Series solutions to elastic opening of double cantilever beam for several traction–separation laws

IF 2.3 4区工程技术 Q3 MECHANICS

Mechanics Research Communications Pub Date : 2025-03-01 DOI:10.1016/j.mechrescom.2025.104391

Zhenghao Yang , Konstantin Naumenko , Guozhao Dai , Nan-You Lu

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引用次数: 0

Abstract

The aim of this paper is to develop semi-analytical solutions for double cantilever beam (DCB) problems using eigenfunction series expansions. This approach provides explicit expressions for deflection as a function of the axial coordinate for various traction–separation laws (TSL) and different external loading conditions. For a given cohesive zone length, the solutions are presented in a closed analytical form. Once the deflection function is derived, the length of the interaction zone is related to TSL parameters, bending stiffness, and applied loads through transcendental equations, which are solved numerically. To validate the accuracy of the derived expressions, results are compared with numerical solutions obtained via finite element analysis. The good agreement observed between the analytical and numerical solutions confirms the robustness of the proposed method and its ability to accurately capture both global (deflection) and local (cohesive traction distribution) behavior. Compared to general solutions for semi-infinite beams found in the literature, eigenfunction series offer greater flexibility, accommodating a wider range of boundary conditions and loading types.

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几种牵引分离规律下双悬臂梁弹性开口的系列解

本文的目的是利用特征函数级数展开式给出双悬臂梁问题的半解析解。该方法给出了在不同牵引-分离规律（TSL）和不同外载荷条件下挠度随轴向坐标的显式表达式。对于给定的内聚区长度，解以封闭解析形式给出。推导出挠度函数后，通过超越方程将相互作用区长度与TSL参数、弯曲刚度和外加载荷相关，并进行数值求解。为了验证导出表达式的准确性，将结果与有限元数值解进行了比较。解析解和数值解之间的良好一致性证实了所提出方法的鲁棒性及其准确捕获全局（挠度）和局部（内聚牵引力分布）行为的能力。与文献中发现的半无限梁的一般解相比，特征函数级数提供了更大的灵活性，适应更广泛的边界条件和加载类型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mechanics Research Communications 物理-力学

CiteScore

4.10

自引率

4.20%

发文量

114

审稿时长

9 months

期刊介绍： Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.