使用基于B-spline的同位测分析,对轴向函数分级的形蒂莫申科梁进行自由振动和曲折分析
Farzad Abdi1, Aazam Ghasemi2, Alireza Ariaei3
1Department of Mechanical Engineering, University of Delaware, Newark, DE, 19716, USA.
Heliyon
|January 21, 2025
概括
这项研究使用蒂莫申科束理论和同位测分析分析了轴向函数分级的形束. 该方法准确地预测了各种边界条件的临界屈曲负荷和自然频率.
科学领域:
- 机械工程 机械工程
- 结构分析 结构分析
- 计算力学 计算力学 计算力学
背景情况:
- 蒂莫申科光束理论对于分析较厚的光束而言至关重要,在这些光束中剪切变形是显著的.
- 同地形分析 (IGA) 在表示复杂的几何形状和精确的边界条件方面具有优势.
- 功能分级材料 (FGM) 提供了量身定制的材料特性,但它们在形梁中的分析需要先进的方法.
研究的目的:
- 为了研究轴向功能分级 (AFG) 形梁的自由振动和曲行为.
- 实施同立方分析 (IGA) 方法与蒂莫申科光束理论相结合,用于AFG形光束.
- 分析材料不均性,渐变率和边界条件对动态和稳定性特征的影响.
主要方法:
- 使用蒂莫申科束理论和汉密尔顿原理,推导治理方程.
- 用1D B-spline基础函数实现异地形分析 (IGA) 方法,用于位移近似.
- 选择性减少集成的应用,以减轻IGA方法中的剪切锁定.
主要成果:
- 这项研究成功地将IGA与蒂莫申科光束理论应用于AFG形光束.
- 选择性减少集成有效地减少了剪切锁定现象.
- 量化了材料特性 (密度,扬模量),缩比和边界条件对自然频率和临界曲折负荷的影响.
结论:
- 开发的IGA方法对于分析AFG形光束是准确和可靠的.
- 这些发现为在结构应用中设计和分析FGM提供了有价值的参考数据.
- 这项研究表明IGA在解决涉及FGM的复杂结构力学问题的有效性.
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