scholarly journals Dynamics of Nonlocal Rod by Means of Fractional Laplacian

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1933
Author(s):  
Vittorio Gusella ◽  
Giuseppina Autuori ◽  
Patrizia Pucci ◽  
Federico Cluni
Keyword(s):  
Fractional Laplacian ◽  
Free Vibrations ◽  
Dynamic Loads ◽  
Model Parameters ◽  
Local Response ◽  
Proposed Model ◽  
Fractional Models ◽  
Static And Dynamic Loads ◽  
The Difference ◽  
The Time Domain

The use of fractional models to analyse nonlocal behaviour of solids has acquired great importance in recent years. The aim of this paper is to propose a model that uses the fractional Laplacian in order to obtain the equation ruling the dynamics of nonlocal rods. The solution is found by means of numerical techniques with a discretisation in the space domain. At first, the proposed model is compared to a model that uses Eringen’s classical approach to derive the differential equation ruling the problem, showing how the parameters used in the proposed fractional model can be estimated. Moreover, the physical meaning of the model parameters is assessed. The model is then extended in dynamics by means of a discretisation in the time domain using Newmark’s method, and the responses to different dynamic conditions, such as an external load varying with time and free vibrations due to an initial deformation, are estimated, showing the difference of behaviour between the local response and the nonlocal response. The obtained results show that the proposed model can be used efficiently to estimate the response of the nonlocal rod both to static and dynamic loads.

scholarly journals Distilling Deep Structural Facial Relationships for FAU Intensity Estimation

2021 ◽  
Author(s):  
Yingruo Fan ◽  
Jacqueline CK Lam ◽  
Victor On Kwok Li
Keyword(s):  
Structural Characteristics ◽  
Model Performance ◽  
Training Model ◽  
Model Parameters ◽  
Intensity Estimation ◽  
Structural Relationships ◽  
Proposed Model ◽  
Comparable Performance ◽  
Knowledge Distillation ◽  
The Difference

<div> <div> <div> <p>Facial emotions are expressed through a combination of facial muscle movements, namely, the Facial Action Units (FAUs). FAU intensity estimation aims to estimate the intensity of a set of structurally dependent FAUs. Contrary to the existing works that focus on improving FAU intensity estimation, this study investigates how knowledge distillation (KD) incorporated into a training model can improve FAU intensity estimation efficiency while achieving the same level of performance. Given the intrinsic structural characteristics of FAU, it is desirable to distill deep structural relationships, namely, DSR-FAU, using heatmap regression. Our methodology is as follows: First, a feature map-level distillation loss was applied to ensure that the student network and the teacher network share similar feature distributions. Second, the region-wise and channel-wise relationship distillation loss functions were introduced to penalize the difference in structural relationships. Specifically, the region-wise relationship can be represented by the structural correlations across the facial features, whereas the channel-wise relationship is represented by the implicit FAU co-occurrence dependencies. Third, we compared the model performance of DSR-FAU with the state-of-the-art models, based on two benchmarking datasets. Our proposed model achieves comparable performance with other baseline models, though requiring a lower number of model parameters and lower computation complexities. </p> </div> </div> </div>

scholarly journals A Car-Following Model Based on Quantified Homeostatic Risk Perception

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Guangquan Lu ◽  
Bo Cheng ◽  
Yunpeng Wang ◽  
Qingfeng Lin
Keyword(s):  
Perceived Risk ◽  
Safety Margin ◽  
Model Parameters ◽  
Perceived Safety ◽  
Car Following ◽  
Stimulus Response ◽  
Proposed Model ◽  
Car Following Model ◽  
The Difference ◽  
Level Of Risk

This study attempts to elucidate individual car-following behavior using risk homeostasis theory (RHT). On the basis of this theory and the stimulus-response concept, we develop a desired safety margin (DSM) model. Safety margin, defined as the level of perceived risk in car-following processes, is proposed and considered to be a stimulus parameter. Acceleration is assessed in accordance with the difference between the perceived safety margin (perceived level of risk) and desired safety margin (acceptable level of risk) of a driver in a car-following situation. Sixty-three cases selected from Next Generation Simulation (NGSIM) are used to calibrate the parameters of the proposed model for general car-following behavior. Other eight cases with two following cars taken from NGSIM are used to validate the model. A car-following case with stop-and-go processes is also used to demonstrate the performance of the proposed model. The simulation results are then compared with the calculations derived using the Gazis-Herman-Rothery (GHR) model. As a result, the DSM and GHR models yield similar results and the proposed model is effective for simulation of car following. By adjusting model parameters, the proposed model can simulate different driving behaviors. The proposed model gives a new way to explain car-following process by RHT.

scholarly journals Distilling Deep Structural Facial Relationships for FAU Intensity Estimation

2021 ◽  
Author(s):  
Yingruo Fan ◽  
Jacqueline CK Lam ◽  
Victor On Kwok Li
Keyword(s):  
Structural Characteristics ◽  
Model Performance ◽  
Training Model ◽  
Model Parameters ◽  
Intensity Estimation ◽  
Structural Relationships ◽  
Proposed Model ◽  
Comparable Performance ◽  
Knowledge Distillation ◽  
The Difference

