Peridynamics model of torsion-warping: Application to lattice beam structures

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2024-10-21 DOI:10.1016/j.tws.2024.112603

Sajal, Pranesh Roy

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引用次数: 0

Abstract

This paper presents a finite deformation beam model based on Simo-Reissner theory in peridynamics (PD) framework to deal with torsion induced warping deformation. Seven degrees of freedom, viz. three translational, three rotational, and one warping amplitude are considered at each material point. The governing equations of the beam are obtained by employing global balance of linear and angular momenta in conjunction with Simo's assumption on the deformation field. The relation between PD resultant force, moment, bi-moment, and bi-shear states with their classical counterparts is established using the constitutive correspondence method. Numerical implementation strategy is furnished for both quasi-static and dynamic cases. The solution for quasi-static load is obtained through the Newton-Raphson method. The proposed model is validated against finite element solutions considering cantilever beam and lattice structures. Quasi-static deformation responses of 3

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3 octet and single unit compression-torsion lattice structures are presented further to demonstrate the effectiveness of proposed beam model. A new bond breaking criterion is proposed based on critical stretch, critical relative rotation, and critical relative warping amplitude and failure of the compression-torsion lattice structures under compressive load is simulated. The Newmark-beta method is utilized to solve the governing equations for dynamic loading. Numerical simulations include dynamic analysis of octet and compression-torsion lattice structures.

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扭转变形的周动力学模型：晶格梁结构的应用

本文提出了一种基于周动力学（PD）框架中 Simo-Reissner 理论的有限变形梁模型，用于处理扭转引起的翘曲变形。在每个材料点上考虑了七个自由度，即三个平移自由度、三个旋转自由度和一个翘曲振幅自由度。通过采用线性和角矩的全局平衡以及西莫对变形场的假设，得到了梁的控制方程。使用构成对应法建立了 PD 结果力、力矩、双力矩和双剪切状态与其经典对应状态之间的关系。提供了准静态和动态情况下的数值实施策略。准静态载荷的求解是通过牛顿-拉斐森方法获得的。考虑到悬臂梁和晶格结构，提出的模型与有限元解法进行了验证。进一步介绍了 3 × 3 × 3 八面体结构和单一单元压缩-扭转晶格结构的准静态变形响应，以证明所提议的梁模型的有效性。根据临界拉伸、临界相对旋转和临界相对翘曲振幅，提出了一种新的粘结断裂标准，并模拟了压缩-扭转晶格结构在压缩载荷作用下的破坏情况。利用纽马克-贝塔法求解动态加载的控制方程。数值模拟包括八面体和压缩-扭转晶格结构的动态分析。

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

Thin-Walled Structures 工程技术-工程：土木

CiteScore

9.60

自引率

20.30%

发文量

801

审稿时长

66 days

期刊介绍： Thin-walled structures comprises an important and growing proportion of engineering construction with areas of application becoming increasingly diverse, ranging from aircraft, bridges, ships and oil rigs to storage vessels, industrial buildings and warehouses. Many factors, including cost and weight economy, new materials and processes and the growth of powerful methods of analysis have contributed to this growth, and led to the need for a journal which concentrates specifically on structures in which problems arise due to the thinness of the walls. This field includes cold– formed sections, plate and shell structures, reinforced plastics structures and aluminium structures, and is of importance in many branches of engineering. The primary criterion for consideration of papers in Thin–Walled Structures is that they must be concerned with thin–walled structures or the basic problems inherent in thin–walled structures. Provided this criterion is satisfied no restriction is placed on the type of construction, material or field of application. Papers on theory, experiment, design, etc., are published and it is expected that many papers will contain aspects of all three.