Fast and accurate closed form solutions for post-buckling of laminated plates with different boundary conditions

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-04-07 DOI:10.1016/j.tws.2025.113278

Mehdi Bohlooly Fotovat, Monika Zaczynska

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引用次数: 0

Abstract

The aim of the current paper is to derive some novel closed form solutions for nonlinear equilibrium paths of thin rectangular laminated plates under in-plane compressive loads. Different layer arrangements, i.e., symmetric and/or unsymmetric cases are considered. For the first time in literature, the obtained closed form equations cover different combinations of clamped, sliding and simply supported boundary conditions. The innovative aspect of this research lies in the consideration of three distinct trigonometric functions to describe the plate's deflection. For such a deflection, the compatibility equation is solved analytically, and the explicit form of stress function is calculated. The equilibrium equations based on classical theory and geometrically nonlinear von-Kármán relations are solved by Galerkin integrals. Then, some closed form relations are obtained for applied compression and amplitudes of trigonometric terms in assumed deflection. The accuracy of the closed form solutions is verified under different conditions through finite element method in ANSYS software.

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不同边界条件下层合板后屈曲的快速精确闭合解

本文的目的是推导出矩形薄层合板在面内压缩载荷作用下的非线性平衡路径的一些新颖的闭形式解。考虑了不同的层排列，即对称和/或不对称的情况。在文献中第一次，得到的封闭形式方程涵盖了夹固、滑动和简支边界条件的不同组合。本研究的创新之处在于考虑了三个不同的三角函数来描述板的挠度。针对这种挠度，对配伍方程进行了解析求解，并计算了应力函数的显式形式。基于经典理论和几何非线性von-Kármán关系的平衡方程用伽辽金积分求解。在此基础上，得到了假定挠度下的实际压缩与三角项幅值的封闭关系。在ANSYS软件中通过有限元法验证了不同条件下封闭形式解的精度。

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.