Journal articles: 'Discrete ply model'

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Serra, Joël, Christophe Bouvet, Bruno Castanié, and Caroline Petiot. "Scaling effect in notched composites: The Discrete Ply Model approach." Composite Structures 148 (July 2016): 127–43. http://dx.doi.org/10.1016/j.compstruct.2016.03.062.

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Adam, Louis, Christophe Bouvet, Bruno Castanié, Alain Daidié, and Elodie Bonhomme. "Discrete ply model of circular pull-through test of fasteners in laminates." Composite Structures 94, no. 10 (October 2012): 3082–91. http://dx.doi.org/10.1016/j.compstruct.2012.05.008.

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Chen, Hailong, and Yongming Liu. "Deformation and failure analyses of cross-ply laminates using a nonlocal discrete model." Composite Structures 152 (September 2016): 1007–13. http://dx.doi.org/10.1016/j.compstruct.2016.06.054.

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Cui, Xiaodong, Eugene Fang, and Jim Lua. "A discrete crack network toolkit for Abaqus for damage and residual strength prediction of laminated composites." Journal of Composite Materials 51, no. 10 (July 18, 2016): 1355–78. http://dx.doi.org/10.1177/0021998316659914.

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The main objective of this article is to exploit a phantom paired element based discrete crack network toolkit for predicting the damage progression and residual strength of laminated composites without and with a hole under tension and compression. Both intra-ply matrix cracking and inter-ply delamination are considered under a co-simulation framework in the discrete crack network toolkit. A mesh-independent kinematic description of discrete matrix cracks is accomplished via user-defined phantom paired solid elements to capture the initiation and evolution of fiber orientation dependent matrix cracking. In-ply matrix crack initiation is realized by inserting a crack along the fiber direction when a matrix driven failure criterion is satisfied and a cohesive injection along the matrix crack interface is applied to account for energy dissipation during matrix crack opening. The delamination failure mode is characterized by applying Abaqus’ cohesive interaction at ply interfaces. The non-linear shear behavior is introduced by employing a power law based curve-fit model and the fiber failure is described using a continuum damage mechanics based model. Both the blind and recalibrated predictions are performed for specimens of three different layups under the Air Force Tech Scout 1 program. The predicted damage progression and the load displacement curves are compared with the testing results provided by the Air Force Research Laboratory.

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Mahmud, Jamaluddin, Wahyu Kuntjoro, and Aidah Jumahat. "Failure Analysis of Fiber Reinforced Composite Materials Used in Malaysian Industries." Scientific Research Journal 4, no. 2 (December 31, 2007): 41. http://dx.doi.org/10.24191/srj.v4i2.5658.

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The main objective of this paper is to determine the curves bounding the actual load carrying capacity in terms of the First Ply Failure and the Last Ply Failure of composite materials used in Malaysian Industries. A mathematical model and computational model are presented for the analysis. Higher Order Shear Deformation plate theory is employed to predict the deformation of the plate. The selected material properties through thickness is used and accommodated by a discrete layer approach. A program based on finite element method is developed using Fortran-90 to determine the lamina stresses. These stresses are then used in the present failure model to determine the First Ply Failure and Last Ply Failure, by progressively reducing the stiffness of the laminas. Finally, the First Ply Failure and Last Ply failure results are analysed, in terms of lower and upper bound within which the true load carrying capacity lies.

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Mahmud, Jamaluddin, Wahyu Kuntjoro, and Aidah Jumahat. "Failure Analysis of Fiber Reinforced Composite Materials Used in Malaysian Industries." Scientific Research Journal 4, no. 2 (December 31, 2007): 41. http://dx.doi.org/10.24191/srj.v4i2.9343.

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The main objective of this paper is to determine the curves bounding the actual load carrying capacity in terms of the First Ply Failure and the Last Ply Failure of composite materials used in Malaysian Industries. A mathematical model and computational model are presented for the analysis. Higher Order Shear Deformation plate theory is employed to predict the deformation of the plate. The selected material properties through thickness is used and accommodated by a discrete layer approach. A program based on finite element method is developed using Fortran-90 to determine the lamina stresses. These stresses are then used in the present failure model to determine the First Ply Failure and Last Ply Failure, by progressively reducing the stiffness of the laminas. Finally, the First Ply Failure and Last Ply failure results are analysed, in terms of lower and upper bound within which the true load carrying capacity lies.

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Serra, J., A. Trellu, C. Bouvet, S. Rivallant, B. Castanié, and L. Ratsifandrihana. "Combined loadings after medium velocity impact on large CFRP laminated plates: Discrete ply model simulations." Composites Part C: Open Access 6 (October 2021): 100203. http://dx.doi.org/10.1016/j.jcomc.2021.100203.

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McCartney, L. N. "Physically based damage models for laminated composites." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 217, no. 3 (July 1, 2003): 163–99. http://dx.doi.org/10.1177/146442070321700301.

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The computing power that is available for engineering calculation continues to grow at a dramatic pace. Engineers in industry want to have seamless models that can be used to design across the scale range from atoms to structures, including simulation of the manufacturing process. A limited aspect of this wish is the requirement to deal effectively with the progressive growth of microstructural damage in composites and its effect on both property degradation and the catastrophic failure event. This paper reviews progress that is being made at the National Physical Laboratory (NPL) with the development and validation of physically based damage growth models for laminated composites. The review includes: (a) prediction of undamaged ply properties determined from the properties of the fibre and the matrix, with emphasis on comparison of analytical models with each other, and with finite and boundary element solutions; (b) discussion of various stress transfer models, and their validation, that have been developed for application to the prediction of the properties of composite laminates having ply crack damage; (c) prediction of ply cracking in multiple-ply cross-ply laminates subject to triaxial loading (without shear) and bending; (d) prediction of ply cracking in general symmetric laminates subject to combined triaxial loading and in-plane shear loading; (e) consideration in a damage mechanics context of progressive ply crack formation in general symmetric laminates subject to thermal residual stresses and general in-plane loading, where an important new methodology is described that results from attempting to develop a continuum damage model from a physically based discrete ply cracking model based on energy concepts; (f) discussion of how the models might be integrated into finite element analysis (FEA) systems to enable strain softening in structures to be adequately modelled. The paper also includes statements concerning the status of the various models in relation to alternative approaches, and to model validation.

