论文标题
使用稀疏网格中的木材样梁中的不确定性定量:理论和示例带有现成的软件利用率
Uncertainty quantification in timber-like beams using sparse grids: theory and examples with off-the-shelf software utilization
论文作者
论文摘要
在处理木材结构时,材料的特征强度和刚度是由不可避免的但几乎无法预测的结和其他缺陷的高度变化和不确定的。在这项工作中,我们将稀疏的网格随机搭配方法应用于上述情况下对结构工程的不确定性定量。在过去的几十年中,数学社区已经开发了稀疏的网格,其理论背景经过严格而广泛的研究。该文档提出了一个简短的练习介绍,其理论背景最少,为使用已经实现的稀疏网格MATLAB试剂盒(在线免费提供)提供了详细的说明,并讨论了来自木材工程问题启发的两个数值示例,这些示例来自木材工程问题,突出了与普通的Monte Carlo Carlo方法相比,稀疏网格表现出卓越的性能。稀疏的网格MATLAB套件仅需要几行代码即可与任何用于机械问题的数值求解器连接(在这项工作中,我们使用了ISOOGEMONETRIC POTICOTACTACTACE方法),并提供可以在工程实践中轻松解释和使用的输出。
When dealing with timber structures, the characteristic strength and stiffness of the material are made highly variable and uncertain by the unavoidable, yet hardly predictable, presence of knots and other defects. In this work we apply the sparse grids stochastic collocation method to perform uncertainty quantification for structural engineering in the scenario described above. Sparse grids have been developed by the mathematical community in the last decades and their theoretical background has been rigorously and extensively studied. The document proposes a brief practice-oriented introduction with minimal theoretical background, provides detailed instructions for the use of the already implemented Sparse Grid Matlab kit (freely available on-line) and discusses two numerical examples inspired from timber engineering problems that highlight how sparse grids exhibit superior performances compared to the plain Monte Carlo method. The Sparse Grid Matlab kit requires only a few lines of code to be interfaced with any numerical solver for mechanical problems (in this work we used an isogeometric collocation method) and provides outputs that can be easily interpreted and used in the engineering practice.