High-Order Three-Scale Computational Method for Thermoelastic Behavior Analysis of Axisymmetric Composite Structures with Multiple Spatial Scales
Year: 2020
Author: Hao Dong, Junzhi Cui, Yufeng Nie, Zihao Yang, Zhiqiang Yang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 599–642
Abstract
This study develops a novel high-order three-scale (HOTS) computational method to accurately simulate and analyze the thermoelastic behaviors of axisymmetric composite structures with multiple spatial scales. The inhomogeneities in composite structures are taken into account by periodic distributions of representative unit cells on the mesoscale and microscale. Firstly, the multiscale asymptotic analysis for these multiscale problems is given in detail, and the new unified micro-meso-macro HOTS approximate solutions for these multiscale problems are established based on the above-mentioned multiscale analysis. Two types of auxiliary cell functions are established on mesoscale and microscale. Also, two kinds of equivalent material parameters are calculated by up-scaling procedure on the mesoscale and microscale, and the homogenized problems are subsequently defined on global structure. Then, the numerical accuracy analyses for the conventional two-scale solutions, low-order three-scale (LOTS) solutions and HOTS solutions are obtained in the pointwise sense. By the foregoing error analyses, the vital necessity of developing HOTS solutions for simulating these three-scale problems is illustrated clearly. Furthermore, the corresponding HOTS numerical algorithm based on finite element method (FEM) is brought forward in detail. Finally, some numerical examples are presented to verify the usability and effectiveness of the HOTS computational method developed in this work.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0071
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 599–642
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 44
Keywords: Multiscale asymptotic analysis thermoelastic problems axisymmetric composite structures multiple spatial scales HOTS numerical algorithm.