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Wang, Yanfeng, and Qi Wu. "A Microscale Analysis of Thermal Residual Stresses in Composites with Different Ply Orientations." Materials 16, no. 19 (October 6, 2023): 6567. http://dx.doi.org/10.3390/ma16196567.

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Composites, such as fiber-reinforced plastics, are produced using layering prepregs with varying ply orientations to achieve enhanced mechanical properties. However, this results in intricate residual stresses, which are influenced by the forming process and ply orientation. In this study, three representative microscopic models—featuring discrete fiber and resin—represent unidirectional, cross-ply, and angle-ply laminates. These models underwent simulations under three different cooling histories using the finite element method. The findings suggest that ply orientation does not significantly influence temperature distribution. However, it significantly impacts the von Mises stress in the fiber closest to the interface between two stacked laminae. This differs from the inter-laminar stresses determined with the macroscopic lamination model. Apart from the free edge, which exhibits a complex stress distribution, the von Mises stress within a unit cell displays a recurring pattern. The magnitude of the von Mises stress decreases as the ply orientation angle increases and shifts when a temperature gradient is present throughout the composite’s thickness. This study provides valuable insights into the mechanics of residual stresses at the microscopic level and highlights potential defect areas influenced by these stresses.

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Jäger, Sebastian, Anthony Pickett, and Peter Middendorf. "A Discrete Model for Simulation of Composites Plate Impact Including Coupled Intra- and Inter-ply Failure." Applied Composite Materials 23, no. 2 (July 21, 2015): 179–95. http://dx.doi.org/10.1007/s10443-015-9455-2.

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Žmindák, Milan, Michal Kaco, Pavol Novák, Leszek Radziszewski, and Josef Soukup. "Determination of the laminate strains using discrete damage mechanics." MATEC Web of Conferences 254 (2019): 06005. http://dx.doi.org/10.1051/matecconf/201925406005.

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In this paper discrete damage mechanics (DDM) is used to predict inter-laminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the laminate. The finite element method (FEM) is one of the most widely and most popular numerical methods for analyzing composite structures, therefore ANSYS commercial software is used for analysis of layered plate composite structure reinforced with long unidirectional fibers with Carbon/Epoxy material. Because ANSYS does not have a built-in capability for calculating crack density, we have to use plugin. A methodology for determination of the fracture toughness is based on fitting DDM model and these data are obtained from literature. Also, prediction of modulus vs. applied strain is contrasted with ply discount results and the effect of in situ correction of strength is highlighted. Evaluation of matrix cracking detected in lamina has been solved using return mapping algorithm.

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McGinty, R. D., T. B. Rhyne, and S. M. Cron. "Analytical Solution for the Stresses Arising in +/− Angle Ply Belts of Radial Tires." Tire Science and Technology 36, no. 4 (December 1, 2008): 244–74. http://dx.doi.org/10.2346/1.2999704.

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Abstract Stresses arising in the belts of radial ply tires, particularly those at the belt edge, are known to be critical to tire durability. Belt edge stresses are commonly calculated using finite element (FE) methods that provide estimates of the levels but do not necessarily give significant insight into the underlying mechanics. In contrast, analytical models can provide physical insight into the mechanisms affecting tire durability but are currently incomplete due to the challenges faced in obtaining closed-form mathematical solutions. Nevertheless, analytical solutions remain important to tire design and development because they can expose the entire design space, show the mathematical relationships between the variables, and allow rapid parameter studies. This work develops an analytical description of the belt deformations and stresses, particularly at the belt edge. The formulation captures all the first-order mechanics pertinent to finite width, antisymmetric +/− angle belt packages present in radial tires. It incorporates interply shear stresses already recognized in the literature and adds to that a new mechanism controlling the interaction of the plies via a Poisson effect. The analytical model is validated by comparison to FE simulations and is also contrasted with a classical analytical model in the literature. The design space for the belt composite is then explored by parameter variation. Finally, since all these solutions depend on homogenization of the belt layers, the analytical solution is compared to a FE model of discrete cables embedded in rubber to explore the accuracy of the homogenization step.

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Guzman Maldonado, Eduardo, Nahiene Hamila, Philippe Boisse, and Philippe Chaudet. "Thermoforming Simulation of Multilayer Composites with Continuous Fibre and Thermoplastic Matrix." Key Engineering Materials 611-612 (May 2014): 368–74. http://dx.doi.org/10.4028/www.scientific.net/kem.611-612.368.

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CFRTP prepreg laminates thermoforming (Continuous Fibre Reinforcements and Thermoplastic Resin) is a fast composite manufacturing process. Furthermore the thermoplastic matrix is favourable to recycling. The development of a thermoforming process is complex and expensive to achieve by trial/error. A simulation approach for thermoforming of multilayer thermoplastic is presented. Each prepreg layer is modelled by semi-discrete shell elements. These elements consider the tension, in-plane shear and bending behaviour of the ply at different temperatures around the fusion point. The contact/friction during the forming process is taken into account using forward increment Lagrange multipliers. A lubricated friction model is implemented between the layers and for ply/tool friction. Thermal and forming simulations are presented and compared to experimental results. The computed shear angles after forming and wrinkles are in good agreement with the thermoforming experiment.

