This paper describes a stochastic homogenization analysis of a particle reinforced composite material using an approximation technique. In order to analyze the influence of a microscopic random variation of an elastic property of a component material on the homogenized elastic property of a particle reinforced composite material, the Monte-Carlo simulation is employed. Since the conventional Monte-Carlo simulation sometimes involves a higher computational cost, an approximate stochastic homogenization method using the Monte-Carlo simulation combined with a polynomial-based approximation technique is employed, and accuracy of the approximate Monte-Carlo simulation is investigated. In order to apply a lower order approximation to the approximate Monte-Carlo simulation effectively, the weighted least square method is proposed, and its effectiveness is discussed with the numerical results.
{"title":"Stochastic Homogenization Analysis of a Particle Reinforced Composite Material using an Approximate Monte-Carlo Simulation with the Weighted Least Square Method","authors":"S. Sakata, F. Ashida, Daiki Iwahashi","doi":"10.1299/JCST.7.1","DOIUrl":"https://doi.org/10.1299/JCST.7.1","url":null,"abstract":"This paper describes a stochastic homogenization analysis of a particle reinforced composite material using an approximation technique. In order to analyze the influence of a microscopic random variation of an elastic property of a component material on the homogenized elastic property of a particle reinforced composite material, the Monte-Carlo simulation is employed. Since the conventional Monte-Carlo simulation sometimes involves a higher computational cost, an approximate stochastic homogenization method using the Monte-Carlo simulation combined with a polynomial-based approximation technique is employed, and accuracy of the approximate Monte-Carlo simulation is investigated. In order to apply a lower order approximation to the approximate Monte-Carlo simulation effectively, the weighted least square method is proposed, and its effectiveness is discussed with the numerical results.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"239 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123872157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The general solutions for a penny-shaped crack in an infinite solid, subjected to arbitrary tractions on the crack surfaces were derived. The applicability was demonstrated deriving the closed-form solutions for a penny-shaped crack subjected to the lower-order loading such as constant tension, shear, bending, and torsion. Furthermore, we consider a circular crack subjected to cubic-order normal stresses. It is shown that the stress intensity factor distribution derived from the general solution exactly agree with the analytical solutions derived by Shah-Kobayashi.
{"title":"On the General Solutions for Mixed-Mode Penny-Shaped Crack and Their Applications","authors":"T. Nishioka, G. Zhou, T. Fujimoto","doi":"10.1299/JCST.2.34","DOIUrl":"https://doi.org/10.1299/JCST.2.34","url":null,"abstract":"The general solutions for a penny-shaped crack in an infinite solid, subjected to arbitrary tractions on the crack surfaces were derived. The applicability was demonstrated deriving the closed-form solutions for a penny-shaped crack subjected to the lower-order loading such as constant tension, shear, bending, and torsion. Furthermore, we consider a circular crack subjected to cubic-order normal stresses. It is shown that the stress intensity factor distribution derived from the general solution exactly agree with the analytical solutions derived by Shah-Kobayashi.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125258907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Slip deformation in Cu-9at.% Al symmetric type bicrystal models subjected to tensile loading is investigated by a finite element crystal plasticity analysis code. Accumulation of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) are studied in detail. Results of the analysis show asymmetric non-uniform deformation and accumulation of GNDs on the primary and secondary slip systems with activation of secondary slip system near the grain boundary. Mechanism of asymmetric non-uniform deformation with GNDs accumulated near the grain boundary in the Cu-9at.% Al symmetric type bicrystal models is discussed from the viewpoint of the effects of the elastic anisotropy of Cu-9at.% Al and the heterogeneity of initial statically stored dislocations density.
{"title":"Relationship between Micro-Incompatibility and Heterogeneity of Dislocation Density Distribution in Cu-9at.% Al Symmetric Type Bicrystal Models under Tensile Loading","authors":"Ryouji Kondou, T. Ohashi, S. Miura","doi":"10.1299/JCST.2.162","DOIUrl":"https://doi.org/10.1299/JCST.2.162","url":null,"abstract":"Slip deformation in Cu-9at.% Al symmetric type bicrystal models subjected to tensile loading is investigated by a finite element crystal plasticity analysis code. Accumulation of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) are studied in detail. Results of the analysis show asymmetric non-uniform deformation and accumulation of GNDs on the primary and secondary slip systems with activation of secondary slip system near the grain boundary. Mechanism of asymmetric non-uniform deformation with GNDs accumulated near the grain boundary in the Cu-9at.% Al symmetric type bicrystal models is discussed from the viewpoint of the effects of the elastic anisotropy of Cu-9at.% Al and the heterogeneity of initial statically stored dislocations density.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131165702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We verified the generalization ability of the response surfaces of artificial neural networks (NNs), and that the surfaces could be applied to an engineering-design problem. A Bayesian framework to regularize NNs, which was proposed by Gull and Skilling, can be used to generate NN response surfaces with excellent generalization ability, i.e., to determine the regularizing constants in an objective function minimized during NN learning. This well-generalized NN might be useful to find an optimal solution in the process of response surface methodology (RSM). We, therefore, describe three rules based on the Bayesian framework to update the regularizing constants, utilizing these rules to generate NN response surfaces with noisy teacher data drawn from a typical unimodal or multimodal function. Good generalization ability was achieved with regularized NN response surfaces, even though an update rule including trace evaluation failed to determine the regularizing constants regardless of the response function. We, next, selected the most appropriate update rule, which included eigenvalue evaluation, and then the NN response surface regularized using the update rule was applied to finding the optimal solution to an illustrative engineering-design problem. The NN response surface did not fit the noise in the teacher data, and consequently, it could effectively be used to achieve a satisfactory solution. This may increase the opportunities for using NN in the process of RSM.
