Search results for: mathematical shape deformation model

Authors: R. Bennai, H. Ait Atmane, H. Fourne, B. Ayache

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In this work, an analytical approach using a refined theory of hyperbolic shear deformation of a beam was developed to study the buckling of graduated sandwiches beams under different boundary conditions. The effects of transverse shear strains and the transverse normal deformation are considered. The constituent materials of the beam are supposed gradually variable depending on the height direction based on a simple power distribution law in terms of the volume fractions of the constituents; the two materials with which we worked are metals and ceramics. The core layer is taken homogeneous and made of an isotropic material; while the banks layers consist of functionally graded materials with a homogeneous fraction compared to the middle layer. In the end, illustrative examples are presented to show the effects of changes in different parameters such as (material graduation, the stretching effect of the thickness, boundary conditions and thickness ratio-length) on the vibration free of an FGM sandwich beams.

Keywords: FGM materials, refined shear deformation theory, stretching effect, buckling

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Authors: A. Elmikaty, Z. Thanawarothon, L. Mezeix

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This paper presents a finite element model to simulate the teeth failure of non-circular composite chainring. Model consists of the chainring and a part of the chain. To reduce the size of the model, only the first 11 rollers are simulated. In order to validate the model, it is firstly applied to a circular aluminum chainring and evolution of the stress in the teeth is compared with the literature. Then, effect of the non-circular shape is studied through three different loading positions. Strength of non-circular composite chainring and failure scenario is investigated. Moreover, two composite lay-ups are proposed to observe the influence of the stacking. Results show that composite material can be used but the lay-up has a large influence on the strength. Finally, loading position does not have influence on the first composite failure that always occurs in the first tooth.

Keywords: CFRP, composite failure, FEA, non-circular chainring

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Authors: A. B. M. Rezaul Islam, Ernur Karadogan

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Shape memory alloys (SMAs) are known for their shape memory effect and pseudoelasticity behavior. Their thermomechanical behaviors are modeled by numerous researchers using microscopic thermodynamic and macroscopic phenomenological point of view. Tanaka, Liang-Rogers and Ivshin-Pence models are some of the most popular SMA macroscopic phenomenological constitutive models. They describe SMA behavior in terms of stress, strain and temperature. These models involve material parameters and they have associated uncertainty present in them. At different operating temperatures, the uncertainty propagates to the output when the material is subjected to loading followed by unloading. The propagation of uncertainty while utilizing these models in real-life application can result in performance discrepancies or failure at extreme conditions. To resolve this, we used probabilistic approach to perform the sensitivity and uncertainty analysis of Tanaka, Liang-Rogers, and Ivshin-Pence models. Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods have been used to perform the sensitivity analysis for simulated isothermal loading/unloading at various operating temperatures. As per the results, it is evident that the models vary due to the change in operating temperature and loading condition. The average and stress-dependent sensitivity indices present the most significant parameters at several temperatures. This work highlights the sensitivity and uncertainty analysis results and shows comparison of them at different temperatures and loading conditions for all these models. The analysis presented will aid in designing engineering applications by eliminating the probability of model failure due to the uncertainty in the input parameters. Thus, it is recommended to have a proper understanding of sensitive parameters and the uncertainty propagation at several operating temperatures and loading conditions as per Tanaka, Liang-Rogers, and Ivshin-Pence model.

Keywords: constitutive models, FAST sensitivity analysis, sensitivity analysis, sobol, shape memory alloy, uncertainty analysis

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Asrat M.Belachew, Tiago Pereira, Institute of Mathematics, Computer Sciences, Avenida Trabalhador São Carlense, 400, São Carlos, 13566-590, Brazil

