An analytic solution for bending of multilayered structures with interlayer-slip

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences Pub Date : 2024-08-12 DOI:10.1016/j.ijmecsci.2024.109642

{"title":"An analytic solution for bending of multilayered structures with interlayer-slip","authors":"","doi":"10.1016/j.ijmecsci.2024.109642","DOIUrl":null,"url":null,"abstract":"<div>Layered structures are prevalent in both natural environments and engineered composite materials. The elastic bending behavior of these structures is primarily governed by properties of their abundant interfaces. While the behavior of two- and three-layered beams has been extensively studied, this research shifts the focus to the impact of elastic shearing at interfaces on the deflection of multilayered structures comprising a substantial number of layers. We present an analytical solution indicating that the bending properties of multilayered beams and plates are nonlinearly dependent on interfacial stiffness. Denoting Se as the effective bending stiffness of an n-layered beam of length L, and S0 as the bending stiffness of a perfectly bound counterpart, we arrive at <math><mrow><mfrac><msub><mi>S</mi><mi>e</mi></msub><msub><mi>S</mi><mn>0</mn></msub></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><mrow><mo>(</mo><mrow><msup><mrow><mi>n</mi></mrow><mn>2</mn></msup><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mfrac><mrow><mi>tanh</mi><mi>α</mi><mi>L</mi></mrow><mrow><mi>α</mi><mi>L</mi></mrow></mfrac></mrow></mfrac></mrow></math> where αL represents a dimensionless parameter related to geometry and material properties. The analytical solutions, validated through finite element simulations, highlight the substantial variations in stiffness across different layered structures. This solution could also be instrumental in assessing interfacial damage and delamination in lamellar composites.</div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":null,"pages":null},"PeriodicalIF":7.1000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanical Sciences","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020740324006830","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}

引用次数: 0

Abstract

Layered structures are prevalent in both natural environments and engineered composite materials. The elastic bending behavior of these structures is primarily governed by properties of their abundant interfaces. While the behavior of two- and three-layered beams has been extensively studied, this research shifts the focus to the impact of elastic shearing at interfaces on the deflection of multilayered structures comprising a substantial number of layers. We present an analytical solution indicating that the bending properties of multilayered beams and plates are nonlinearly dependent on interfacial stiffness. Denoting S_e as the effective bending stiffness of an n-layered beam of length L, and S₀ as the bending stiffness of a perfectly bound counterpart, we arrive at $\frac{S_{e}}{S_{0}} = \frac{1}{1 + (n^{2} - 1) \frac{\tanh α L}{α L}}$ where αL represents a dimensionless parameter related to geometry and material properties. The analytical solutions, validated through finite element simulations, highlight the substantial variations in stiffness across different layered structures. This solution could also be instrumental in assessing interfacial damage and delamination in lamellar composites.

Abstract Image

查看原文本刊更多论文

具有层间滑移的多层结构弯曲的解析解

层状结构在自然环境和工程复合材料中都很普遍。这些结构的弹性弯曲行为主要受其丰富界面特性的制约。虽然对两层和三层梁的行为进行了广泛的研究，但本研究将重点转移到了界面处的弹性剪切对包含大量层的多层结构挠度的影响。我们提出的分析解决方案表明，多层梁和板的弯曲特性与界面刚度呈非线性关系。将 Se 称为长度为 L 的 n 层梁的有效弯曲刚度，将 S0 称为完全约束对应梁的弯曲刚度，我们得出 SeS0=11+(n2-1)tanhαLαL 其中，αL 代表与几何形状和材料特性相关的无量纲参数。通过有限元模拟验证的分析解决方案突出显示了不同分层结构在刚度上的巨大差异。该解决方案还有助于评估层状复合材料的界面损伤和分层。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal of Mechanical Sciences 工程技术-工程：机械

CiteScore

12.80

自引率

17.80%

发文量

769

审稿时长

19 days

期刊介绍： The International Journal of Mechanical Sciences (IJMS) serves as a global platform for the publication and dissemination of original research that contributes to a deeper scientific understanding of the fundamental disciplines within mechanical, civil, and material engineering. The primary focus of IJMS is to showcase innovative and ground-breaking work that utilizes analytical and computational modeling techniques, such as Finite Element Method (FEM), Boundary Element Method (BEM), and mesh-free methods, among others. These modeling methods are applied to diverse fields including rigid-body mechanics (e.g., dynamics, vibration, stability), structural mechanics, metal forming, advanced materials (e.g., metals, composites, cellular, smart) behavior and applications, impact mechanics, strain localization, and other nonlinear effects (e.g., large deflections, plasticity, fracture). Additionally, IJMS covers the realms of fluid mechanics (both external and internal flows), tribology, thermodynamics, and materials processing. These subjects collectively form the core of the journal's content. In summary, IJMS provides a prestigious platform for researchers to present their original contributions, shedding light on analytical and computational modeling methods in various areas of mechanical engineering, as well as exploring the behavior and application of advanced materials, fluid mechanics, thermodynamics, and materials processing.