使用连续光束的象征矩阵结构分析推导分析解决方案
1Department of Civil and Environmental Engineering, College of Engineering, Qatar University, P.O. Box: 2713, Doha, Qatar. vplevris@qu.edu.qa.
Scientific reports
|May 7, 2025
概括
在矩阵结构分析 (MatSA) 中的符号计算为连续束提供了分析解决方案. 这种方法增强了设计探索,并通过明确的参数关系来帮助理解结构力学.
科学领域:
- 结构工程 结构工程
- 计算力学 计算力学 计算力学
- 符号计算是一种象征性计算.
背景情况:
- 传统的矩阵结构分析 (MatSA) 通常依赖于数值方法.
- 导出复杂结构的分析表达式,如连续束,可能是具有挑战性的.
- 对于在结构力学中进行深入,符号驱动的灵敏度分析的工具有限.
研究的目的:
- 调查在MatSA中对连续光束的符号计算的应用.
- 开发一个开源的 MATLAB 程序用于连续光束的符号分析.
- 展示象征性MatSA在设计探索和教育中的好处.
主要方法:
- 使用 MATLAB 符号数学工具箱进行符号计算.
- 应用象征性的MatSA来导出对位移,反应和内部力的分析表达式.
- 将衍生方法实施到一个开源的 MATLAB 程序中.
主要成果:
- 对于移位,支反应和内部力量的分析表达式被成功衍生出来.
- 通过直接计算部分导数,实现了高效和可扩展的灵敏度分析能力.
- 一个开源的 MATLAB 程序被开发用于在各种负载下对连续光束进行象征性分析.
- 该程序有助于导出影响线和确定最大响应值.
结论:
- 符号计算为连续光束提供了一个对MatSA的强大方法,为结构行为提供了更深入的见解.
- 这种方法提升了设计探索,并通过澄清参数关系来帮助工程教育.
- 开发的开源工具促进了在结构工程中更广泛地采用和理解象征性的MatSA.
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