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Infectious diseases are among the most prominent threats to human beings. They cause morbidity and mortality to an individual and collapse the social, economic, and political systems of the whole world collectively. Mathematical models are fundamental tools and provide a comprehensive understanding of how infectious diseases spread and designing the control strategy to mitigate infectious diseases from the host population. Modeling the spread of infectious diseases using a compartmental model of inhomogeneous populations is good in terms of complexity. However, in the real world, there is a situation that accounts for heterogeneity, such as ages, locations, and contact patterns of the population which are ignored in a homogeneous setting. In this work, we study how classical an SEIR infectious disease spreading of the compartmental model can be extended by incorporating the mobility of population between heterogeneous cities during an outbreak of infectious disease. We have formulated an SEIR multi-cities epidemic spreading model using a system of 4k ordinary differential equations to describe the disease transmission dynamics in k-cities during the day and night. We have shownthat the model is epidemiologically (i.e., variables have biological interpretation) and mathematically (i.e., a unique bounded solution exists all the time) well-posed. We constructed the next-generation matrix (NGM) for the model and calculated the basic reproduction number R0for SEIR-epidemic spreading model with cities mobility. R0of the disease depends on the spectral radius mobility operator, and it is a threshold between asymptotic stability of the disease-free equilibrium and disease persistence. Using the eigenvalue perturbation theorem, we showed that sending a fraction of the population between cities decreases the reproduction number of diseases in interconnected cities. As a result, disease transmissiondecreases in the population.

Keywords: SEIR-model, mathematical model, city mobility, epidemic spreading

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Authors: Jiahui Song

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In order to predict or explain a complicated biological process, it is important first to construct mathematical models that can be used to yield analytical solutions. Through numerical simulation, mathematical model results can be used to test scenarios that might not be easily attained in a laboratory experiment, or to predict parameters or phenomena. High-intensity, nanosecond pulse electroporation has been a recent development in bioelectrics. The dynamic pore model can be achieved by including a dynamic aspect and a dependence on the pore population density into pore formation energy equation to analyze and predict such electroporation effects. For greater accuracy, with inclusion of atomistic details, molecular dynamics (MD) simulations were also carried out during this study. Besides inducing pores in cells, external voltages could also be used in principle to modulate action potential generation in nerves. This could have an application in electrically controlled ‘pain management’. Also a simple model-based rate equation treatment of the various cellular bio-chemical processes has been used to predict the pulse number dependent cell survival trends.

Keywords: model, high-intensity, nanosecond, bioelectrics

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Authors: Tai-Yue Wang, Yi-Ho Chen

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In this study, we investigate a two-echelon supply chain with two suppliers and three retailers among which one retailer dominates other retailers. A price competition demand function is used to model this dominant retailer, which is leading market. The promotion strategies and negotiation schemes are integrated to form decision-making models under different scenarios. These models are then formulated into different mathematical programming models. The decision variables such as promotional costs, retailer prices, wholesale price, and order quantity are included in these models. At last, the distributions of promotion costs under different cost allocation strategies are discussed. Finally, an empirical example used to validate our models. The results from this empirical example show that the profit model will create the largest profit for the supply chain but with different profit-sharing results. At the same time, the more risk a member can take, the more profits are distributed to that member in the utility model.

Keywords: supply chain, price promotion, mathematical models, dominant retailer

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Authors: Rida B. Arieby, Hameed N. Hameed

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In this work, tensile tests on high density polyethylene have been carried out under various constant strain rate and strain rate jump tests. The dependency of the true stress and specially the variation of volume strain have been investigated, the volume strain due to the phenomena of damage was determined in real time during the tests by an optical extensometer called Videotraction. A modified constitutive equations, including strain rate and damage effects, are proposed, such a model is based on a non-equilibrium thermodynamic approach called (DNLR). The ability of the model to predict the complex nonlinear response of this polymer is examined by comparing the model simulation with the available experimental data, which demonstrate that this model can represent the deformation behavior of the polymer reasonably well.

Keywords: strain rate jump tests, volume strain, high density polyethylene, large strain, thermodynamics approach

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Authors: Ella Tyuryumina, Alexey Neznanov

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Finding algorithms to predict the growth of tumors has piqued the interest of researchers ever since the early days of cancer research. A number of studies were carried out as an attempt to obtain reliable data on the natural history of breast cancer growth. Mathematical modeling can play a very important role in the prognosis of tumor process of breast cancer. However, mathematical models describe primary tumor growth and metastases growth separately. Consequently, we propose a mathematical growth model for primary tumor and primary metastases which may help to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoM-IV and corresponding software. We are interested in: 1) modelling the whole natural history of primary tumor and primary metastases; 2) developing adequate and precise CoM-IV which reflects relations between PT and MTS; 3) analyzing the CoM-IV scope of application; 4) implementing the model as a software tool. The CoM-IV is based on exponential tumor growth model and consists of a system of determinate nonlinear and linear equations; corresponds to TNM classification. It allows to calculate different growth periods of primary tumor and primary metastases: 1) ‘non-visible period’ for primary tumor; 2) ‘non-visible period’ for primary metastases; 3) ‘visible period’ for primary metastases. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. Thus, the CoM-IV model and predictive software: a) detect different growth periods of primary tumor and primary metastases; b) make forecast of the period of primary metastases appearance; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of BC and facilitate optimization of diagnostic tests. The following are calculated by CoM-IV: the number of doublings for ‘nonvisible’ and ‘visible’ growth period of primary metastases; tumor volume doubling time (days) for ‘nonvisible’ and ‘visible’ growth period of primary metastases. The CoM-IV enables, for the first time, to predict the whole natural history of primary tumor and primary metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on primary tumor sizes. Summarizing: a) CoM-IV describes correctly primary tumor and primary distant metastases growth of IV (T1-4N0-3M1) stage with (N1-3) or without regional metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and manifestation of primary metastases.