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Hoos, Kevin, Endel V. Iarve, Michael Braginsky, Eric Zhou, and David H. Mollenhauer. "Static strength prediction in laminated composites by using discrete damage modeling." Journal of Composite Materials 51, no. 10 (June 2, 2016): 1473–92. http://dx.doi.org/10.1177/0021998316651986.

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Discrete Damage Modeling of complex local failure patterns in laminated composites including matrix cracking, delamination, and fiber failure was performed. Discrete Damage Modeling uses the Regularized eXtended Finite Element Method for the simulation of matrix cracking at initially unknown locations and directions independent of the mesh orientation. Cohesive interface model is used both for Mesh Independent Cracking as well as delamination propagation. The fiber failure mode is modeled by two different methods in tension and compression. Tensile failure is predicted by Critical Failure Volume criterion, which takes into account volumetric scaling of tensile strength. Compression fiber failure is simulated with a single parameter continuum damage mechanics model with non-compressibility condition in the failed region. Ply level characterization input data were used for prediction of notched and unnotched laminate strength. All input data required for model application is directly measured by ASTM tests except tensile fiber scaling parameter and compression fiber failure fracture toughness, which were taken from literature sources. The model contains no internal calibration parameters. Tensile and compressive strength of unnotched and open hole composite laminates IM7/977-3 has been predicted and compared with experimental data. Three different layups, [0/45/90/−45]2S, [30/60/90/−60/−30]2S, and the [60/0/−60]3S, were modeled and tested and showed good agreement with experiment in the case of tensile loading, whereas the compressive strength was generally under predicted for unnotched laminates and overpredicted for open hole laminates.

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Stamatelos, Dimitrios G., and George N. Labeas. "Buckling Analysis of Laminated Stiffened Plates with Material Anisotropy Using the Rayleigh–Ritz Approach." Computation 11, no. 6 (May 30, 2023): 110. http://dx.doi.org/10.3390/computation11060110.

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An energy-based solution for calculating the buckling loads of partially anisotropic stiffened plates is presented, such as antisymmetric cross-ply and angle-ply laminations. A discrete approach, for the mathematical modelling and formulations of the stiffened plates, is followed. The developed formulations extend the Rayleigh–Ritz method and explore the available anisotropic unstiffened plate buckling solutions to the interesting cases of stiffened plates with some degree of material anisotropy. The examined cases consider simply supported unstiffened and stiffened plates under uniform and linearly varying compressive loading. Additionally, a reference finite element (FE) model is developed to compare the calculated buckling loads and validate the modelling approach for its accuracy. The results of the developed method are also compared with the respective experimental results for the cases where they were available in the literature. Finally, an extended discussion regarding the assumptions and restrictions of the applied Rayleigh–Ritz method is made, so that the limitations of the developed method are identified and documented.

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Žmindák, Milan, Eva Kormaníková, Pavol Novák, Josef Soukup, and Kamila Kotrasová. "Application of discrete damage mechanics for determination of the crack density in composite laminates." MATEC Web of Conferences 310 (2020): 00002. http://dx.doi.org/10.1051/matecconf/202031000002.

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The finite element method (FEM) is one of the most widely and most popular numerical methods for analyzing damage of composite structures, In this paper discrete damage mechanics (DDM) is used to predict inter-laminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the laminate. ANSYS commercial software is used for analysis of layered plate composite structure reinforced with long unidirectional fibers with Carbon/Epoxy material. Because ANSYS does not have a built-in capability for calculating crack density, we have to use plagin. A methodology for determination of the fracture toughness is based on fitting DDM model and these data are obtained from literature. Also, prediction of modulus vs. applied strain is contrasted with ply discount results and the effect of in situ correction of strength is highlighted. Evaluation of matrix cracking detected in lamina has been solved using return mapping algorithm.

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Jin, P., Y. Wang, X. Zhong, J. Yang, and Z. Sun. "Blending design of composite laminated structure with panel permutation sequence." Aeronautical Journal 122, no. 1248 (January 4, 2018): 333–47. http://dx.doi.org/10.1017/aer.2017.132.

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ABSTRACTPreviously, the concept of Ply Drop Sequence (PDS) is introduced by the authors for the designing of composite laminated structures with multiple regions. Compared to deleting a contiguous innermost/outermost plies in the classical guide-based blending, using PDS is more flexible than dropping plies between adjacent regions. In this article, a new blending model called the Permutation for Panel Sequence (PPS) blending model is proposed to correct the problem of repeated searching of discrete points in the design space for the previous PDS blending model. The proposed method is also applied to an 18-panel horseshoe benchmark problem. The results demonstrate that the useful searching points in the PPS method are less than those in the PDS method when the number of the panels is less than the number of plies in the guide laminate, and the PPS method obtains a faster convergence speed compared with the PDS method.

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Zhang, X., F. Bianchi, and H. Liu. "Predicting low-velocity impact damage in composites by a quasi-static load model with cohesive interface elements." Aeronautical Journal 116, no. 1186 (December 2012): 1367–81. http://dx.doi.org/10.1017/s0001924000007685.

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AbstractA numerical model is developed for predicting low-velocity impact damage in laminated composites. Stacked shell elements are employed to model laminate plies with discrete interface elements in pre-determined zones to model the onset and propagation of matrix cracks and delamination. These interface elements are governed by a bi-linear cohesive failure law. Cohesive element zone size is determined by a separate finite element analysis using solid elements to identify the stress concentration sites. In order to save the computational effort, low-velocity impact load is modelled by quasi-static loading. Influence of contact force induced friction on shear driven mode II delamination is modelled by a friction model. For a clustered cross-ply laminate, calculated impact force and damage area are in good agreement with the test results. It is shown that matrix cracks should be included in the model in order to simulate delamination in adjacent interface. The practical outcome of this research is a validated modelling approach that can be further improved for predicting low-velocity impact damage in other stacking sequences.