{"title":"Response Surfaces of Neural Networks Learned Using Bayesian Framework and Its Application to Optimization Problem","authors":"N. Takeda","doi":"10.1299/JCST.3.315","DOIUrl":"https://doi.org/10.1299/JCST.3.315","url":null,"abstract":"We verified the generalization ability of the response surfaces of artificial neural networks (NNs), and that the surfaces could be applied to an engineering-design problem. A Bayesian framework to regularize NNs, which was proposed by Gull and Skilling, can be used to generate NN response surfaces with excellent generalization ability, i.e., to determine the regularizing constants in an objective function minimized during NN learning. This well-generalized NN might be useful to find an optimal solution in the process of response surface methodology (RSM). We, therefore, describe three rules based on the Bayesian framework to update the regularizing constants, utilizing these rules to generate NN response surfaces with noisy teacher data drawn from a typical unimodal or multimodal function. Good generalization ability was achieved with regularized NN response surfaces, even though an update rule including trace evaluation failed to determine the regularizing constants regardless of the response function. We, next, selected the most appropriate update rule, which included eigenvalue evaluation, and then the NN response surface regularized using the update rule was applied to finding the optimal solution to an illustrative engineering-design problem. The NN response surface did not fit the noise in the teacher data, and consequently, it could effectively be used to achieve a satisfactory solution. This may increase the opportunities for using NN in the process of RSM.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127706137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An efficient homogenization method for nonlinear problems is introduced. We have already developed a homogenization technique using characteristic deformation mode superposition that avoids prohibitive computational cost. However, in the mode superposition technique, the approximation error created depends on the analysis case. In this paper a new method is proposed, in which the same accuracy as the exact method is preserved by solving the microscopic equilibrium equation, while approximating the tangential matrix of the multi-scale equilibrium equation using the mode superposition method. The performance of the proposed method is examined together with the block LU factorization algorithm, and satisfactory results are obtained.
{"title":"Nonlinear Homogenization Algorithms with Low Computational Cost","authors":"J. Okada, T. Washio, T. Hisada","doi":"10.1299/JCST.3.101","DOIUrl":"https://doi.org/10.1299/JCST.3.101","url":null,"abstract":"An efficient homogenization method for nonlinear problems is introduced. We have already developed a homogenization technique using characteristic deformation mode superposition that avoids prohibitive computational cost. However, in the mode superposition technique, the approximation error created depends on the analysis case. In this paper a new method is proposed, in which the same accuracy as the exact method is preserved by solving the microscopic equilibrium equation, while approximating the tangential matrix of the multi-scale equilibrium equation using the mode superposition method. The performance of the proposed method is examined together with the block LU factorization algorithm, and satisfactory results are obtained.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"474 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132588650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, the circumferential strain concentrations in cylindrical and square tubes with corrugated surfaces subjected to axial compression are studied using the finite element method. In cylindrical tubes, the yield strength σy, the hardening coefficient Eh of the material and the thickness t of the tube wall exert only a small influence on the strain concentration, so that the maximum circumferential strain can be approximately evaluated as a function of the wavelength 2λ and the amplitude a of the corrugations, and the cylinder radius R. For square tubes, however, the effect of the corner radius r, the thickness t, the yield strength σy, and the hardening coefficient Eh on the strain concentration is comparable to that of the wavelength 2λ and the amplitude a of the corrugations. The maximum circumferential strain increases with a decrease in the corner radius r/D, with a decrease in the thickness t, and with an increase in the ratio σy/Eh.
{"title":"Circumferential Strain Concentration of Corrugated Tubes Subjected to Axial Collapse","authors":"Dai-heng Chen, S. Ozaki","doi":"10.1299/JCST.2.632","DOIUrl":"https://doi.org/10.1299/JCST.2.632","url":null,"abstract":"In this study, the circumferential strain concentrations in cylindrical and square tubes with corrugated surfaces subjected to axial compression are studied using the finite element method. In cylindrical tubes, the yield strength σy, the hardening coefficient Eh of the material and the thickness t of the tube wall exert only a small influence on the strain concentration, so that the maximum circumferential strain can be approximately evaluated as a function of the wavelength 2λ and the amplitude a of the corrugations, and the cylinder radius R. For square tubes, however, the effect of the corner radius r, the thickness t, the yield strength σy, and the hardening coefficient Eh on the strain concentration is comparable to that of the wavelength 2λ and the amplitude a of the corrugations. The maximum circumferential strain increases with a decrease in the corner radius r/D, with a decrease in the thickness t, and with an increase in the ratio σy/Eh.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124794006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The three-dimensional incremental finite element formulation for the multiaxial behavior of shape memory alloy devices is proposed in the present study by considering the coupling effect of the axial and torsional behaviors of shape memory alloys. The previously proposed one-dimensional constitutive model for shape memory alloy devices is extended to take account of the multiaxial stress state introducing some new material constants. The calculated results are compared with the uniaxial, purely torsional and multiaxial test results for NiTi tubes to illustrate the validity of the proposed computational modeling.
