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| Statistical higher-order multi-scale method for nonlinear thermo-mechanical simulation of composite structures with periodically random configurations |
| Received:September 05, 2023 Revised:October 27, 2023 |
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| DOI：10.7511/jslx20230905005 |
| KeyWord:random composite structures nonlinear thermo-mechanical simulation SHOMS computational model space-time multi-scale algorithm local error analysis |
| Author | Institution |
| 董灏 |
西安电子科技大学 数学与统计学院, 西安 |
| 崔俊芝 |
中国科学院数学与系统科学研究院, 北京 |
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| Abstract: |
| Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite structures with complicated random microstructures remains a challenging issue.In this paper, we develop a novel statistical higher-order multi-scale (SHOMS) method for nonlinear thermo-mechanical simulation of composite structures with periodically random configurations, which is designed to overcome limitations of prohibitive computation involving the macro-scale and micro-scale.By virtue of statistical multi-scale asymptotic analysis and Taylor series method, the SHOMS computational model is rigorously derived for accurately analyzing nonlinear thermo-mechanical responses of random composite structures both in the macro-scale and micro-scale.Moreover, the local error analysis of SHOMS solutions in the point-wise sense clearly illustrates the crucial indispensability of establishing the higher-order asymptotic corrected terms in SHOMS computational model for keeping the conservation of local energy and momentum.Then, the corresponding space-time multi-scale numerical algorithm with off-line and on-line stages is designed to efficiently simulate nonlinear thermo-mechanical behaviors of random composite structures.Finally, extensive numerical experiments are presented to gauge the efficiency and accuracy of the proposed SHOMS approach. |