Nonlinear finite element formulation for thin-walled conical shells

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2024-10-22 DOI:10.1016/j.tws.2024.112617

Saher Attia , Magdi Mohareb , Samer Adeeb

引用次数: 0

Abstract

This study presents a novel finite element formulation to predict the geometrically nonlinear response of conical shells under a wide range of practical loading conditions. The formulation expresses the discretized equilibrium equations in terms of the first Piola-Kirchhoff stress tensor and its conjugate gradient of the virtual displacements, is based on the kinematics of Love-Kirchhoff thin shell theory and the Saint-Venant-Kirchhoff constitutive model, and captures the follower effect of pressure loading. The formulation takes advantage of the axisymmetric nature of the shell geometries by adopting a Fourier series to characterize the displacement distributions along the circumferential direction while using Hermitian interpolation along the meridional direction. Comparisons with general shell models show the accuracy of the formulation under various loading conditions with a minimal number of degrees of freedom, resulting in a significant computational efficiency compared to conventional general-purpose shell solutions.

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薄壁锥形壳的非线性有限元计算公式

本研究提出了一种新的有限元计算方法，用于预测锥壳在各种实际加载条件下的几何非线性响应。该公式用第一皮奥拉-基尔霍夫应力张量及其虚拟位移的共轭梯度来表示离散平衡方程，以 Love-Kirchhoff 薄壳理论的运动学和 Saint-Venant-Kirchhoff 构成模型为基础，并捕捉了压力加载的随动效应。该公式利用了壳体几何的轴对称性质，采用傅里叶级数来描述沿圆周方向的位移分布，同时沿经线方向使用赫米特插值法。与一般壳体模型的比较表明，该公式在各种载荷条件下都能以最少的自由度实现精确计算，与传统的通用壳体解决方案相比，计算效率显著提高。

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.