Keywords: breast cancer, exponential growth model, mathematical modelling, primary metastases, primary tumor, survival

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Authors: Hyo Lim Kang, Tae An Kim, Seung Ho Han

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A 3-way reversing valve has been used in automotive washing machines to remove remaining oil and dirt on machined engine and transmission blocks. It provides rapid and accurate changes of water flow direction without any precise control device. However, due to its complicated bottom-plug shape, a cavitation occurs in a wide range of the bottom-plug in a downstream. In this study, the cavitation index and POC (percent of cavitation) were used to evaluate quantitatively the cavitation phenomena occurring at the bottom-plug. An optimal shape design was carried out via parametric study for geometries of the bottom-plug, in which a simple CAE-model was used in order to avoid time-consuming CFD analysis and hard to achieve convergence. To verify the results of numerical analysis, a flow visualization test was carried out using a test specimen with a transparent acryl pipe according to ISA-RP75.23. The flow characteristics such as the cavitation occurring in the downstream were investigated by using a flow test equipment with valve and pump including a flow control system and high-speed camera.

Keywords: cavitation, flow visualization test, optimal shape design, percent of cavitation, reversing valve

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Authors: Linda A. O’Higgins, Astrid Wingler, Jorge Oliveira

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The growth of Chlorella vulgaris was characterized as a function of irradiance in a laboratory turbidostat (1 L) and compared to batch growth in sunlit modules (5–25 L) of the commercial Phytobag photobioreactor. The effects of variable sunlight and culture density were deconvoluted by a mathematical model. The analysis showed that algal growth was light-limited due to shading by external construction elements and due to light attenuation within the algal bags. The model was also used to predict maximum biomass productivity. The manipulative experiments and the model predictions were confronted with data from a production season of a 10m2 pilot-scale photobioreactor, Phytobag (10,000 L). The analysis confirmed light limitation in all three photobioreactors. An additional limitation of biomass productivity was caused by the nitrogen starvation that was used to induce lipid accumulation. Reduction of shading and separation of biomass and lipid production are proposed for future optimization.

Keywords: microalgae, batch cultivation, Chlorella vulgaris, Mathematical model, photobioreactor, scale-up

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Cihan Çetinkaya, Eren Özceylan, Kerem Elibal

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This paper presents a solution method for selection of production facility. The motivation has been taken from a real life case, an automotive subcontractor which has two production facilities at different cities and parts. The problem is to decide which part(s) should be produced at which facility. To the best of our knowledge, until this study, there was no scientific approach about this problem at the firm and decisions were being given intuitively. In this study, some logistic cost parameters have been defined and with these parameters a mathematical model has been constructed. Defined and collected cost parameters are handling cost of parts, shipment cost of parts and shipment cost of welding fixtures. Constructed multi-objective mathematical model aims to minimize these costs while aims to balance the workload between two locations. Results showed that defined model can give optimum solutions in reasonable computing times. Also, this result gave encouragement to develop the model with addition of new logistic cost parameters.

Keywords: automotive subcontract, facility assignment, logistic costs, multi-objective models

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Authors: Mahmudjon Kuchkarov, Marufjon Kuchkarov

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The origin of ‘Human Language’ is still a secret and the most interesting subject of historical linguistics. The core element is the nature of labeling or coding the things or processes with symbols and sounds. In this paper, we investigate human’s involuntary Paired Sounds and Shape Production (PSSP) and its contribution to the development of early human communication. Aimed at twenty-six volunteers who provided many physical movements with various difficulties, the research team investigated the natural, repeatable, and paired sounds and shape productions during human activities. The paper claims the involvement of Paired Sounds and Shape Production (PSSP) in the phonetic origin of some modern words and the existence of similarities between elements of PSSP with characters of the classic Latin alphabet. The results may be used not only as a supporting idea for existing theories but to create a closer look at some fundamental nature of the origin of the languages as well.

