Finite element buckling analysis for micro structures based on the couple stress theory

IF 6.6 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-09-24 DOI:10.1016/j.tws.2025.114023

Yang Bae Jeon , Gi-Dong Sim , Jae-Hoon Choi

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引用次数: 0

Abstract

Mechanical behavior at the micro- and nano-scale exhibits size-dependent effects, such as increased stiffness, which are not captured by classical continuum mechanics. These effects become particularly important in thin structures, where buckling is a critical failure mode; however, previous studies have been limited to simple geometries due to the complexity of the governing equations. This study develops a finite element framework for buckling analysis based on the modified couple stress theory (MCST), applicable to arbitrary geometries. Beam and shell elements are formulated to incorporate size effects, enabling buckling analysis of general structures. The framework is demonstrated on various configurations, including thin membranes under residual stress, stiffened plates, and tensile bars, highlighting its versatility. Numerical results show that accounting for size effects consistently increases the predicted critical buckling loads compared to classical continuum mechanics. The proposed approach offers a broadly applicable tool for stability assessment in micro-electromechanical systems (MEMS), flexible electronics, and thin-film micro sensors and actuators.

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基于耦合应力理论的微结构有限元屈曲分析

微观和纳米尺度上的力学行为表现出尺寸依赖效应，例如刚度增加，这是经典连续介质力学所不能捕捉到的。这些影响在薄结构中尤为重要，因为屈曲是一种关键的破坏模式；然而，由于控制方程的复杂性，以前的研究仅限于简单的几何形状。本研究基于修正耦合应力理论（MCST）开发了一种适用于任意几何形状的屈曲分析有限元框架。梁和壳单元的制定纳入尺寸效应，使一般结构的屈曲分析。该框架在各种配置上进行了演示，包括残余应力下的薄膜、加筋板和拉伸杆，突出了其多功能性。数值结果表明，与经典连续介质力学相比，考虑了尺寸效应后的临界屈曲载荷预测值不断提高。该方法为微机电系统（MEMS）、柔性电子器件、薄膜微传感器和执行器的稳定性评估提供了一种广泛适用的工具。

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.