  
...  
Keyword(s):  
Mechanical Response ◽  
Quantitative Imaging ◽  
High Load ◽  
Length Scales ◽  
Hydrocarbon Production ◽  
Mechanical Responses ◽  
Calcareous Shale ◽  
Low Load ◽  
Using Data ◽  
Pm 10

Abstract The geomechanical integrity of shale overburden is a highly significant geological risk factor for a range of engineering and energy-related applications including CO$$_2$$ 2 storage and unconventional hydrocarbon production. This paper aims to provide a comprehensive set of high-quality nano- and micro-mechanical data on shale samples to better constrain the macroscopic mechanical properties that result from the microstructural constituents of shale. We present the first study of the mechanical responses of a calcareous shale over length scales of 10 nm to 100 $$\upmu$$ μ m, combining approaches involving atomic force microscopy (AFM), and both low-load and high-load nanoindentation. PeakForce quantitative nanomechanical mapping AFM (PF-QNM) and quantitative imaging (QI-AFM) give similar results for Young’s modulus up to 25 GPa, with both techniques generating values for organic matter of 5–10 GPa. Of the two AFM techniques, only PF-QNM generates robust results at higher moduli, giving similar results to low-load nanoindentation up to 60 GPa. Measured moduli for clay, calcite, and quartz-feldspar are $$22 \pm 2\,\hbox { GPa}$$ 22 ± 2 GPa , $$42 \pm 8\,\hbox { GPa}$$ 42 ± 8 GPa , and $$55 \pm 10\,\hbox { GPa}$$ 55 ± 10 GPa respectively. For calcite and quartz-feldspar, these values are significantly lower than measurements made on highly crystalline phases. High-load nanoindentation generates an unimodal mechanical response in the range of 40–50 GPa for both samples studied here, consistent with calcite being the dominant mineral phase. Voigt and Reuss bounds calculated from low-load nanoindentation results for individual phases generate the expected composite value measured by high-load nanoindentation at length scales of 100–600 $$\upmu$$ μ m. In contrast, moduli measured on more highly crystalline mineral phases using data from literature do not match the composite value. More emphasis should, therefore, be placed on the use of nano- and micro-scale data as the inputs to effective medium models and homogenisation schemes to predict the bulk shale mechanical response.

On the Existence of a Solution for a Solid Circular Plate Bilaterally Supported Along Two Antipodal Boundary Arcs and Loaded by a Central Transverse Concentrated Force

2000 ◽  
Vol 68 (5) ◽  
pp. 809-812 ◽  
Author(s):  
G. Monegato ◽  
A. Strozzi
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Reaction Force ◽  
Mechanical Analysis ◽  
Square Root ◽  
Existence Of A Solution ◽  
Concentrated Force ◽  
Boundary Constraints ◽  
Title Problem ◽  
The One

A purely flexural mechanical analysis is presented for a thin, solid, circular plate, deflected by a central transverse concentrated force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. This problem is modeled in terms of a singular integral equation of the Prandtl type, which possesses a unique solution expressed in terms of a reaction force containing a factor exhibiting square root endpoint singularities. This solution is then shown not to respect the requested boundary constraints. It is therefore concluded that, within the framework of the purely flexural plate theory, the title problem cannot admit the weighted L2 solution here examined. It cannot, however, be excluded that a solution to the title problem exists, which possesses stronger endpoint singularities than those examined in this paper, or is of a more general form than the one considered here.

Analysis of Nanoindentation Response of Diatom Frustules

2007 ◽  
Vol 7 (12) ◽  
pp. 4465-4472 ◽  
Author(s):  
S. Yao ◽  
G. Subhash ◽  
S. Maiti
Keyword(s):  
Computational Model ◽  
Deformation Behavior ◽  
Mechanical Response ◽  
Contact Process ◽  
Experimental Studies ◽  
Computational Framework ◽  
Porosity Level ◽  
Mechanical Responses ◽  
Pore Architecture ◽  
Level Of Understanding

Diatom frustules have been suggested for numerous nanotechnological applications. Experimental studies using nanoindenter have shown that the hardness and the stiffness of the frustules vary with location of indentation. To gain further insight, a computational framework has been developed where the Berkovich nanoindentation experiments were simulated by a rigid-deformable contact process. Three different approaches that provide progressively increasing level of understanding of the deformation behavior of frustules were adopted. The differences in the mechanical responses of the frustule due to variation of indentation location, size of pores, and distribution of pores were analyzed. It has been found that the effective stiffness of the frustule is linearly related to the porosity level and does not depend on the frustule size or its pore architecture. It has been shown that a 3D porous shell computational model is more appropriate to simulate the experimentally obtained mechanical response of diatom frustules.

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