{"title":"Stress-constrained concurrent multiscale topological design of porous composites based on discrete material optimisation","authors":"","doi":"10.1016/j.apm.2024.115730","DOIUrl":null,"url":null,"abstract":"<div><div>Porous composites have attracted increasing attention in recent decades. This study develops a concurrent multiscale topology optimisation (CMTO) method under a prescribed stress constraint for designing porous composites with multi-domain microstructures. First, to address the difficulty of predicting local stress due to varying of microstructural type throughout the optimisation process, a continuous and differentiable stress measure is proposed to effectively approximate the local stress. Second, an inverse homogenisation method based on isogeometric analysis (IGA) is developed to improve the accuracy of stress prediction, and then it is integrated into a CMTO which is developed based on the discrete material optimisation (DMO) interpolation scheme. Third, a stress constraint which is differentiable with respect to both macro and micro design variables is proposed to enable the stress-constrained concurrent optimisation of the macrostructural configuration, microstructural configuration and distribution. Fourth, a novel post-processing approach is established to achieve smooth while volume preserving contour of unit cells with layouts. Finally, two benchmark design examples, namely l-bracket and Crack problems, are implemented using the presented CMTO under a global stress constraint to demonstrate the effectiveness of the proposed method. The result indicates that the proposed method can effectively decrease the stress concentration via three design manners, i.e., the macrostructural configuration, microstructural configuration and distribution. Also, an “interface-enlarging” phenomenon was interestingly but reasonably found in those cases when subjected to stress-constraint considerations.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4000,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematical Modelling","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0307904X24004839","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Porous composites have attracted increasing attention in recent decades. This study develops a concurrent multiscale topology optimisation (CMTO) method under a prescribed stress constraint for designing porous composites with multi-domain microstructures. First, to address the difficulty of predicting local stress due to varying of microstructural type throughout the optimisation process, a continuous and differentiable stress measure is proposed to effectively approximate the local stress. Second, an inverse homogenisation method based on isogeometric analysis (IGA) is developed to improve the accuracy of stress prediction, and then it is integrated into a CMTO which is developed based on the discrete material optimisation (DMO) interpolation scheme. Third, a stress constraint which is differentiable with respect to both macro and micro design variables is proposed to enable the stress-constrained concurrent optimisation of the macrostructural configuration, microstructural configuration and distribution. Fourth, a novel post-processing approach is established to achieve smooth while volume preserving contour of unit cells with layouts. Finally, two benchmark design examples, namely l-bracket and Crack problems, are implemented using the presented CMTO under a global stress constraint to demonstrate the effectiveness of the proposed method. The result indicates that the proposed method can effectively decrease the stress concentration via three design manners, i.e., the macrostructural configuration, microstructural configuration and distribution. Also, an “interface-enlarging” phenomenon was interestingly but reasonably found in those cases when subjected to stress-constraint considerations.
期刊介绍:
Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged.
This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.
Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.