Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations

In this paper, we applied a multiscale numerical scheme called the seamless-domain method (SDM) to nonlinear elliptic boundary value problems. Although the SDM is meshfree, it can obtain a high-resolution solution whose dependent-variable gradient(s) is sufficiently smooth and continuous. The SDM mo...

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Autores principales:	Yoshiro SUZUKI, Akira TODOROKI, Yoshihiro MIZUTANI
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2016
Materias:	composite material numerical analysis nonlinear problem finite element method heat conduction multiscale solver meshfree method homogenization Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/dd567252fedf4126a3f604cd2659c9fb
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spelling	oai:doaj.org-article:dd567252fedf4126a3f604cd2659c9fb2021-11-26T06:53:45ZMultiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations2187-974510.1299/mej.15-00491https://doaj.org/article/dd567252fedf4126a3f604cd2659c9fb2016-02-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/3/4/3_15-00491/_pdf/-char/enhttps://doaj.org/toc/2187-9745In this paper, we applied a multiscale numerical scheme called the seamless-domain method (SDM) to nonlinear elliptic boundary value problems. Although the SDM is meshfree, it can obtain a high-resolution solution whose dependent-variable gradient(s) is sufficiently smooth and continuous. The SDM models with only coarse-grained points can produce accurate solutions for both linear heat conduction problems and linear elastic problems. This manuscript presents a simple nonlinear solver for the SDM analysis of heterogeneous materials. Although the solver can easily approximate the solutions to nonlinear multiscale problems, it does not require an iterative multiscale analysis at every convergence calculation. In other words, the proposed scheme does not completely interactively couple the multiple scales. We present numerical examples of nonlinear stationary heat conduction analyses of heterogeneous fields and compare the SDM model, the direct finite-element model, and the homogenized model based on the homogenization theory. For a real heterogeneous structure (graphite fiber composite) that did not have strong material nonlinearities, the SDM model using only 925 points gave a solution with similar precisions as an ordinary finite element solution using hundreds of thousands of nodes. To investigate the limitations of the method, we also applied the SDM to imaginary materials with various strengths of thermal property nonlinearities.Yoshiro SUZUKIAkira TODOROKIYoshihiro MIZUTANIThe Japan Society of Mechanical Engineersarticlecomposite materialnumerical analysisnonlinear problemfinite element methodheat conductionmultiscale solvermeshfree methodhomogenizationMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 3, Iss 4, Pp 15-00491-15-00491 (2016)
institution	DOAJ
collection	DOAJ
language	EN
topic	composite material numerical analysis nonlinear problem finite element method heat conduction multiscale solver meshfree method homogenization Mechanical engineering and machinery TJ1-1570
spellingShingle	composite material numerical analysis nonlinear problem finite element method heat conduction multiscale solver meshfree method homogenization Mechanical engineering and machinery TJ1-1570 Yoshiro SUZUKI Akira TODOROKI Yoshihiro MIZUTANI Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations
description	In this paper, we applied a multiscale numerical scheme called the seamless-domain method (SDM) to nonlinear elliptic boundary value problems. Although the SDM is meshfree, it can obtain a high-resolution solution whose dependent-variable gradient(s) is sufficiently smooth and continuous. The SDM models with only coarse-grained points can produce accurate solutions for both linear heat conduction problems and linear elastic problems. This manuscript presents a simple nonlinear solver for the SDM analysis of heterogeneous materials. Although the solver can easily approximate the solutions to nonlinear multiscale problems, it does not require an iterative multiscale analysis at every convergence calculation. In other words, the proposed scheme does not completely interactively couple the multiple scales. We present numerical examples of nonlinear stationary heat conduction analyses of heterogeneous fields and compare the SDM model, the direct finite-element model, and the homogenized model based on the homogenization theory. For a real heterogeneous structure (graphite fiber composite) that did not have strong material nonlinearities, the SDM model using only 925 points gave a solution with similar precisions as an ordinary finite element solution using hundreds of thousands of nodes. To investigate the limitations of the method, we also applied the SDM to imaginary materials with various strengths of thermal property nonlinearities.
format	article
author	Yoshiro SUZUKI Akira TODOROKI Yoshihiro MIZUTANI
author_facet	Yoshiro SUZUKI Akira TODOROKI Yoshihiro MIZUTANI
author_sort	Yoshiro SUZUKI
title	Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations
title_short	Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations
title_full	Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations
title_fullStr	Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations
title_full_unstemmed	Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations
title_sort	multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations
publisher	The Japan Society of Mechanical Engineers
publishDate	2016
url	https://doaj.org/article/dd567252fedf4126a3f604cd2659c9fb
work_keys_str_mv	AT yoshirosuzuki multiscaleseamlessdomainmethodforsolvingnonlinearheatconductionproblemswithoutiterativemultiscalecalculations AT akiratodoroki multiscaleseamlessdomainmethodforsolvingnonlinearheatconductionproblemswithoutiterativemultiscalecalculations AT yoshihiromizutani multiscaleseamlessdomainmethodforsolvingnonlinearheatconductionproblemswithoutiterativemultiscalecalculations
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Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations

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