热-机荷载作用的P-FGM扁球壳跳跃屈曲分析

doi:10.3901/JME.2022.24.111

机械工程学报 ›› 2022, Vol. 58 ›› Issue (24): 111-120.doi: 10.3901/JME.2022.24.111

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热-机荷载作用的P-FGM扁球壳跳跃屈曲分析

郭冬梅¹, 龚雪蓓¹, 赵伟东^1,2

1. 青海大学土木工程学院西宁 810016;
2. 青海省建筑节能材料与工程安全重点实验室西宁 810016

收稿日期:2022-03-29 修回日期:2022-08-10 出版日期:2022-12-20 发布日期:2023-04-03
通讯作者: 赵伟东(通信作者),男,1972年出生,硕士,副教授,硕士研究生导师。主要研究方向为结构非线性振动和结构屈曲分析。E-mail:10773243@qq.com
作者简介:郭冬梅,女,1996年出生,硕士研究生。主要研究方向为功能梯度材料结构的力学行为。E-mail:948921494@qq.com;赵伟东(通信作者),男,1972年出生,硕士,副教授,硕士研究生导师。主要研究方向为结构非线性振动和结构屈曲分析。E-mail:10773243@qq.com

Snap-through Buckling Analysis of P-FGM Shallow Spherical Shells under Thermomechanical Loads

GUO Dongmei¹, GONG Xuebei¹, ZHAO Weidong^1,2

1. School of Civil Engineering, Qinghai University, Xining 810016;
2. Qinghai Provincial Key Laboratory of Energy-saving Building Materials and Engineering Safety, Xining 810016

Received:2022-03-29 Revised:2022-08-10 Online:2022-12-20 Published:2023-04-03

摘要/Abstract

摘要： 基于经典壳体理论和Sanders非线性应变-位移关系，导出了幂律型功能梯度材料（P-FGM）扁球壳在热-机械荷载作用下的几何非线性常微分控制方程。推导过程考虑了沿厚度存在一维热传导温度场和法向均布荷载作用。采用打靶法求解了由控制方程和固定夹紧边界条件构成的两点边值问题。得到了FGM扁球壳的一些典型的屈曲平衡路径和双稳态构形。对热-机械荷载作用的FGM扁球壳的跳跃屈曲行为进行了参数影响分析。结果表明：温度上升时，球壳上临界荷载显著增加、下临界荷载变化不明显。梯度指数增加时，球壳上、下临界荷载均显著减小。组分材料模量增加时，球壳上、下临界荷载均显著增加。当底圆半径和厚度给定时，随壳体中面曲率半径增加，球壳上、下临界荷载均显著增加。当中面曲率半径和厚度给定时，随底圆半径增加，球壳下临界荷载显著减小，上临界荷载几乎不变。

关键词: 功能梯度材料, 扁球壳, 非均匀温度场, 法向均布荷载, 跳跃屈曲, 打靶法

Abstract: Based on the classical shell theory and Sanders nonlinear strain-displacement relationship, the geometric nonlinear ordinary differential governing equations of power-law functionally graded material (P-FGM) shallow spherical shells under thermal mechanical loads are derived. One-dimensional heat conduction temperature field along the thickness and normal uniformly distributed load are considered in the derivation. The two-point boundary value problem composed of the governing equations and clamped boundary condition is solved by the shooting method. Some typical buckling equilibrium paths and bistable configurations of FGM shallow spherical shells are obtained. The influence of parameters on the snap-through buckling behavior of FGM shallow spherical shells under thermal mechanical load is analyzed. The results show that when the temperature rises, the upper critical load of the shells increases significantly and the lower critical load does not change obviously. When gradient index increases, the upper and lower critical loads of the shells decrease significantly. When the constituent material modulus increases, the upper and lower critical loads of the shells increase significantly. When bottom circle radius and thickness are given, the upper and lower critical loads of the shells increase significantly with the decrease of the radius of curvature of the shells middle surface. When middle surface curvature radius and thickness of the shells are given, with the increase of the radius of the bottom circle, the lower critical load of the spherical shell decreases significantly, and the upper critical load is almost unchanged.

Key words: FGM, shallow spherical shell, non-uniform temperature field, normal uniformly distributed load, snap-through buckling, shooting method

中图分类号:

O343

郭冬梅, 龚雪蓓, 赵伟东. 热-机荷载作用的P-FGM扁球壳跳跃屈曲分析[J]. 机械工程学报, 2022, 58(24): 111-120.

GUO Dongmei, GONG Xuebei, ZHAO Weidong. Snap-through Buckling Analysis of P-FGM Shallow Spherical Shells under Thermomechanical Loads[J]. Journal of Mechanical Engineering, 2022, 58(24): 111-120.

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热-机荷载作用的P-FGM扁球壳跳跃屈曲分析

Snap-through Buckling Analysis of P-FGM Shallow Spherical Shells under Thermomechanical Loads

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