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An, Haichao, Shenyan Chen, Yanjie Liu, and Hai Huang. "Optimal design of the stacking sequences of a corrugated central cylinder in a satellite." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 233, no. 2 (September 29, 2016): 239–53. http://dx.doi.org/10.1177/1464420716672097.

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This Case Study is to describe an application of a two-level approximation method in optimally determining the stacking sequences of a practical corrugated central cylinder. Being housed in the center of a practical satellite, this cylinder can support many of the structural components and functional devices in the satellite. For the purpose of reducing its mass meanwhile maintaining good mechanical properties, the stacking sequences of this cylinder are to be optimally designed under given constraints in this paper. To address this problem, an optimization model was first established by minimizing the structural mass based on initial lay-ups. With the given lay-ups for multi-parts of this cylinder, the existence of each ply was to be determined in terms of discrete variables. Meanwhile, the ply thicknesses were also treated as continuous variables. The two-level approximation method combined with a genetic algorithm previously proposed by the authors was adopted as the optimization method. According to the practical engineering considerations, multiple optimizations were conducted by starting from different initial lay-ups to search more possible optimization designs. After optimization, it was found that compared with the empirical designs, the mass of the main cylinder could be significantly decreased by obtaining some reasonable stacking sequences.

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Kant, Tarun, Sandeep S. Pendhari, and Yogesh M. Desai. "A Novel Finite-Element– Numerical-Integration Model for Composite Laminates Supported on Opposite Edges." Journal of Applied Mechanics 74, no. 6 (January 3, 2007): 1114–24. http://dx.doi.org/10.1115/1.2722770.

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An attempt is made here to devise a new methodology for an integrated stress analysis of laminated composite plates wherein both in-plane and transverse stresses are evaluated simultaneously. The method is based on the governing three-dimensional (3D) partial differential equations (PDEs) of elasticity. A systematic procedure is developed for a case when one of the two in-plane dimensions of the laminate is considered infinitely long (y direction) with no changes in loading and boundary conditions in that direction. The laminate could then be considered in a two-dimensional (2D) state of plane strain in x-z plane. It is here that the governing 2D PDEs are transformed into a coupled system of first-order ordinary differential equations (ODEs) in transverse z direction by introducing partial discretization in the finite inplane direction x. The mathematical model thus reduces to solution of a boundary value problem (BVP) in the transverse z direction in ODEs. This BVP is then transformed into a set of initial value problems (IVPs) so as to use the available efficient and effective numerical integrators for them. Through thickness displacement and stress fields at the finite element discrete nodes are observed to be in excellent agreement with the elasticity solution. A few new results for cross-ply laminates under clamped support conditions are also presented for future reference and also to show the generality of the formulation.

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Ma, Jingmin, Jianfeng Xu, Longfei Li, Xingguang Liu, and Ming Gao. "Analysis of Cutting Stability of a Composite Variable-Section Boring Bar with a Large Length-to-Diameter Ratio Considering Internal Damping." Materials 15, no. 15 (August 8, 2022): 5465. http://dx.doi.org/10.3390/ma15155465.

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Chattering in composite deep-hole boring can directly affect surface processing quality and efficiency and has always been a research hotspot in machining mechanics. In this study, based on Euler–Bernoulli beam theory, the fine control equations for the cutting stability of composite variable-section boring bars were established using the Hamilton principle, in which the sectional change and internal damping of the material were considered. Next, using the Galerkin method and semi-discrete method, the effects of the taper ratio, damping ratio, length-to-diameter ratio, and ply angle on the free vibration characteristics and cutting stability were analyzed in detail. The results show that at a low damping ratio, both the first-order inherent frequency and boring stability can be enhanced with the increase in the taper ratio; at a large damping ratio, increasing the taper ratio can reduce the first-order inherent frequency and boring stability. Finally, the effects of the sectional change on the inherent frequency, displacement response, and convergence were analyzed. A numerical simulation was performed for the model reliability validation. The present research results can provide a theoretical basis and technical guidance for analyzing the cutting stability and fine control of composite variable-section boring bars with large length-to-diameter ratios.

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Carson, Richard T., and Mikołaj Czajkowski. "A new baseline model for estimating willingness to pay from discrete choice models." Journal of Environmental Economics and Management 95 (May 2019): 57–61. http://dx.doi.org/10.1016/j.jeem.2019.03.003.

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Prasuna, P. M., Dr Y. Ramadevi, and Dr A. Vinay Babu. "A two level approach to discretize cosmetic data using Rough set theory." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 14, no. 10 (July 10, 2015): 6147–52. http://dx.doi.org/10.24297/ijct.v14i10.1826.

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Discrete values play a very prominent role in extracting knowledge. Most of the machines learning algorithms use discrete values. It is also observed that the rules discovered through discrete values are shorter and precise. The predictive accuracy is more when discrete values are used. Cosmetic industry extracts the features from the face images of the customers to analyze their facial skin problems. These values are continuous in nature. A predictive model with high accuracy is required to determine the cosmetic problems of the customers and suggest suitable cosmetic. Existing traditional discretization techniques are not sufficient for deriving discretized data from continuous valued cosmetic data as it has to balance the loss of information intrinsic to process adapted and generating a reasonable number of cut points, that is, a reasonable search space. This paper proposes a two level discretization method which is a combination of traditional k means clustering technique and rough set theory to discretize continuous features of cosmetic data.

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Grigutis, Andrius, and Jonas Šiaulys. "Recurrent Sequences Play for Survival Probability of Discrete Time Risk Model." Symmetry 12, no. 12 (December 18, 2020): 2111. http://dx.doi.org/10.3390/sym12122111.

