Search results for: Gauss point numerical integration

Authors: Inger Eriksson, Lisbeth Ohlsson, Jeremias Rosenqvist

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Ingress: Focus in the study is directed towards phenomena and concepts of segregation, integration, and inclusion of students attending a special school form in Sweden, namely compulsory school for pupils with learning disabilities (in Swedish 'särskola') as an alternative to mainstream compulsory school. Aim: The aim of the study is to examine the school situation for students attending särskola from a historical perspective focussing the 1980s, 1990s and the 21st century, from an integration perspective, and from a perspective of power. Procedure: Five sub-studies are reported, where integration and inclusion are looked into by observation studies and interviews with school leaders, teachers, special and remedial teachers, psychologists, coordinators, and parents in the special schools/särskola. In brief, the study about special school students attending mainstream classes from 1998 takes its point of departure in the idea that all knowledge development takes place in a social context. A special interest is taken in the school’s role for integration generally, and the role of special education particularly and on whose conditions the integration is taking place – the special school students' or the other students,' or may be equally, in the class. Pedagogical and social conditions for so called individually integrated special school students in elementary school classes were studied in eleven classes. Results: The findings are interpreted in a power perspective supported by Foucault and relationally by Vygotsky. The main part of the data consists of extensive descriptions of the eleven cases, here called integration situations. Conclusions: In summary, this study suggests that the possibilities for a special school student to get into the class community and fellowship and thereby be integrated with the class are to a high degree dependant on to what extent the student can take part in the pedagogical processes. The pedagogical situation for the special school student is affected not only by the class teacher and the support and measures undertaken but also by the other students in the class as they, in turn, are affected by how the special school student is acting. This mutual impact, which constitutes the integration process in itself, might result in a true integration if the special school student attains the status of being accepted on his/her own terms not only being cared for or cherished by some classmates. A special school student who is not accepted even on the terms of the class will often experience severe problems in the contacts with classmates and the school situation might thus be a mere placement.

Keywords: integration/inclusion, mainstream school, power, special school students

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Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

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Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

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Authors: Pawel Flaszynski, Piotr Doerffer, Jan Holnicki-Szulc, Grzegorz Mikulowski

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Results of numerical simulations for transonic flow in a piezoelectric valve are presented. The valve is the main part of an adaptive pneumatic shock absorber. Flow structure in the valve domain and the influence of the flow non-uniformity in the valve on a mass flow rate is investigated. Numerical simulation results are compared with experimental data.

Keywords: pneumatic valve, transonic flow, numerical simulations, piezoelectric valve

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Authors: Jeremiah Madzimure

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In order to stay competitive in business and improve performance, Small and Medium Enterprises (SMEs) need to make use of business networking and logistics integration. Strategic networking and logistics integration in business companies have become critical as they allow supplier partnering, exchange of vital information/ access to valuable resources allowing innovation, gaining access to additional resources, sharing risks and costs which is required for enhancing company performance. The purpose of this study was to examine the influence of strategic networks and logistics integration on company performance: the case of small and medium enterprises in South Africa. A quantitative research design was adopted in this study, and 137 SMEs owners and managers completed and returned the survey questionnaire. Confirmatory Factor Analysis (CFA) was conducted using the Analysis of Moment Structures (AMOS), version 24.0 to assess psychometric properties of the measurement scales. Path modelling techniques were used to test the proposed hypothesis. Three research hypotheses were postulated. The results indicate that strategic networks had a positive and significant influence on logistics integration and company performance. As well logistics integration had a strong positive and significant influence on company performance. This study provides a useful model for analysing the relationship between strategic networks and logistics integration on company performance. Moreover, the findings of the study provide useful insights into how SMEs should benefit from business networking and logistics integration so as to improve their performance. The implications of the study are discussed, and finally, limitations and recommendations are indicated.

