随机分布载荷作用下双向功能梯度材料悬臂梁的半解析模拟方法

doi:10.19936/j.cnki.2096-8000.20250928.003

复合材料科学与工程 ›› 2025, Vol. 0 ›› Issue (9): 16-26.DOI: 10.19936/j.cnki.2096-8000.20250928.003

随机分布载荷作用下双向功能梯度材料悬臂梁的半解析模拟方法

张龙¹, 张伟^1,2, 范钧滔¹, 廖文林^1*

1.中国空气动力研究与发展中心,绵阳621000;
2.国防科技大学空天科学学院,长沙410073

收稿日期:2024-07-05 发布日期:2025-10-23
通讯作者: 廖文林(1984—),男,博士,副研究员,研究方向为飞行器结构设计,liaowenlin1984@163.com。
作者简介:张龙(1991—),男,博士,工程师,研究方向为飞行器结构设计。
基金资助:
全军装备军内科研项目(JK20202A040525);四川省自然科学基金(2024NSFSC1349)

Semi-analytical simulation method for bi-directional FGM cantilever beam under stochastically distributed load

ZHANG Long¹, ZHANG Wei^1,2, FAN Juntao¹, LIAO Wenlin^1*

1. China Aerodynamics Research and Development Center, Mianyang 621000, China;
2. College of Aerospace Science and Engineer, National University of Defense Technology, Changsha 410073, China

Received:2024-07-05 Published:2025-10-23

摘要/Abstract

摘要： 为了研究随机分布载荷作用下的双向功能梯度材料(Functionally Graded Material,FGM)悬臂梁的力学行为,本文发展了一种高精度、高效率的半解析方法。首先介绍了双向FGM悬臂梁的物理模型,然后推导了其在随机分布载荷作用下的基本控制方程,并通过MATLAB编程实现了方程组的迭代求解。在此基础上开展了单向/双向FGM悬臂梁受纯弯曲载荷或均布载荷的算例分析,并与精确解、铁木辛柯梁理论解和梯度有限元方法解对比研究,结果表明本文方法收敛性好、计算精度高。最后,将本文方法用于双向FGM悬臂梁受线性分布载荷、正弦分布载荷或随机分布载荷作用下的力学行为模拟仿真分析,所得结果与梯度有限元方法模拟结果吻合较好,最大挠度、应力相对误差分别为2.11%、3.39%。

关键词: 双向功能梯度材料, 悬臂梁, 随机分布载荷, 半解析法, 有限元方法, 复合材料

Abstract: In order to study the mechanical behavior of bi-directional functionally graded material (FGM) cantilever beam under stochastically distributed load, a semi-analytical method of high precision and efficiency is developed in this paper. Firstly, the physical model of the bi-directional FGM cantilever beam is introduced, and then the basic control equations of the cantilever beam subjected to stochastically distributed load are derived. Then, iterative solution of the equations is complemented through MATLAB programming. Based on this, a case study of unidirectional/bi-directional FGM cantilever beams subjected to pure bending load or uniformly distributed load is carried out, where the results are compared with the exact solution, Timoshenko beam theory results and graded finite element method results, indicating that the proposed method has good convergence and high accuracy. Finally, the proposed method is used to simulate and analyze the mechanical behavior of bi-directional FGM cantilever beams under linearly distributed load, sinusoidally distributed load or stochastically distributed load. The results obtained are in good agreement with the simulation results of the gradient finite element method, where the maximum relative errors for deflection and stress are within 2.11% and 3.39%, respectively.

Key words: bi-directional FGM, cantilever beam, stochastically distributed loads, semi-analytical method, finite element method, composites

中图分类号:

TB332

张龙, 张伟, 范钧滔, 廖文林. 随机分布载荷作用下双向功能梯度材料悬臂梁的半解析模拟方法[J]. 复合材料科学与工程, 2025, 0(9): 16-26.

ZHANG Long, ZHANG Wei, FAN Juntao, LIAO Wenlin. Semi-analytical simulation method for bi-directional FGM cantilever beam under stochastically distributed load[J]. COMPOSITES SCIENCE AND ENGINEERING, 2025, 0(9): 16-26.

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随机分布载荷作用下双向功能梯度材料悬臂梁的半解析模拟方法

Semi-analytical simulation method for bi-directional FGM cantilever beam under stochastically distributed load

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