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In this article we investigate a homogeneous discrete time risk model with a generalized premium income rate which can be any natural number. We derive theorems and give numerical examples for finite and ultimate time survival probability calculation for the mentioned model. Our proved statements for ultimate time survival probability calculation, at some level, are similar to the previously known statements for non-homogeneous risk models, where required initial values of survival probability for some recurrent formulas are gathered by certain limit laws. We also give a simplified proof that a ruin is almost unavoidable with a neutral net profit condition and state several conjectures on a certain type of recurrent matrices non-singularity. All the research done can be interpreted as a possibility that symmetric or asymmetric random walk (r.w.) hits (or not) the line u+κt and that possibility is directly related to the expected value of r.w. generating random variable which might be equal, above or bellow κ.

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Antipova, E. S. "A Discrete Dynamic Conflict Model." Proceedings of the Southwest State University. Series: Economics. Sociology. Management 14, no. 1 (April 13, 2024): 283–96. http://dx.doi.org/10.21869/2223-1552-2024-14-1-283-296.

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Relevance. Conflicts play a significant role in the development of society, the state and all of humanity. They arise in interpersonal relationships, economics, organizational activities, social problems, and world politics. The study of the essence of conflicts, the causes of their emergence and ways to resolve them is carried out by conflictology, which was formed as an interdisciplinary field of knowledge in the middle of the 20th century. Currently, it has become obvious that the conflict itself is not a negative phenomenon, but a competently resolved conflict situation can benefit all parties to the conflict. As a result, it became necessary to consider conflicts not only from a descriptive, philosophical point of view, but also to be able to predict a possible conflict situation, describe its development over time and calculate acceptable ways out of it. This approach to the study of conflicts is mathematical modeling, based on mathematical methods for describing conflict situations, which allow analyzing conflicts and predicting their outcome.The purpose is to describe a general methodology for constructing a conflict scheme of any origin within the framework of the mathematical theory of conflicts. The objectives is to consider and analyze a discrete dynamic model of conflicts using the example of a childparent conflict.Methodology. The work uses algebraic methods and methods of discrete mathematics.Results. Within the framework of the mathematical theory of conflicts, a conflict with a discrete mismatch is considered the example of a child-parent model conflict. A general method for constructing a conflict situation diagram and analyzing it has been developed. Possible ways of influencing the conflicting parties on each other in any conflict situation are discussed. When analyzing possible scenarios for the development of a conflict situation, the possible types of impacts of the conflicting parties on each other are considered.Conclusions. Based on the developed dynamic discrete model, it is shown that the mathematical description of conflicts is reduced to the problem of combinatorial optimization. The developed scheme of mathematical description of conflicts can be applied to a wide class of conflict situations in various subject areas.

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Zhao, Liang, Bin Qin, and Fengde Chen. "Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls." Discrete Dynamics in Nature and Society 2020 (January 13, 2020): 1–17. http://dx.doi.org/10.1155/2020/7023075.

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A discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the extinction of the system are obtained. Our results extend and supplement some known results and show that the feedback controls and toxic substances play a crucial role on the permanence and extinction of the system.

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Kulikov, G. M. "Computational Models for Multilayered Composite Shells with Application to Tires." Tire Science and Technology 24, no. 1 (January 1, 1996): 11–38. http://dx.doi.org/10.2346/1.2137509.

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Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

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Kuzmin, E. V., and V. A. Sokolov. "On Construction and Verification of PLC-Programs." Modeling and Analysis of Information Systems 19, no. 4 (February 28, 2015): 25–36. http://dx.doi.org/10.18255/1818-1015-2012-4-25-36.

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We review some methods and approaches to programming discrete problems for Programmable Logic Controllers on the example of constructing PLC-programs for controling a code lock. For these approaches we evaluate the usability of the model checking method for the analysis of program correctness with respect to the automatic verification tool Cadence SMV. Some possible PLC-program vulnerabilities arising at a number approaches to programming of PLC are revealed.

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GORDON, MIRTA B., JEAN-PIERRE NADAL, DENIS PHAN, and VIKTORIYA SEMESHENKO. "DISCRETE CHOICES UNDER SOCIAL INFLUENCE: GENERIC PROPERTIES." Mathematical Models and Methods in Applied Sciences 19, supp01 (August 2009): 1441–81. http://dx.doi.org/10.1142/s0218202509003887.

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We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. However, even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non-monotonic. Thus, depending on the price, there are either one or several equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited. We also discuss the links between the model and the random field Ising model studied in the physics literature.

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Alberini, Anna. "Testing Willingness-to-Pay Models of Discrete Choice Contingent Valuation Survey Data." Land Economics 71, no. 1 (February 1995): 83. http://dx.doi.org/10.2307/3146760.

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Hess, Stephane, John M. Rose, and David A. Hensher. "Asymmetric preference formation in willingness to pay estimates in discrete choice models." Transportation Research Part E: Logistics and Transportation Review 44, no. 5 (September 2008): 847–63. http://dx.doi.org/10.1016/j.tre.2007.06.002.

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Daly, Andrew, Stephane Hess, and Juan de Dios Ortúzar. "Estimating willingness-to-pay from discrete choice models: Setting the record straight." Transportation Research Part A: Policy and Practice 176 (October 2023): 103828. http://dx.doi.org/10.1016/j.tra.2023.103828.

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BRODÉN, MATS, and PETER TANKOV. "TRACKING ERRORS FROM DISCRETE HEDGING IN EXPONENTIAL LÉVY MODELS." International Journal of Theoretical and Applied Finance 14, no. 06 (September 2011): 803–37. http://dx.doi.org/10.1142/s0219024911006760.

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We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Lévy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice of delta hedging, and show that for discontinuous option pay-offs the latter strategy may suffer from very large discretization errors. For options with discontinuous pay-offs, the convergence rate depends on the underlying Lévy process, and we give an explicit relation between the rate and the Blumenthal-Getoor index of the process.

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Du, Boya, and Fei Deng. "The Method of Network Intrusion Detection Based on Descriptive Statistics Model and Logistic Model." WSEAS TRANSACTIONS ON INFORMATION SCIENCE AND APPLICATIONS 18 (December 31, 2021): 190–94. http://dx.doi.org/10.37394/23209.2021.18.23.

