{"title":"基于 MLS-ANCF 的超弹性柔性梁动态特性分析","authors":"","doi":"10.1016/j.enganabound.2024.105881","DOIUrl":null,"url":null,"abstract":"<div><p>Due to the dual characteristics of material nonlinearity and geometric nonlinearity exhibited by silicone rubber-like hyperelastic incompressible materials, the dynamic problems involving such materials become complex and challenging. In previous research, the Absolute Nodal Coordinate Formulation (ANCF) has demonstrated its effectiveness in addressing geometric nonlinearities during large deformations. However, ANCF tends to suffer from mesh distortion and configuration distortion issues. On the other hand, the Moving Least Squares Method (MLS) from meshfree methods uses a substantial number of nodes when constructing shape functions, which effectively improves mesh distortion problems in finite element methods when dealing with large deformations. Therefore, this paper employs Hermite-type MLS approximation functions to construct three-dimensional interpolation shape functions that replace the finite element shape function used in the traditional ANCF, thus creating an MLS-ANCF(Absolute node coordinate method based on the moving least square method) approach. Additionally, three nonlinear material models are introduced to tackle the material nonlinearity of hyperelastic beams. Moreover, Lagrange multipliers and Hamilton's principle are used to derive the static and dynamic equations for the hyperelastic beams system. To further validate the correctness of the MLS-ANCF method, this study first compares its results with those obtained from commercial software ABAQUS and static equilibrium experiments, thereby demonstrating the accuracy and effectiveness of MLS-ANCF; Next, dynamic analysis of a cantilevered silicone rubber beam under gravity alone is conducted to show the advantages of MLS-ANCF over other methods and effectively solve the issue of geometric configuration distortion caused by meshing; Furthermore, this paper also investigates the influencing factor of dynamics analysis, such as the incompressibility constant <em>k</em>, weight function, damping coefficient, number of elements, and different nonlinear material models; Ultimately, a comparison with experimental data reveals that MLS-ANCF outperforms conventional ANCF beam elements in terms of agreement with experimental data. This demonstrates the significant role of MLS-ANCF in analyzing the dynamic characteristics of nonlinear hyperelastic beams.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamic characteristics analysis of hyperelastic flexible beam based on MLS-ANCF\",\"authors\":\"\",\"doi\":\"10.1016/j.enganabound.2024.105881\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Due to the dual characteristics of material nonlinearity and geometric nonlinearity exhibited by silicone rubber-like hyperelastic incompressible materials, the dynamic problems involving such materials become complex and challenging. In previous research, the Absolute Nodal Coordinate Formulation (ANCF) has demonstrated its effectiveness in addressing geometric nonlinearities during large deformations. However, ANCF tends to suffer from mesh distortion and configuration distortion issues. On the other hand, the Moving Least Squares Method (MLS) from meshfree methods uses a substantial number of nodes when constructing shape functions, which effectively improves mesh distortion problems in finite element methods when dealing with large deformations. Therefore, this paper employs Hermite-type MLS approximation functions to construct three-dimensional interpolation shape functions that replace the finite element shape function used in the traditional ANCF, thus creating an MLS-ANCF(Absolute node coordinate method based on the moving least square method) approach. Additionally, three nonlinear material models are introduced to tackle the material nonlinearity of hyperelastic beams. Moreover, Lagrange multipliers and Hamilton's principle are used to derive the static and dynamic equations for the hyperelastic beams system. To further validate the correctness of the MLS-ANCF method, this study first compares its results with those obtained from commercial software ABAQUS and static equilibrium experiments, thereby demonstrating the accuracy and effectiveness of MLS-ANCF; Next, dynamic analysis of a cantilevered silicone rubber beam under gravity alone is conducted to show the advantages of MLS-ANCF over other methods and effectively solve the issue of geometric configuration distortion caused by meshing; Furthermore, this paper also investigates the influencing factor of dynamics analysis, such as the incompressibility constant <em>k</em>, weight function, damping coefficient, number of elements, and different nonlinear material models; Ultimately, a comparison with experimental data reveals that MLS-ANCF outperforms conventional ANCF beam elements in terms of agreement with experimental data. This demonstrates the significant role of MLS-ANCF in analyzing the dynamic characteristics of nonlinear hyperelastic beams.</p></div>\",\"PeriodicalId\":51039,\"journal\":{\"name\":\"Engineering Analysis with Boundary Elements\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.2000,\"publicationDate\":\"2024-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Analysis with Boundary Elements\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0955799724003552\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0955799724003552","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}
Dynamic characteristics analysis of hyperelastic flexible beam based on MLS-ANCF
Due to the dual characteristics of material nonlinearity and geometric nonlinearity exhibited by silicone rubber-like hyperelastic incompressible materials, the dynamic problems involving such materials become complex and challenging. In previous research, the Absolute Nodal Coordinate Formulation (ANCF) has demonstrated its effectiveness in addressing geometric nonlinearities during large deformations. However, ANCF tends to suffer from mesh distortion and configuration distortion issues. On the other hand, the Moving Least Squares Method (MLS) from meshfree methods uses a substantial number of nodes when constructing shape functions, which effectively improves mesh distortion problems in finite element methods when dealing with large deformations. Therefore, this paper employs Hermite-type MLS approximation functions to construct three-dimensional interpolation shape functions that replace the finite element shape function used in the traditional ANCF, thus creating an MLS-ANCF(Absolute node coordinate method based on the moving least square method) approach. Additionally, three nonlinear material models are introduced to tackle the material nonlinearity of hyperelastic beams. Moreover, Lagrange multipliers and Hamilton's principle are used to derive the static and dynamic equations for the hyperelastic beams system. To further validate the correctness of the MLS-ANCF method, this study first compares its results with those obtained from commercial software ABAQUS and static equilibrium experiments, thereby demonstrating the accuracy and effectiveness of MLS-ANCF; Next, dynamic analysis of a cantilevered silicone rubber beam under gravity alone is conducted to show the advantages of MLS-ANCF over other methods and effectively solve the issue of geometric configuration distortion caused by meshing; Furthermore, this paper also investigates the influencing factor of dynamics analysis, such as the incompressibility constant k, weight function, damping coefficient, number of elements, and different nonlinear material models; Ultimately, a comparison with experimental data reveals that MLS-ANCF outperforms conventional ANCF beam elements in terms of agreement with experimental data. This demonstrates the significant role of MLS-ANCF in analyzing the dynamic characteristics of nonlinear hyperelastic beams.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.