ON THE ASYMPTOTIC SOLUTION OF THE AXISYMMETRIC PROBLEM OF FUNCTIONALLY GRADED HOLLOW SPHERE IN RADIALLY DIRECTION

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-04-22 DOI:10.1016/j.tws.2025.113352

N.K. Akhmedov , A.H. Sofiyev

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引用次数: 0

Abstract

In this study, the axisymmetric problem of functionally graded (FG) transversely isotropic spheres in the radial direction, which do not contain 0 and Pi poles, is investigated within the framework of 3D-elasticity theory. In this study, firstly, the elasticity theory of spheres made of homogeneous materials extended to the elasticity theory of functionally graded transversely isotropic (FGTI) spheres. Arbitrary stresses are applied to the slots that keep the hollow sphere, whose lateral surface is assumed to be fixed, in balance. Asymptotic formulas are obtained to calculate the displacements and stresses of FGTI hollow spheres for the first time. The solution of the problem consists of solutions belonging to the nature of the boundary layer localized in the slots (conical sections) inside the sphere, which is equivalent to the Saint-Venant boundary effect for FG plates. Unlike the FG isotropic sphere, weak transitional boundary layer solutions that spread far from the conical sections for FGTI spheres emerge. In addition, an asymptotic solution to the torsion problem for thin FGTI spheres is presented for the first time. The realized asymptotic solutions can be a criterion for determining the fields of application of the existing applied theories of FGTI spheres. Based on the proposed solutions, more accurate new applied theories for heterogeneous transversely isotropic spherical shells can be constructed. Finally, the changes in displacements and stresses compared to the homogeneous case are analyzed in detail when the modulus of elasticity changes linearly and inversely proportional to the radius.

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径向上功能梯度空心球轴对称问题的渐近解

本文在三维弹性理论的框架下，研究了不含0极和Pi极的径向功能梯度（FG）横各向同性球体的轴对称问题。本研究首先将均质球弹性理论推广到功能梯度横各向同性（FGTI）球弹性理论。任意应力被施加到保持中空球体的槽上，中空球体的侧面被假定为固定的，保持平衡。首次得到了FGTI空心球位移和应力的渐近计算公式。该问题的解由属于边界层性质的解组成，边界层定位于球体内部的槽（圆锥截面），相当于FG板的Saint-Venant边界效应。与FG各向同性球不同，FGTI球的弱过渡边界层解在远离圆锥形部分的地方出现。此外，本文还首次给出了FGTI薄球扭转问题的渐近解。已实现的渐近解可作为确定FGTI球的现有应用理论的应用领域的判据。基于所提出的解，可以构建更精确的非均质横向各向同性球壳的新应用理论。最后，详细分析了弹性模量与半径成线性和反比变化时的位移和应力变化情况。

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.