Keywords: strategic networking, logistics integration, company performance, SMEs

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Authors: Hooman Dabirmanesh, Attila M. Zsaki

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Traditionally, rock slope stability is carried out using limit equilibrium analysis when investigating toppling failure. In these equilibrium methods, internal forces exerted between columns are not clearly defined, and to the authors’ best knowledge, there is no consensus in literature with respect to the results of analysis. A discrete element method-based numerical model was developed and applied to simulate the behavior of rock layers subjected to toppling failure. Based on this calibrated numerical model, a study of the location and distribution of internal forces that result in equilibrium was carried out. The sum of side forces was applied at a point on a block which properly represents the force to determine the inter-column force distribution. In terms of the side force distribution coefficient, the result was compared to those obtained from laboratory centrifuge tests. The results of the simulation show the suitable criteria to select the correct position for the internal exerted force between rock layers. In addition, the numerical method demonstrates how a theoretical method could be reliable by considering the interaction between the rock layers.

Keywords: contact bond, discrete element, force distribution, limit equilibrium, tensile stress

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Sonia Ben Hamza, Sabra Habli, Nejla Mahjoub Said, Hervé Bournot, Georges Le Palec

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The distribution characteristics of pollutants released at different vertical inlet positions of an open channel are investigated with a three-dimensional numerical model. Pollutants are injected from time-dependent sources in a turbulent free surface flow. Numerical computations were carried out using ANSYS Fluent which is based on the finite volume approach. The air/water interface was modeled with the volume of the fluid method (VOF). By focusing on investigating the influences of flow on pollutants, it is found that pollutant released from the bottom position of the channel takes more time to disperse in the longitudinal direction of the flow in comparison with the case of pollutant released near the free surface. On the other hand, the pollutant released from the bottom position generates a vertical dispersion with decreased amplitude. These findings may assist in cost-effective scientific countermeasures to be taken for accident or planned pollutant discharged into a river.

Keywords: numerical simulation, pollutant release, turbulent free surface flow, VOF model

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Authors: Halil Ibrahim Demir, Caner Erden, Abdullah Hulusi Kokcam, Mumtaz Ipek

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Process planning, scheduling, and due date assignment are three important manufacturing functions which are studied independently in literature. There are hundreds of works on IPPS and SWDDA problems but a few works on IPPSDDA problem. Integrating these three functions is very crucial due to the high relationship between them. Since the scheduling problem is in the NP-Hard problem class without any integration, an integrated problem is even harder to solve. This study focuses on the integration of these functions. Sum of weighted tardiness, earliness, and due date related costs are used as a penalty function. Random search and hybrid metaheuristics are used to solve the integrated problem. Marginal improvement in random search is very high in the early iterations and reduces enormously in later iterations. At that point directed search contribute to marginal improvement more than random search. In this study, random and genetic search methods are combined to find better solutions. Results show that overall performance becomes better as the integration level increases.

Keywords: process planning, genetic algorithm, hybrid search, random search, weighted due-date assignment, weighted scheduling

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Authors: Hudson Akewe

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This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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Authors: V. Sankaranarayanan, V. Amrita Sundari, Sunit P. Gopal

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This paper presents the design and implementation of a nonlinear controller for the point to point control of a mobile inverted pendulum (MIP). The controller is designed based on the kinematic model of the MIP to stabilize all the four coordinates. The stability of the closed-loop system is proved using Lyapunov stability theory. The proposed controller is validated through numerical simulations and also implemented in a laboratory prototype. The results are presented to evaluate the performance of the proposed closed loop system.

Keywords: mobile inverted pendulum, switched control, nonlinear systems, lyapunov stability

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Authors: Renzhong Peng, Weiping Wu

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Based on the framework of Hofstede’s cultural dimension, this study conducted a comparative study on the similarities and differences between national cultures and corporate cultural values, analyzed and interpreted the reasons why Chinese overseas Mergers and Acquisitions (M&A) cultural integration results in the success or failure. The findings of this study indicate that in the process of M&A, the corporate cultural values from Chinese and western corporations are proved to be quite different as a result of their diversities of national cultures, and the strategies for the integration of cultural corporate values are of vital importance and can determine the effects of the M&A, which can be referential to managers who intend to have the idea of M&A and those who have cultural integration in the process of M&A.

