{"title":"基于经典层压板理论和深能量法的层压薄板几何非线性弯曲分析","authors":"Zhong-Min Huang , Lin-Xin Peng","doi":"10.1016/j.compstruct.2024.118314","DOIUrl":null,"url":null,"abstract":"<div><p>This paper establishes a geometrically nonlinear bending analysis framework using the deep energy method and the classical laminated plate theory (CLPT) for laminated plates. Inspired by the transfer learning technique, a load applied to a laminated plate can be divided into multiple load steps. The network parameters for the current load step, with the exception of the initial step, are initialized by inheriting values from their preceding steps. Including both von Kármán and Green-Lagrange strains, the plate strains are computed using the automatic differentiation and integrated along the thickness direction per laminate plate based on the constitutive theory. By combining the outputs of neural network, the external potential energy can be obtained, and the optimized network parameters are given by minimizing the total system potential energy of the laminated plate. In order to validate the proposed approach, several numerical examples are calculated, and the present solutions are compared with those given by the literature and the Finite Element Analysis (FEA). The results show that the proposed approach is indeed feasible, can reach high levels of precision under varying loads while offering a simplified calculation strategy.</p></div>","PeriodicalId":281,"journal":{"name":"Composite Structures","volume":null,"pages":null},"PeriodicalIF":6.3000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometrically nonlinear bending analysis of laminated thin plates based on classical laminated plate theory and deep energy method\",\"authors\":\"Zhong-Min Huang , Lin-Xin Peng\",\"doi\":\"10.1016/j.compstruct.2024.118314\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper establishes a geometrically nonlinear bending analysis framework using the deep energy method and the classical laminated plate theory (CLPT) for laminated plates. Inspired by the transfer learning technique, a load applied to a laminated plate can be divided into multiple load steps. The network parameters for the current load step, with the exception of the initial step, are initialized by inheriting values from their preceding steps. Including both von Kármán and Green-Lagrange strains, the plate strains are computed using the automatic differentiation and integrated along the thickness direction per laminate plate based on the constitutive theory. By combining the outputs of neural network, the external potential energy can be obtained, and the optimized network parameters are given by minimizing the total system potential energy of the laminated plate. In order to validate the proposed approach, several numerical examples are calculated, and the present solutions are compared with those given by the literature and the Finite Element Analysis (FEA). The results show that the proposed approach is indeed feasible, can reach high levels of precision under varying loads while offering a simplified calculation strategy.</p></div>\",\"PeriodicalId\":281,\"journal\":{\"name\":\"Composite Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.3000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Composite Structures\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0263822324004422\",\"RegionNum\":2,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATERIALS SCIENCE, COMPOSITES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Composite Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0263822324004422","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATERIALS SCIENCE, COMPOSITES","Score":null,"Total":0}
引用次数: 0
摘要
本文利用深能量法和经典层压板理论(CLPT)为层压板建立了一个几何非线性弯曲分析框架。受迁移学习技术的启发,施加在层压板上的载荷可分为多个载荷步骤。当前负载步骤的网络参数(初始步骤除外)通过继承前一步骤的值进行初始化。包括 von Kármán 应变和格林-拉格朗日应变在内的板应变是通过自动微分计算得出的,并根据构成理论沿厚度方向对每个层压板进行积分。结合神经网络的输出,可以得到外部势能,并通过最小化层压板的总系统势能给出优化的网络参数。为了验证所提出的方法,计算了几个数值实例,并将目前的解决方案与文献和有限元分析(FEA)给出的解决方案进行了比较。结果表明,所提出的方法确实可行,能在不同载荷下达到很高的精度,同时提供了一种简化的计算策略。
Geometrically nonlinear bending analysis of laminated thin plates based on classical laminated plate theory and deep energy method
This paper establishes a geometrically nonlinear bending analysis framework using the deep energy method and the classical laminated plate theory (CLPT) for laminated plates. Inspired by the transfer learning technique, a load applied to a laminated plate can be divided into multiple load steps. The network parameters for the current load step, with the exception of the initial step, are initialized by inheriting values from their preceding steps. Including both von Kármán and Green-Lagrange strains, the plate strains are computed using the automatic differentiation and integrated along the thickness direction per laminate plate based on the constitutive theory. By combining the outputs of neural network, the external potential energy can be obtained, and the optimized network parameters are given by minimizing the total system potential energy of the laminated plate. In order to validate the proposed approach, several numerical examples are calculated, and the present solutions are compared with those given by the literature and the Finite Element Analysis (FEA). The results show that the proposed approach is indeed feasible, can reach high levels of precision under varying loads while offering a simplified calculation strategy.
期刊介绍:
The past few decades have seen outstanding advances in the use of composite materials in structural applications. There can be little doubt that, within engineering circles, composites have revolutionised traditional design concepts and made possible an unparalleled range of new and exciting possibilities as viable materials for construction. Composite Structures, an International Journal, disseminates knowledge between users, manufacturers, designers and researchers involved in structures or structural components manufactured using composite materials.
The journal publishes papers which contribute to knowledge in the use of composite materials in engineering structures. Papers deal with design, research and development studies, experimental investigations, theoretical analysis and fabrication techniques relevant to the application of composites in load-bearing components for assemblies, ranging from individual components such as plates and shells to complete composite structures.