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使用符号矩阵结构分析推导分析解决方案:第二部分 - 平面托架
1College of Engineering, Qatar University, P.O. Box: 2713, Doha, Qatar.
Heliyon
|March 4, 2025
概括
本研究介绍了一种开源的 MATLAB 程序,用于对 2D 托架进行符号分析,为结构行为提供准确的解决方案. 该工具可实现高效的灵敏度分析,并与商业软件进行验证.
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通常依赖于数值方法,限制了对参数敏感性的洞察力.
- 以前的符号计算应用主要集中在连续束上,为其他结构留下分析的空白.
- 开发先进的计算工具对于提高结构设计和工程教育至关重要.
研究的目的:
- 将符号计算扩展到二维平面托架的矩阵结构分析.
- 开发和介绍一个完全开源的 MATLAB 程序,用于对任何 2D 架构配置进行符号分析.
- 为结构性反应提供封闭形式的分析表达式,并实现高效的灵敏度分析.
主要方法:
- 使用MATLAB的符号数学工具箱来导出对位移,支反应和轴力的符号表达式.
- 开发了一个可扩展的框架,能够处理大规模的木架结构.
- 通过计算结构反应的部分导数来实现灵敏度分析.
主要成果:
- 为二维结构分析生成封闭形式的分析解决方案,为结构行为提供更深入的见解.
- 证明了符号计算对灵敏度分析的效率,帮助设计探索和优化.
- 与商业有限元软件和文献数据相比,成功验证了符号结果,证实了准确性和可靠性.
结论:
- 开发的符号计算方法是可靠的,可扩展的,并且广泛适用于2D结构分析.
- 开源的 MATLAB 工具通过澄清参数关系来增强工程实践和教育.
- 符号分析在理解和优化结构系统的数值方法上提供了显著的优势.
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