Keywords: comparative study, cultural integration, corporate cultural values, Mergers and Acquisitions

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Authors: Amira Amamou, Mnaouar Chouchane

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This paper investigates the bifurcation and nonlinear behavior of two degrees of freedom model of a symmetrical balanced rigid rotor supported by two identical journal bearings. The fluid film hydrodynamic reactions are modeled by applying both the short and the long bearing approximation and using half Sommerfeld solution. A numerical integration of equations of the journal centre motion is presented to predict the presence and the size of stable or unstable limit cycles in the neighborhood of the stability critical speed. For their stability margins, a continuation method based on the predictor-corrector mechanism is used. The numerical results of responses show that stability and bifurcation behaviors of periodic motions depend strongly on bearing parameters and its dynamic characteristics.

Keywords: hydrodynamic journal bearing, nonlinear stability, continuation method, bifurcations

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

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Authors: Yue Zhang, Bo Yang, Gang Xiong, Mohamed Elchalakanic, Shidong Nie

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This study aims to investigate the lateral torsional buckling of I-shaped cross-section beams fabricated from Q460GJ structural steel plates. Both experimental and numerical simulation results are presented in this paper. A total of eight specimens were tested under a three-point bending, and the corresponding numerical models were established to conduct parametric studies. The effects of some key parameters such as the non-dimensional member slenderness and the height-to-width ratio, were investigated based on the verified numerical models. Also, the results obtained from the parametric studies were compared with the predictions calculated by different design codes including the Chinese design code (GB50017-2003, 2003), the new draft version of Chinese design code (GB50017-201X, 2012), Eurocode 3 (EC3, 2005) and the North America design code (ANSI/AISC360-10, 2010). These comparisons indicated that the sectional height-to-width ratio does not play an important role to influence the overall stability load-carrying capacity of Q460GJ structural steel beams with welded I-shaped cross-sections. It was also found that the design methods in GB50017-2003 and ANSI/AISC360-10 overestimate the overall stability and load-carrying capacity of Q460GJ welded I-shaped cross-section beams.

Keywords: experimental study, finite element analysis, global stability, lateral torsional buckling, Q460GJ structural steel

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Authors: Amal Machtalay

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In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

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Authors: Abdalla Manur, Daniel Offin, Alessandro Arsie

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In this paper, we study the extension of the minimizing equal mass parallelogram solutions which was derived by Chen in 2001. Chen’s solution was minimizing for one quarter of the period [0; T], where numerical integration had been used in his proof. This paper focuses on extending the minimization property to intervals of time [0; 2T] and [0; 4T].

Keywords: action, Hamiltoian, N-body, symmetry

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Authors: Matjaz Prek

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Impact of three different combinations of cooling and ventilation systems on the indoor environmental quality (IEQ) has been studied. Comparison of chilled ceiling cooling in combination with displacement ventilation, cooling with fan coil unit and cooling with flat wall displacement outlets was performed. All three combinations were evaluated from the standpoint of whole-body and local thermal comfort criteria as well as from the standpoint of ventilation effectiveness. The comparison was made on the basis of numerical simulation with DesignBuilder and Fluent. Numerical simulations were carried out in two steps. Firstly the DesignBuilder software environment was used to model the buildings thermal performance and evaluation of the interaction between the environment and the building. Heat gains of the building and of the individual space, as well as the heat loss on the boundary surfaces in the room, were calculated. In the second step Fluent software environment was used to simulate the response of the indoor environment, evaluating the interaction between building and human, using the simulation results obtained in the first step. Among the systems presented, the ceiling cooling system in combination with displacement ventilation was found to be the most suitable as it offers a high level of thermal comfort with adequate ventilation efficiency. Fan coil cooling has proved inadequate from the standpoint of thermal comfort whereas flat wall displacement outlets were inadequate from the standpoint of ventilation effectiveness. The study showed the need in evaluating indoor environment not solely from the energy use point of view, but from the point of view of indoor environmental quality as well.