{"title":"Computational Modeling of Superelastic Behaviors of Shape Memory Alloy Devices Under Combined Stresses","authors":"Y. Toi, Daegon Choi","doi":"10.1299/JCST.2.535","DOIUrl":"https://doi.org/10.1299/JCST.2.535","url":null,"abstract":"The three-dimensional incremental finite element formulation for the multiaxial behavior of shape memory alloy devices is proposed in the present study by considering the coupling effect of the axial and torsional behaviors of shape memory alloys. The previously proposed one-dimensional constitutive model for shape memory alloy devices is extended to take account of the multiaxial stress state introducing some new material constants. The calculated results are compared with the uniaxial, purely torsional and multiaxial test results for NiTi tubes to illustrate the validity of the proposed computational modeling.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134244682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, tightly coupled partitioned iterative methods have drawn a great deal of attentions due to easy implementation and encapsulation features, and several nonlinear algorithms have been proposed so far. However, their practical performances have not been well understood yet. This paper describes the intensive parametric study on convergence and stability performances of four nonlinear algorithms and their relaxed variations for partitioned iterative methods of steady / unsteady fluid-structure interaction (FSI) problems. Here we choose three typical FSI problems as test problems, i.e. (1) Collapsible channel as a steady problem, (2) Cavity with flexible bottom membrane and (3) Channel with flexible wall as unsteady problems. Efficiency and robustness dependency of those nonlinear algorithms on physical parameters such as degree of nonlinearity, added mass effect, time step, and on control parameters peculiar to each algorithm are clarified. Through those tests, we demonstrate that Broyden method is the fastest algorithm for easy FSI problems such as weakly coupling and Line Search method has robustness even for difficult FSI problems such as strongly coupling.
{"title":"Practical Performances of Non-linear Algorithms for Partitioned Iterative Method of Fluid-Structure Interaction Problems","authors":"S. Minami, S. Yoshimura","doi":"10.1299/JCST.3.396","DOIUrl":"https://doi.org/10.1299/JCST.3.396","url":null,"abstract":"Recently, tightly coupled partitioned iterative methods have drawn a great deal of attentions due to easy implementation and encapsulation features, and several nonlinear algorithms have been proposed so far. However, their practical performances have not been well understood yet. This paper describes the intensive parametric study on convergence and stability performances of four nonlinear algorithms and their relaxed variations for partitioned iterative methods of steady / unsteady fluid-structure interaction (FSI) problems. Here we choose three typical FSI problems as test problems, i.e. (1) Collapsible channel as a steady problem, (2) Cavity with flexible bottom membrane and (3) Channel with flexible wall as unsteady problems. Efficiency and robustness dependency of those nonlinear algorithms on physical parameters such as degree of nonlinearity, added mass effect, time step, and on control parameters peculiar to each algorithm are clarified. Through those tests, we demonstrate that Broyden method is the fastest algorithm for easy FSI problems such as weakly coupling and Line Search method has robustness even for difficult FSI problems such as strongly coupling.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132538211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To investigate the effect of liquid water saturation on the efficiency of polymer electrolyte fuel cells, it is important to determine the exact relationship between the liquid water saturation profile and other parameters. In this paper, the pore size distribution (PSD) is used to calculate the liquid water saturation in a fuel cell. Using the PSD, liquid water saturation is calculated from experimental data for the capillary pressure on a porous media. Numerical analysis is used to analyze and evaluate the liquid water pressure and temperature profiles in a fuel cell. This paper uses two-phase, three-dimensional analysis to determine the effects of using the PSD.
{"title":"Numerical Analysis of a Three-Dimensional Sandwich Model for Investigating the Effect of Using the Pore Size Distribution","authors":"Y. Tachikawa, Yuya Matsuda, H. Kanayama","doi":"10.1299/JCST.4.89","DOIUrl":"https://doi.org/10.1299/JCST.4.89","url":null,"abstract":"To investigate the effect of liquid water saturation on the efficiency of polymer electrolyte fuel cells, it is important to determine the exact relationship between the liquid water saturation profile and other parameters. In this paper, the pore size distribution (PSD) is used to calculate the liquid water saturation in a fuel cell. Using the PSD, liquid water saturation is calculated from experimental data for the capillary pressure on a porous media. Numerical analysis is used to analyze and evaluate the liquid water pressure and temperature profiles in a fuel cell. This paper uses two-phase, three-dimensional analysis to determine the effects of using the PSD.","PeriodicalId":196913,"journal":{"name":"Journal of Computational Science and Technology","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131513946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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