利用稀疏网格的类木材梁的不确定性量化：理论和实例与现成的软件利用
Uncertainty quantification in timber-like beams using sparse grids: theory and examples with off-the-shelf software utilization
摘要：
在处理木结构时，由于不可避免但难以预测的节和其他缺陷的存在，材料的特征强度和刚度变得高度可变和不确定。在这项工作中，我们应用稀疏网格随机配置法进行不确定性量化的结构工程在上述情况下。稀疏网格是近几十年来数学界发展起来的一种网格模型，其理论背景得到了广泛而深入的研究。该文件提出了一个简短的面向实践的介绍与最小的理论背景，提供了详细的说明，使用已经实现的稀疏网格Matlab工具包（免费提供在线），并讨论了两个数值例子的启发木材工程问题，突出稀疏网格如何表现出优越的性能相比，平原蒙特卡罗方法。稀疏网格Matlab工具包只需要几行代码就可以与任何力学问题的数值求解器连接（在这项工作中，我们使用了等几何配置法），并提供了可以很容易地解释和在工程实践中使用的输出。
英文摘要：
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.
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