Keywords: body shape, body language, coding, Latin alphabet, merging method, movement language, movement sound, natural sound, origin of language, pairing, phonetics, sound and shape production, word origin, word semantic

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Authors: Geetika Barman, B. S. Daya Sagar

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In this article, we proposed a pixel-wise classification of hyperspectral images using a mathematical morphology operator-based distance metric called “dilation distance” and “erosion distance”. This method involves measuring the spatial distance between the spectral features of a hyperspectral image across the bands. The key concept of the proposed approach is that the “dilation distance” is the maximum distance a pixel can be moved without changing its classification, whereas the “erosion distance” is the maximum distance that a pixel can be moved before changing its classification. The spectral signature of the hyperspectral image carries unique class information and shape for each class. This article demonstrates how easily the dilation and erosion distance can measure spatial distance compared to other approaches. This property is used to calculate the spatial distance between hyperspectral image feature vectors across the bands. The dissimilarity matrix is then constructed using both measures extracted from the feature spaces. The measured distance metric is used to distinguish between the spectral features of various classes and precisely distinguish between each class. This is illustrated using both toy data and real datasets. Furthermore, we investigated the role of flat vs. non-flat structuring elements in capturing the spatial features of each class in the hyperspectral image. In order to validate, we compared the proposed approach to other existing methods and demonstrated empirically that mathematical operator-based distance metric classification provided competitive results and outperformed some of them.

Keywords: dilation distance, erosion distance, hyperspectral image classification, mathematical morphology

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Authors: Ledeza Jordan Babiano

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Translating statements into mathematical notations is one of the processes in word problem-solving. However, based on the literature, students still have difficulties with this skill. The purpose of this study was to investigate the translation errors of the students when they translate algebraic word problems into mathematical structures and locate the errors via the lens of the Translation-Verification Model. Moreover, this qualitative research study employed content analysis. During the data-gathering process, the students were asked to answer a six-item algebra word problem questionnaire, and their answers were analyzed by experts through blind coding using the Translation-Verification Model to determine their translation errors. After this, a focus group discussion was conducted, and the data gathered was analyzed through thematic analysis to determine the causes of the students’ translation errors. It was found out that students’ prevalent error in translation was the interpretation error, which was situated in the Attribute construct. The emerging themes during the FGD were: (1) The procedure of translation is strategically incorrect; (2) Lack of comprehension; (3) Algebra concepts related to difficulty; (4) Lack of spatial skills; (5) Unprepared for independent learning; and (6) The content of the problem is developmentally inappropriate. These themes boiled down to the major concept of independent learning preparedness in solving mathematical problems. This concept has subcomponents, which include contextual and conceptual factors in translation. Consequently, the results provided implications for instructors and professors in Mathematics to innovate their teaching pedagogies and strategies to address translation gaps among students.

Keywords: mathematical structure, algebra word problems, translation, errors

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Authors: Ji Chen, Chunhui Zhang, Fanming Zeng, Lei Zhang, Ying Li, Wei Zhang

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Based on the synthetic principle of force, a pre-compressed nonlinear isolator with quasi-zero-stiffness (QZS) is developed for shock isolation of ship equipment. The proposed isolator consists of a vertical spring with positive stiffness and several lateral springs with negative stiffness. An analytical expression of vertical stiffness of the nonlinear isolator is derived and numerical simulation on the effect of the geometric design parameters is carried out. Besides, a pre-compressed QZS shock isolation system model is established. The stiffness characteristic of the system is studied and the effects of excitation amplitude and friction damping on shock isolation performance are discussed respectively. The research results show that in comparison with linear shock isolation system, the pre-compressed QZS shock isolation system could realize constant-force or approximately constant-force function and perform better anti-impact performance.