Keywords: cooling, ventilation, thermal comfort, ventilation effectiveness, indoor environmental quality, IEQ, computational fluid dynamics

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Authors: Hassan J. Al Salman, Ahmed A. Al Ghafli

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In this study, we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed-point theorem to prove existence of the approximations at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

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Authors: Ghussoun Al-Jeiroudi

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Stochastic programming is one of the powerful technique which is used to solve real-life problems. Hence, the data of real-life problems is subject to significant uncertainty. Uncertainty is well studied and modeled by stochastic programming. Each day, problems become bigger and bigger and the need for a tool, which does deal with large scale problems, increase. Interior point method is a perfect tool to solve such problems. Interior point method is widely employed to solve the programs, which arise from stochastic programming. It is an iterative technique, so it is required a starting point. Well design starting point plays an important role in improving the convergence speed. In this paper, we propose a starting point for interior point method for multistage stochastic programming. Usually, the optimal solution of stage k+1 is used as starting point for the stage k. This point has the advantage of being close to the solution of the current program. However, it has a disadvantage; it is not in the feasible region of the current program. So, we suggest to take this point and modifying it. That is by adding to it a vector in the null space of the matrix of the unchanged constraints because the solution will change only in the null space of this matrix.

Keywords: interior point methods, stochastic programming, null space, starting points

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Authors: Peng Li, Er-xiang Song

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Numerical analysis of longitudinal tunnel seismic response due to spatial variation of earthquake ground motion is an important issue that cannot be ignored in the design and safety evaluation of tunnel structures. In this paper, numerical methods for analysis of tunnel longitudinal response under asynchronous seismic wave is extensively studied, including the improvement of the 1D time-domain finite element method, three dimensional numerical simulation technique for the site asynchronous earthquake response as well as the 3-D soil-tunnel structure interaction analysis. The study outcome will be beneficial to aid further research on the nonlinear meticulous numerical analysis and seismic response mechanism of tunnel structures under asynchronous earthquake motion.

Keywords: asynchronous input, longitudinal seismic response, tunnel structure, numerical simulation, traveling wave effect

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Authors: Jianqin Qu

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This paper proposes a rigid point set matching algorithm in arbitrary dimensions based on the idea of symmetric covariant function. A group of functions of the points in the set are formulated using rigid invariants. Each of these functions computes a pair of correspondence from the given point set. Then the computed correspondences are used to recover the unknown rigid transform parameters. Each computed point can be geometrically interpreted as the weighted mean center of the point set. The algorithm is compact, fast, and dimension free without any optimization process. It either computes the desired transform for noiseless data in linear time, or fails quickly in exceptional cases. Experimental results for synthetic data and 2D/3D real data are provided, which demonstrate potential applications of the algorithm to a wide range of problems.

Keywords: covariant point, point matching, dimension free, rigid registration

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Authors: Surayyo Shaamirova, Anwar Hasan Abdullah Othman

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This study investigates the co-integration association between the top 10 cryptocurrencies, namely Bitcoin, Ethereum, Ripple, Bitcoin Cash, EOS, Cardano, Litecoin, Stellar, IOTA, and NEO. The study applies Johansen Juselius co-integration test to examine the long-run co-integration and utilize the Engle and Granger casualty test to examine the short-run relationship. The findings of the study show that there is a strong co-integration relationship among the cryptocurrencies; however, in the short run, there is no causal relationship among the crypto currencies. These results, therefore, suggest that there are portfolio diversification opportunities in the cryptocurrencies industry when it comes to long run investment decisions, on the other hand, the cryptocurrencies industry shows the characteristics of efficiency in the short-run. This is an indication of a non-speculation investment in the cryptocurrencies industry in the short term investment.

Keywords: cryptocurrencies, Johansen-Juselius co-integration test, Engle and Granger casualty test, portfolio diversification

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Authors: M. Manohari, Himanshu Gupta, S. Priyadharshini, R.Santhanam, S.Chandrasekaran, B|.Venkatraman

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Injection is one of the potential routes of intake in a radioactive facility. The internal dose due to this intake is monitored at the radiation emergency medical centre, IGCAR using a portable planar HPGe detector. The contaminated wound may be having different shapes. In a reprocessing potential of wound contamination with actinide is more. Efficiency is one of the input parameters for estimation of internal dose. Estimating these efficiencies experimentally would be tedious and cumbersome. Numerical estimation can be a supplement to experiment. As an initial step in this study 241Am contamination of different shapes are studied. In this study portable planar HPGe detector was modeled using Monte Carlo code FLUKA and the effect of different parameters like distance of the contamination from the detector, radius of the circular contamination were studied. Efficiency values for point and surface contamination located at different distances were estimated. The effect of efficiency on the radius of the surface source was more predominant when the source is at 1 cm distance compared to when the source to detector distance is 10 cm. At 1 cm the efficiency decreased quadratically as the radius increased and at 10 cm it decreased linearly. The point source efficiency varied exponentially with source to detector distance.