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In order to improve the efficiency of network intrusion detection, we want to find simpler models and detection rules, so we research the network intrusion detection with the descriptive statistics model and Logistic model. We pay attention to the features law about discrete distribution and concentrated distribution, and answer the question, which is better of relative optimal results between the descriptive statistics model and Logistic model. Firstly, for finding the features law about discrete distribution and concentrated distribution, we analysis the netflows with every feature. In this situation, the satisfactory accuracy can be given. Secondly, considering the redundant information with principal component analysis, the principal components are used as new variables to establish the logistic model. Using confusion matrix and ROC curve, the optimal cutting value and the corresponding accuracy can be obtained. Finally, by the experiments and evaluation with dataset CIC-IDS2017, the descriptive statistics model is the optimal model, which the corresponding accuracy rate is 99.93%.

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Bhandari, Sunil, and Roberto A. Lopez-Anido. "Discrete-Event Simulation Thermal Model for Extrusion-Based Additive Manufacturing of PLA and ABS." Materials 13, no. 21 (November 5, 2020): 4985. http://dx.doi.org/10.3390/ma13214985.

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The material properties of thermoplastic polymer parts manufactured by the extrusion-based additive manufacturing process are highly dependent on the thermal history. Different numerical models have been proposed to simulate the thermal history of a 3D-printed part. However, they are limited due to limited geometric applicability; low accuracy; or high computational demand. Can the time–temperature history of a 3D-printed part be simulated by a computationally less demanding, fast numerical model without losing accuracy? This paper describes the numerical implementation of a simplified discrete-event simulation model that offers accuracy comparable to a finite element model but is faster by two orders of magnitude. Two polymer systems with distinct thermal properties were selected to highlight differences in the simulation of the orthotropic response and the temperature-dependent material properties. The time–temperature histories from the numerical model were compared to the time–temperature histories from a conventional finite element model and were found to match closely. The proposed highly parallel numerical model was approximately 300–500 times faster in simulating thermal history compared to the conventional finite element model. The model would enable designers to compare the effects of several printing parameters for specific 3D-printed parts and select the most suitable parameters for the part.

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Masiero, Lorenzo, Cindy Yoonjoung Heo, and Bing Pan. "Determining guests’ willingness to pay for hotel room attributes with a discrete choice model." International Journal of Hospitality Management 49 (August 2015): 117–24. http://dx.doi.org/10.1016/j.ijhm.2015.06.001.

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Haj Ahmad, Hanan, Dina A. Ramadan, and Ehab M. Almetwally. "Evaluating the Discrete Generalized Rayleigh Distribution: Statistical Inferences and Applications to Real Data Analysis." Mathematics 12, no. 2 (January 5, 2024): 183. http://dx.doi.org/10.3390/math12020183.

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Various discrete lifetime distributions have been observed in real data analysis. Numerous discrete models have been derived from a continuous distribution using the survival discretization method, owing to its simplicity and appealing formulation. This study focuses on the discrete analog of the newly generalized Rayleigh distribution. Both classical and Bayesian statistical inferences are performed to evaluate the efficacy of the new discrete model, particularly in terms of relative bias, mean square error, and coverage probability. Additionally, the study explores different important submodels and limiting behavior for the new discrete distribution. Various statistical functions have been examined, including moments, stress–strength, mean residual lifetime, mean past time, and order statistics. Finally, two real data examples are employed to evaluate the new discrete model. Simulations and numerical analyses play a pivotal role in facilitating statistical estimation and data modeling. The study concludes that the discrete generalized Rayleigh distribution presents a notably appealing alternative to other competing discrete distributions.

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Shan, Yuanchuang, Huisheng Shu, and Haoran Yi. "Pricing Equity-Indexed Annuities under a Stochastic Dividend Model." Mathematics 11, no. 3 (January 25, 2023): 603. http://dx.doi.org/10.3390/math11030603.

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In this paper, we examine the valuations of equity-indexed annuities (EIAs) when their reference stocks distribute stochastic dividends. Due to the fact that stocks typically pay dividends at discrete times after the payment dates are announced, pricing EIAs with dividends is deemed to be practically significant. We directly model the discrete dividend payments using the jump diffusion process with regime switching, and then determine the dynamics of the stock price. The equivalent martingale measure of fair valuation in incomplete markets is determined by employing the Esscher transform. Finally, the pricing formulas of several of the most common EIAs in the market under the stochastic dividend model are obtained. Our model incorporates and extends the present literature on EIAs with accurate and effective valuation methods.

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Chen, Ningyuan, and Ying-Ju Chen. "Duopoly Competition with Network Effects in Discrete Choice Models." Operations Research 69, no. 2 (March 2021): 545–59. http://dx.doi.org/10.1287/opre.2020.2079.

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It has been realized for a long time that network effects play an important role in how market participants compete with each other. Arguably, companies like Facebook and Google are able to gain immense market power by leveraging the network effects of their consumers, despite potential competitors. This paper investigates how the dynamics play out in duopoly competition. We find that when the network effects per unit of consumption are weak, the competitors can co-exist and gain even market shares. As network effects become stronger, it is unstable, and even impossible, for the firms to coexist, and one firm emerges victorious, taking the majority of the market. The study provides a theoretical analysis for commonly observed market phenomena. It may also have implications for antitrust legislation: Special policies need to be created to maintain a competitive market structure for products and services with strong network effects.

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Ali Eshtewy, Neveen, and Lena Scholz. "Model Reduction for Kinetic Models of Biological Systems." Symmetry 12, no. 5 (May 25, 2020): 863. http://dx.doi.org/10.3390/sym12050863.