Keywords: quasi-zero-stiffness, constant-force, pre-compressed, large deformation, shock isolation, friction damping

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Authors: E. Tandis, E. Assareh

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Designing the optimal shape of MW wind turbine blades is provided in a number of cases through evolutionary algorithms associated with mathematical modeling (Blade Element Momentum Theory). Evolutionary algorithms, among the optimization methods, enjoy many advantages, particularly in stability. However, they usually need a large number of function evaluations. Since there are a large number of local extremes, the optimization method has to find the global extreme accurately. The present paper introduces a new population-based hybrid algorithm called Genetic-Based Bees Algorithm (GBBA). This algorithm is meant to design the optimal shape for MW wind turbine blades. The current method employs crossover and neighborhood searching operators taken from the respective Genetic Algorithm (GA) and Bees Algorithm (BA) to provide a method with good performance in accuracy and speed convergence. Different blade designs, twenty-one to be exact, were considered based on the chord length, twist angle and tip speed ratio using GA results. They were compared with BA and GBBA optimum design results targeting the power coefficient and solidity. The results suggest that the final shape, obtained by the proposed hybrid algorithm, performs better compared to either BA or GA. Furthermore, the accuracy and speed convergence increases when the GBBA is employed

Keywords: Blade Design, Optimization, Genetic Algorithm, Bees Algorithm, Genetic-Based Bees Algorithm, Large Wind Turbine

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Authors: Kayode Oshinubi, Brice Kammegne, Jacques Demongeot

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The use of mathematical tools like Partial Differential Equations and Ordinary Differential Equations have become very important to predict the evolution of a viral disease in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China causing a severe and potentially fatal respiratory syndrome, i.e., COVID-19. Since then, it has become a pandemic declared by World Health Organization (WHO) on March 11, 2020 which has spread around the globe. A reaction-diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process in which different substances are transformed, and a diffusion process that causes a distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined using the Lyapunov function are considered and the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. Also, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We showed the spatial distribution of the model compartments when the basic reproduction rate $\mathcal{R}_0 < 1$ and $\mathcal{R}_0 > 1$ and sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations. We investigate the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. To the public health policymakers, we offered a better understanding of the COVID-19 management.

Keywords: COVID-19, SEIRV epidemic model, reaction-diffusion equation, basic reproduction number, vaccination, spatial distribution

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Authors: Mahbub C. Mishu, Venktesh N. Dubey, Tamas Hickish, Jonathan Cole

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Pressure ulcer is a common problem for today's healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body,blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

Keywords: pressure ulcer, viscoelastic material, mathematical model, experimental validation

Procedia PDF Downloads 314

Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

Abstract:

The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Khaled R. Khater

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This paper fits in soil-structure interaction division. Its theme is soil retaining structures. Hence, the cantilever secant-pile wall imposed itself, focusing on the capping beam. Four research questions are prompted and beg an answer. How to calculate the forces that control capping beam design? What is the statical system of ‘capping beam-secant pile’ as one unit? Is it possible to design it to satisfy pre-specific lateral deformation? Is it possible to suggest permissible lateral deformation limits? Briefly, pile head displacements induced by Plaxis-2D are converted to forces needed for STAAD-Pro 3D models. Those models are constructed based on the proposed structural system. This is the paper’s idea and methodology. Parametric study performed considered three sand densities, one pile rigidity, and two excavation depths, i.e., 3.0 m and 5.0 m. The research questions are satisfactorily answered. This paper could be a first step towards standardizing analysis, design, and lateral deformations checks.

Keywords: capping beam, secant pile, numerical, design aids, sandy soil

Procedia PDF Downloads 117

Authors: Sara A. Pakvis, Giulia Scalet, Stefania Marconi, Ferdinando Auricchio, Matthijs Langelaar