<div> <div> <div> <p>Facial emotions are expressed through a combination of facial muscle movements, namely, the Facial Action Units (FAUs). FAU intensity estimation aims to estimate the intensity of a set of structurally dependent FAUs. Contrary to the existing works that focus on improving FAU intensity estimation, this study investigates how knowledge distillation (KD) incorporated into a training model can improve FAU intensity estimation efficiency while achieving the same level of performance. Given the intrinsic structural characteristics of FAU, it is desirable to distill deep structural relationships, namely, DSR-FAU, using heatmap regression. Our methodology is as follows: First, a feature map-level distillation loss was applied to ensure that the student network and the teacher network share similar feature distributions. Second, the region-wise and channel-wise relationship distillation loss functions were introduced to penalize the difference in structural relationships. Specifically, the region-wise relationship can be represented by the structural correlations across the facial features, whereas the channel-wise relationship is represented by the implicit FAU co-occurrence dependencies. Third, we compared the model performance of DSR-FAU with the state-of-the-art models, based on two benchmarking datasets. Our proposed model achieves comparable performance with other baseline models, though requiring a lower number of model parameters and lower computation complexities. </p> </div> </div> </div>

In-Plane Flexible Ring Tire Model—Part 1: Modeling and Parameter Identification

2018 ◽  
Vol 46 (3) ◽  
pp. 174-219 ◽  
Author(s):  
Bin Li ◽  
Xiaobo Yang ◽  
James Yang ◽  
Yunqing Zhang ◽  
Zeyu Ma
Keyword(s):  
Static Load ◽  
Model Parameters ◽  
Tire Model ◽  
Test Results ◽  
Lumped Mass ◽  
Virtual Test ◽  
Proposed Model ◽  
Particle Swarm Method ◽  
Vehicle Dynamic Simulation ◽  
Flexible Ring

ABSTRACT The tire model is essential for accurate and efficient vehicle dynamic simulation. In this article, an in-plane flexible ring tire model is proposed, in which the tire is composed of a rigid rim, a number of discretized lumped mass belt points, and numerous massless tread blocks attached on the belt. One set of tire model parameters is identified by approaching the predicted results with ADAMS® FTire virtual test results for one particular cleat test through the particle swarm method using MATLAB®. Based on the identified parameters, the tire model is further validated by comparing the predicted results with FTire for the static load-deflection tests and other cleat tests. Finally, several important aspects regarding the proposed model are discussed.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Modeling of Dynamic Loads on the Polished Rod of Pumping Unit in Case of Mulfunction of Rod Pump Operating

2014 ◽  
Vol 10 ◽  
pp. 95-101
Author(s):  
A.S. Topolnikov
Keyword(s):  
Multiphase Flow ◽  
Satisfactory Agreement ◽  
Model Simulation ◽  
Theoretical Modeling ◽  
Dynamic Loads ◽  
Plunger Pump ◽  
Proposed Model ◽  
Pumping Unit ◽  
Polished Rod

The paper presents the results of theoretical modeling of joined movement of pump rods and plunger pump and multiphase flow in a well for determination of dynamic loads on the polished rod of pumping unit. The specificity of the proposed model is the possibility of taking into account for complications in rod pump operating, such as leakage in valve steam, presence of gas and emulsion, incorrect fitting of plunger inside the cylinder pump. The satisfactory agreement of results of the model simulation with filed measurements are obtained.

scholarly journals A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1393
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Proposed Model ◽  
Single Temperature ◽  
Testing Data ◽  
Bonded Composite ◽  
Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

New Research on the Use of Hardening Plastics for Aircraft Construction

1940 ◽  
Vol 44 (349) ◽  
pp. 44-73
Author(s):  
Wilhelm Kuech
Keyword(s):  
Strength Properties ◽  
Dynamic Loads ◽  
Absorbed Energy ◽  
Good Strength ◽  
Different Temperatures ◽  
Bonding Properties ◽  
Static And Dynamic Loads ◽  
Impact Bending ◽  
New Research ◽  
Laminated Materials

Laminated materials incorporating plastics seem to be especially well suited lor highly stressed aircraft components, by reason of their good strength properties. Paper, fabric and wood veneers treated with plastics on a phenolic basis were tested with regard to their strength, especially in bending, shear, absorbed energy in impact bending, notching strength and in their resistance against moisture. Further, the behaviour of compressed plastics was studied at different temperatures under static and dynamic loads. A part of the research was extended to pure phenol resin and to thermoplastics based on methacrylate and polyvinylchloride. The bonding properties of laminated compressed plastics were established. Concluding, some experiments relating to the practical manufacture of aeroplane components are communicated.

scholarly journals Flexural behavior of composite structural insulated panels with magnesium oxide board facings

2020 ◽  
Vol 20 (4) ◽  
Author(s):  
Łukasz Smakosz ◽  
Ireneusz Kreja ◽  
Zbigniew Pozorski
Keyword(s):  
Magnesium Oxide ◽  
Material Model ◽  
Expanded Polystyrene ◽  
Flexural Behavior ◽  
Joint Analysis ◽  
Model Parameters ◽  
Fe Model ◽  
Computational Results ◽  
Four Point Bending ◽  
Proposed Model

Abstract The current report is devoted to the flexural analysis of a composite structural insulated panel (CSIP) with magnesium oxide board facings and expanded polystyrene (EPS) core, that was recently introduced to the building industry. An advanced nonlinear FE model was created in the ABAQUS environment, able to simulate the CSIP’s flexural behavior in great detail. An original custom code procedure was developed, which allowed to include material bimodularity to significantly improve the accuracy of computational results and failure mode predictions. Material model parameters describing the nonlinear range were identified in a joint analysis of laboratory tests and their numerical simulations performed on CSIP beams of three different lengths subjected to three- and four-point bending. The model was validated by confronting computational results with experimental results for natural scale panels; a good correlation between the two results proved that the proposed model could effectively support the CSIP design process.

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