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High dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to reduce the computational complexity of high-dimensional systems by approximation with lower dimensional systems, while retaining the important information and properties of the full order system. Proper orthogonal decomposition (POD) is a method based on Galerkin projection that can be used for reducing the model order. POD is considered an optimal linear approach since it obtains the minimum squared distance between the original model and its reduced representation. However, POD may represent a restriction for nonlinear systems. By applying the POD method for nonlinear systems, the complexity to solve the nonlinear term still remains that of the full order model. To overcome the complexity for nonlinear terms in the dynamical system, an approach called the discrete empirical interpolation method (DEIM) can be used. In this paper, we discuss model reduction by POD and DEIM to reduce the order of kinetic models of biological systems and illustrate the approaches on some examples. Additional computational costs for setting up the reduced order system pay off for large-scale systems. In general, a reduced model should not be expected to yield good approximations if different initial conditions are used from that used to produce the reduced order model. We used the POD method of a kinetic model with different initial conditions to compute the reduced model. This reduced order model is able to predict the full order model for a variety of different initial conditions.

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Ali, Sajid, Muhammad Shafqat, Ismail Shah, and Sanku Dey. "Bivariate discrete Nadarajah and Haghighi distribution: Properties and different methods of estimation." Filomat 33, no. 17 (2019): 5589–610. http://dx.doi.org/10.2298/fil1917589a.

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The exponential distribution is commonly used to model different phenomena in statistics and reliability engineering. A new extension of exponential distribution known as the Nadarajah and Haghighi [An extension of the exponential distribution, Statistics: A Journal of Theoretical and Applied Statistics 45 (2011) 543-558.] distribution was introduced in the literature to accommodate the inflation of zero in the data. In practice, however, discrete data are easy to collect as compared to continuous data. Discrete bivariate distributions play important roles in modeling bivariate lifetime count data. Thus focusing on the utility of discrete data, this study presents a new bivariate discrete Nadarajah and Haghighi distribution. We discuss some basic properties of the proposed distribution and study seven different methods of estimation for the unknown parameters to assess the performance of the proposed bivariate discrete model. Two data sets are also analyzed to demonstrate how the proposed model may work in practice. Results show that the proposed model is very flexible and performs better than some of the existing models.

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Ito, Daisuke, Tetsushi Ueta, Takuji Kousaka, and Kazuyuki Aihara. "Bifurcation Analysis of the Nagumo–Sato Model and Its Coupled Systems." International Journal of Bifurcation and Chaos 26, no. 03 (March 2016): 1630006. http://dx.doi.org/10.1142/s0218127416300068.

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The Nagumo–Sato model is a simple mathematical expression of a single neuron, and it is categorized as a discrete-time hybrid dynamical system. To compute bifurcation sets in such a discrete-time hybrid dynamical system accurately, conditions for periodic solutions and bifurcations are formulated herewith as a boundary value problem, and Newton’s method is implemented to solve that problem. As the results of the analysis, the following properties are obtained: border-collision bifurcations play a dominant role in dynamical behavior of the model; chaotic regions are distinguished by tangent bifurcations; and multistable attractors are observed in its coupled system. We demonstrate several bifurcation diagrams and corresponding topological properties of periodic solutions.

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Vázquez-Quesada, Adolfo, and Marco Ellero. "GENERIC-compliant simulations of Brownian multi-particle systems: modeling stochastic lubrication." SeMA Journal 79, no. 1 (January 8, 2022): 165–85. http://dx.doi.org/10.1007/s40324-021-00280-z.

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AbstractA stochastic Lagrangian model for simulating the dynamics and rheology of a Brownian multi-particle system interacting with a simple liquid medium is presented. The discrete particle model is formulated within the GENERIC framework for Non-Equilibrium Thermodynamics and therefore it satisfies discretely the First/Second Laws of Thermodynamics and the Fluctuation Dissipation Theorem (FDT). Long-range fluctuating hydrodynamics interactions between suspended particles are described by an explicit solvent model. To this purpose, the Smoothed Dissipative Particle Dynamics method is adopted, which is a GENERIC-compliant Lagrangian meshless discretization of the fluctuating Navier–Stokes equations. In dense multi-particle systems, the average inter-particle distance is typically small compared to the particle size and short-range hydrodynamics interactions play a major role. In order to bypass an explicit—computationally costly—solution for these forces, a lubrication correction is introduced based on semi-analytical expressions for spheres under Stokes flow conditions. We generalize here the lubrication formalism to Brownian conditions, where an additional thermal-lubrication contribution needs to be taken into account in a way that discretely satisfies FDT. The coupled lubrication dynamics is integrated in time using a generalized semi-implicit splitting scheme for stochastic differential equations. The model is finally validated for a single particle diffusion as well as for a Brownian multi-particle system under homogeneous shear flow. Results for the diffusional properties as well as the rheological behavior of the whole suspension are presented and discussed.

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Gori, Luca, Luca Guerrini, and Mauro Sodini. "Hopf Bifurcation in a Cobweb Model with Discrete Time Delays." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/137090.

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We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected) profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.

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Zhang, Chun You, and Wei Yan. "A Discrete Algorithm for Overload Protection Principle." Applied Mechanics and Materials 543-547 (March 2014): 1219–22. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1219.

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Research thermal overload protection not only to protect the motor winding insulation damage due to temperature is too high, also can give full play to the overload capacity of the motor. This paper proposed overload protection model based on heat effects, and deduces the motor internal discrete recursive algorithm of temperature-rise calculation. Based on this algorithm, we constructed the motor internal temperature-rise model, which can calculate temperature-rise of the motor in real-time, and realized the intelligent control of the motor.

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Ndlovu, Bonginkosi Duncan, Sileshi Fanta Melesse, and Temesgen Zewotir. "A nonparametric analysis of discrete time competing risks data: a comparison of the cause-specific-hazards approach and the vertical approach." Statistics in Transition new series 24, no. 3 (June 13, 2023): 61–76. http://dx.doi.org/10.59170/stattrans-2023-036.