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In recent developments in the field of multi-material additive manufacturing, differences in material properties are exploited to create printed shape-memory structures, which are referred to as 4D-printed structures. New printing techniques allow for the deliberate introduction of prestresses in the specimen during manufacturing, and, in combination with the right design, this enables new functionalities. This research focuses on bi-polymer 4D-printed structures, where the transformation process is based on a heat-induced glass transition in one material lowering its Young’s modulus, combined with an initial prestress in the other material. Upon the decrease in stiffness, the prestress is released, which results in the realization of an essentially pre-programmed deformation. As the design of such functional multi-material structures is crucial but far from trivial, a systematic methodology to find the design of 4D-printed structures is developed, where a finite element model is combined with a density-based topology optimization method to describe the material layout. This modeling approach is verified by a convergence analysis and validated by comparing its numerical results to analytical and published data. Specific aspects that are addressed include the interplay between the definition of the prestress and the material interpolation function used in the density-based topology description, the inclusion of a temperature-dependent stiffness relationship to simulate the glass transition effect, and the importance of the consideration of geometric nonlinearity in the finite element modeling. The efficacy of topology optimization to design 4D-printed structures is explored by applying the methodology to a variety of design problems, both in 2D and 3D settings. Bi-layer designs composed of thermoplastic polymers are printed by means of the fused deposition modeling (FDM) technology. Acrylonitrile butadiene styrene (ABS) polymer undergoes the glass transition transformation, while polyurethane (TPU) polymer is prestressed by means of the 3D-printing process itself. Tests inducing shape transformation in the printed samples through heating are performed to calibrate the prestress and validate the modeling approach by comparing the numerical results to the experimental findings. Using the experimentally obtained prestress values, more complex designs have been generated through topology optimization, and samples have been printed and tested to evaluate their performance. This study demonstrates that by combining topology optimization and 4D-printing concepts, stimuli-responsive structures with specific properties can be designed and realized.

Keywords: 4D-printing, glass transition, shape memory polymer, topology optimization

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Authors: Paras Ram, Vikas Kumar

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The transmission of Malaria with seasonal were studied through the use of mathematical models. The data from the annual number of Malaria cases reported to the Division of Epidemiology, Ministry of Public Health, Thailand during the period 1997-2011 were analyzed. The transmission of Malaria with seasonal was studied by formulating a mathematical model which had been modified to describe different situations encountered in the transmission of Malaria. In our model, the population was separated into two groups: the human and vector groups, and then constructed a system of nonlinear differential equations. Each human group was divided into susceptible, infectious in hot season, infectious in rainy season, infectious in cool season and recovered classes. The vector population was separated into two classes only: susceptible and infectious vectors. The analysis of the models was given by the standard dynamical modeling.

Keywords: ferrofluid, magnetic field, porous medium, rotating disk, Neuringer-Rosensweig Model

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Authors: Jamal Hussain Al-Smail

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Hydrogen fuel cells (HFCs) are environmentally friendly, energy converter devices that convert the chemical energy of the reactants (oxygen and hydrogen) to electricity through electrochemical reactions. The level of the electricity production of HFCs mainly increases depending on the oxygen distribution in the HFC’s cathode gas diffusion layer (GDL). With a constant porosity of the GDL, the electrochemical reaction can have a great variation that reduces the cell’s productivity and stability. Our findings bring a methodology in finding porosity designs of the diffusion layer to improve the oxygen distribution such that it results in a stable oxygen-hydrogen reaction. We first introduce a mathematical model involving the mass and momentum transport equations, in which a porosity function of the GDL is incorporated as a control for the fluid flow. We then derive numerical methods for solving the mathematical model. In conclusion, we present our numerical results to show how to design the GDL porosity to result in a uniform oxygen distribution.

Keywords: fuel cells, material porosity design, mathematical modeling, porous media

Procedia PDF Downloads 157

Authors: Yang Zheng, Wei Sun

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This paper describes a new approach which can be used to interpret the experimental creep deformation data obtained from miniaturized thin plate bending specimen test to the corresponding uniaxial data based on an inversed application of the reference stress method. The geometry of the thin plate is fully defined by the span of the support, l, the width, b, and the thickness, d. Firstly, analytical solutions for the steady-state, load-line creep deformation rate of the thin plates for a Norton’s power law under plane stress (b → 0) and plane strain (b → ∞) conditions were obtained, from which it can be seen that the load-line deformation rate of the thin plate under plane-stress conditions is much higher than that under the plane-strain conditions. Since analytical solution is not available for the plates with random b-values, finite element (FE) analyses are used to obtain the solutions. Based on the FE results obtained for various b/l ratios and creep exponent, n, as well as the analytical solutions under plane stress and plane strain conditions, an approximate, numerical solutions for the deformation rate are obtained by curve fitting. Using these solutions, a reference stress method is utilised to establish the conversion relationships between the applied load and the equivalent uniaxial stress and between the creep deformations of thin plate and the equivalent uniaxial creep strains. Finally, the accuracy of the empirical solution was assessed by using a set of “theoretical” experimental data.