Keywords: Planar HPGe, efficiency value, injection, surface source

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Authors: Ozge Karayalçin

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This study tries to find out the reasons for the integration problems of third generation Dutch-Turkish youngsters by particularly focusing on the socio-cultural and socio-economic situations of these people in the Netherlands. The results obtained from the field research are summed up under four sections. These four sections are education and language, labour market, cultural factors, religion, and nationality. The underlying reasons of the integration problems are reflected from two different perspectives. The first one is the effects of social and economic enforcements implemented on the Turkish immigrant society. The second one is the traditional Turkish values that are quite different from Dutch values. The problems experienced by third generation Turkish origin Dutch youngsters are not one-sided. To conclude, solution-oriented advisements are asserted.

Keywords: acculturation levels, Dutch-Turkish youngsters, integration, transnational migrants, identity conflicts

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Authors: Salim Belouettar, Kodjo Attipou

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The thermal wrinkling behavior of thin membranes is investigated. The Fourier double scale series are used to deduce the macroscopic membrane wrinkling equations. The obtained equations account for the global and local wrinkling modes. Numerical examples are conducted to assess the validity of the approach developed. Compared to the finite element full model, the present model needs only few degrees of freedom to recover accurately the bifurcation curves and wrinkling paths. Different parameters such as membrane’s aspect ratio, wave number, pre-stressed membranes are discussed from a numerical point of view and the properties of the wrinkles (critical load, wavelength, size and location) are presented.

Keywords: wrinkling, thermal stresses, Fourier series, thin membranes

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

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In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

Keywords: base isolation, computational efficiency, mixed explicit-implicit method, partitioned solution approach, stability

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Authors: Iyad Alazzam, Kenneth Magel, Izzat Alsmadi

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The different activities and approaches in software testing try to find the most possible number of errors or failures with the least amount of possible effort. Mutation is a testing approach that is used to discover possible errors in tested applications. This is accomplished through changing one aspect of the software from its original and writes test cases to detect such change or mutation. In this paper, we present a mutation approach for testing software components integration aspects. Several mutation operations related to components integration are described and evaluated. A test case study of several open source code projects is collected. Proposed mutation operators are applied and evaluated. Results showed some insights and information that can help testing activities in detecting errors and improving coverage.

Keywords: software testing, integration testing, mutation, coverage, software design

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Authors: Mohamed Driouich, Kamal Gueraoui, Mohamed Sammouda

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The main objective of this work is to establish a numerical code for studying the flow of molten polymers in deformable pipes. Using an iterative numerical method based on finite differences, we determine the profiles of the fluid velocity, the temperature and the apparent viscosity of the fluid. The numerical code presented can also be applied to other industrial applications.

Keywords: numerical code, molten polymers, deformable pipes, finite differences

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Authors: Bahar Ayhan

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The present paper is concerned with the numerical modeling of the inelastic behavior of the anisotropically damaged ductile materials, which are based on a generalized macroscopic theory within the framework of continuum damage mechanics. Kinematic decomposition of the strain rates into elastic, plastic and damage parts is basis for accomplishing the structure of continuum theory. The evolution of the damage strain rate tensor is detailed with the consideration of anisotropic effects. Helmholtz free energy functions are constructed separately for the elastic and inelastic behaviors in order to be able to address the plastic and damage process. Additionally, the constitutive structure, which is based on the standard dissipative material approach, is elaborated with stress tensor, a yield criterion for plasticity and a fracture criterion for damage besides the potential functions of each inelastic phenomenon. The finite element method is used to approximate the linearized variational problem. Stress and strain outcomes are solved by using the numerical integration algorithm based on operator split methodology with a plastic and damage (multiplicator) variable separately. Numerical simulations are proposed in order to demonstrate the efficiency of the formulation by comparing the examples in the literature.

Keywords: anisotropic damage, finite element method, plasticity, coupling

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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