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icolaie et al. (2010) have advanced a vertical model as the latest continuous time competing risks model. The main objective of this article is to re-cast this model as a nonparametric model for analysis of discrete time competing risks data. Davis and Lawrance (1989) have advanced a cause-specific-hazard driven method for summarizing discrete time data nonparametrically. The secondary objective of this article is to compare the proposed model to this model. We pay particular attention to the estimates for the cause-specific-hazards and the cumulative incidence functions as well as their respective standard errors.

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Dugstad, Anders, Kristine M. Grimsrud, Gorm Kipperberg, Henrik Lindhjem, and Ståle Navrud. "Scope Elasticity of Willingness to pay in Discrete Choice Experiments." Environmental and Resource Economics 80, no. 1 (August 2, 2021): 21–57. http://dx.doi.org/10.1007/s10640-021-00577-7.

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AbstractSensitivity to scope in nonmarket valuation refers to the property that people are willing to pay more for a higher quality or quantity of a nonmarket public good. Establishing significant scope sensitivity has been an important check of validity and a point of contention for decades in stated preference research, primarily in contingent valuation. Recently, researchers have begun to differentiate between statistical and economic significance. This paper contributes to this line of research by studying the significance of scope effects in discrete choice experiments (DCEs) using the scope elasticity of willingness to pay concept. We first formalize scope elasticity in a DCE context and relate it to economic significance. Next, we review a selection of DCE studies from the environmental valuation literature and derive their implied scope elasticity estimates. We find that scope sensitivity analysis as validity diagnostics is uncommon in the DCE literature and many studies assume unitary elastic scope sensitivity by employing a restrictive functional form in estimation. When more flexible specifications are employed, the tendency is towards inelastic scope sensitivity. Then, we apply the scope elasticity concept to primary DCE data on people’s preferences for expanding the production of renewable energy in Norway. We find that the estimated scope elasticities vary between 0.13 and 0.58, depending on the attribute analyzed, model specification, geographic subsample, and the unit of measurement for a key attribute. While there is no strict and universally applicable benchmark for determining whether scope effects are economically significant, we deem these estimates to be of an adequate and plausible order of magnitude. Implications of the results for future DCE research are provided.

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Tapia, Rodrigo J., Gerard de Jong, Ana M. Larranaga, and Helena B. Bettella Cybis. "Exploring Multiple‐discreteness in Freight Transport. A Multiple Discrete Extreme Value Model Application for Grain Consolidators in Argentina." Networks and Spatial Economics 21, no. 3 (May 25, 2021): 581–608. http://dx.doi.org/10.1007/s11067-021-09531-y.

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AbstractThere are some examples where freight choices may be of a multiple discrete nature, especially the ones at more tactical levels of planning. Nevertheless, this has not been investigated in the literature, although several discrete-continuous models for mode/vehicle type and shipment size choice have been developed in freight transport. In this work, we propose that the decision of port and mode of the grain consolidators in Argentina is of a discrete-continuous nature, where they can choose more than one alternative and how much of their production to send by each mode. The Multiple Discrete Extreme Value Model (MDCEV) framework was applied to a stated preference data set with a response variable that allowed this multiple-discreteness. To our knowledge, this is the only application of the MDCEV in regional freight context. Free alongside ship price, freight transport cost, lead-time and travel time were included in the utility function and observed and random heterogeneity was captured by the interaction with the consolidator’s characteristics and random coefficients. In addition, different discrete choice models were used to compare the forecasting performance, willingness to pay measures and structure of the utility function against.

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Jha, Aditi, Zoe C. Ashwood, and Jonathan W. Pillow. "Active Learning for Discrete Latent Variable Models." Neural Computation 36, no. 3 (February 16, 2024): 437–74. http://dx.doi.org/10.1162/neco_a_01646.

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Abstract Active learning seeks to reduce the amount of data required to fit the parameters of a model, thus forming an important class of techniques in modern machine learning. However, past work on active learning has largely overlooked latent variable models, which play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines. Here we address this gap by proposing a novel framework for maximum-mutual-information input selection for discrete latent variable regression models. We first apply our method to a class of models known as mixtures of linear regressions (MLR). While it is well known that active learning confers no advantage for linear-gaussian regression models, we use Fisher information to show analytically that active learning can nevertheless achieve large gains for mixtures of such models, and we validate this improvement using both simulations and real-world data. We then consider a powerful class of temporally structured latent variable models given by a hidden Markov model (HMM) with generalized linear model (GLM) observations, which has recently been used to identify discrete states from animal decision-making data. We show that our method substantially reduces the amount of data needed to fit GLM-HMMs and outperforms a variety of approximate methods based on variational and amortized inference. Infomax learning for latent variable models thus offers a powerful approach for characterizing temporally structured latent states, with a wide variety of applications in neuroscience and beyond.

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Sillano, Mauricio, and Juan de Dios Ortúzar. "Willingness-to-Pay Estimation with Mixed Logit Models: Some New Evidence." Environment and Planning A: Economy and Space 37, no. 3 (March 2005): 525–50. http://dx.doi.org/10.1068/a36137.

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Mixed-logit models are currently the state of the art in discrete-choice modelling, and their estimation in various forms (in particular, mixing revealed-preference and stated-preference data) is becoming increasingly popular. Although the theory behind these models is fairly simple, the practical problems associated with their estimation with empirical data are still relatively unknown and certainly not solved to everybody's satisfaction. In this paper we use a stated-preference dataset—previously used to derive willingness to pay for reduction in atmospheric pollution and subjective values of time—to estimate random parameter mixed logit models with different estimation methods. We use our results to discuss in some depth the problems associated with the derivation of willingness to pay with this class of models.

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Journal articles on the topic 'Discrete ply model'

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