Keywords: bending, creep, thin plate, materials engineering

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Authors: Vineetha Bettaiah, Heggere S. Ranganath

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This paper presents a Hierarchical Piecewise Linear Approximation (HPLA) for the representation of time series data in which the time series is treated as a curve in the time-amplitude image space. The curve is partitioned into segments by choosing perceptually important points as break points. Each segment between adjacent break points is recursively partitioned into two segments at the best point or midpoint until the error between the approximating line and the original curve becomes less than a pre-specified threshold. The HPLA representation achieves dimensionality reduction while preserving prominent local features and general shape of time series. The representation permits course-fine processing at different levels of details, allows flexible definition of similarity based on mathematical measures or general time series shape, and supports time series data mining operations including query by content, clustering and classification based on whole or subsequence similarity.

Keywords: data mining, dimensionality reduction, piecewise linear representation, time series representation

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Authors: Abdurrahim Bolukbasi, Hassan Athari, Dogan Ciloglu

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The modeling lung respiratory system which has complex anatomy and biophysics presents several challenges including tissue-driven flow patterns and wall motion. Also, the lung pulmonary system because of that they stretch and recoil with each breath, has not static walls and structures. The direct relationship between air flow and tissue motion in the lung structures naturally prefers an FSI simulation technique. Therefore, in order to toward the realistic simulation of pulmonary breathing mechanics the development of a coupled FSI computational model is an important step. A simple but physiologically-relevant three dimensional deep long geometry is designed and fluid-structure interaction (FSI) coupling technique is utilized for simulating the deformation of the lung parenchyma tissue which produces airflow fields. The real understanding of respiratory tissue system as a complex phenomenon have been investigated with respect to respiratory patterns, fluid dynamics and tissue visco-elasticity and tidal breathing period.

Keywords: lung deformation and mechanics; Tissue mechanics; Viscoelasticity; Fluid-structure interactions; ANSYS

Procedia PDF Downloads 329

Authors: Lyudmila L. Gracheva

Abstract:

Thermal shield is a multi-layer structure that consists of layers made of different materials. The use of composite materials (CM) reinforced with carbon fibers in rocket technologies (shells, bearings, wings, fairings, inter-step compartments, etc.) is due to a possibility of reducing the weight while increasing a structural strength. Structures made of a unidirectional carbon fiber reinforced plastic based on an epoxy resin are used as load-bearing skins for aircraft fairings. The results of an experimental study of the physical and mechanical properties of epoxy carbon fiber reinforced plastics depending on temperature for different storage times of products are presented. With an increasing temperature, the physical and mechanical properties of CM are determined by the thermal and deformation properties of the components and the geometry of their distribution. Samples for the study were cut from natural skins of the head fairings.

Keywords: composite material, thermal deformation, carbon fiber, heat shield, epoxy resin, thermal expansion

Procedia PDF Downloads 60

Authors: Sharifullah Ahmed

Abstract:

Shallow foundation on soft soils without ground improvement can represent a high level of settlement. In such a case, an alternative to pile foundations may be shallow strip footings placed on a soil system in which the upper layer is untreated or cement-treated compacted sand to limit the settlement within a permissible level. This research work deals with a rigid plane-strain strip footing of 2.5m width placed on a soil consisting of untreated or cement treated sand layer underlain by homogeneous soft clay. Both the thin and thick compared the footing width was considered. The soft inorganic cohesive NC clay layer is considered undrained for plastic loading stages and drained in consolidation stages, and the sand layer is drained in all loading stages. FEM analysis was done using PLAXIS 2D Version 8.0 with a model consisting of clay deposits of 15m thickness and 18m width. The soft clay layer was modeled using the Hardening Soil Model, Soft Soil Model, Soft Soil Creep model, and the upper improvement layer was modeled using only the Hardening Soil Model. The system is considered fully saturated. The value of natural void ratio 1.2 is used. Total displacement fields of strip footing and subsoil layers in the case of Untreated and Cement treated Sand as Upper layer are presented. For Hi/B =0.6 or above, the distribution of major deformation within an upper layer and the influence zone of footing is limited in an upper layer which indicates the complete effectiveness of the upper layer in bearing the foundation effectively in case of the untreated upper layer. For Hi/B =0.3 or above, the distribution of major deformation occurred within an upper layer, and the function of footing is limited in the upper layer. This indicates the complete effectiveness of the cement-treated upper layer. Brittle behavior of cemented sand and fracture or cracks is not considered in this analysis.

Keywords: displacement, ground improvement, influence depth, PLAXIS 2D, primary and secondary settlement, sand mat, soft clay

Procedia PDF Downloads 97