计算力学的可信性问题及其量化模型研究

项目名称： 计算力学的可信性问题及其量化模型研究

项目编号： No.10872146

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 轻工业、手工业

项目作者： 宣兆成

作者单位： 天津职业技术师范大学

项目金额： 31万元

中文摘要： 可信性是计算机软件产品的一个重要质量指标。计算力学软件是一种基于算法的应用软件，它除了要满足作为软件所要具备的可信性以外，还应具有对结果可信性的量化评价功能。计算力学方法求得的是近似解，因为它是用宏观尺度上的结果近似表达无限维尺度上的精确解。项目重点研究了光顺有限元方法，在理论方面不同于传统的以基于极小势能原理的全局结构位移为求解目标，提出一种以工程需求为求解目标的在连续介质范畴内的从有限维到无限维的两尺度算法，利用粗糙网格的计算信息求出在无限维空间中的目标的精确解所在的区间（即精确解的上界和下界），用上下界的平均值作为目标的预报值，用上下界的差值对预报值进行可信度量；同时构造基于可信度的自适应算法。项目将具体针对功能梯度材料的断裂问题，以其二次函数表达的失效指标为求解目标，给出其精确解可信度量。本方法是一种新的计算力学方法，可以处理一次和二次函数表达的目标及其精确解可信度量。已发表了15篇论文，其中2010年发表在国际杂志International Journal for Numerical Methods in Engineering的论文已在2011年被国外同行引用了7次。

中文关键词： 可信性；目标；尺度；自适应；断裂

英文摘要： Trustworthiness is an important computer software product quality index. Computational mechanics software is the algorithm-based application software, in addition to the usual trustworthiness that software should be met; a quantitative evaluation of the trustworthiness of the computation results is required. The results computed by computational mechanics method are an approximate, because the results are of the macro-scale expression of the exact solution that is in the infinite-dimensional scale. The project focuses on the smoothed finite element method, Not using the traditional principle of minimum potential energy that used to solve the global displacement of the structure, we propose, in the context of continuum, a two-scale algorithm that is from finite dimension to infinite dimension for the quantity of engineering interest, the information on the coarse mesh is used to find the interval, that is the upper and lower bounds, of the exact solution of the output that is in the infinite dimensional space, then the average of the upper and lower bounds can be used as a prediction of the output, and the difference between the upper and lower bounds as a quantitative evaluation of the trustworthiness, and a trustworthiness based adaptive algorithm can be constructed. The project will specifically address the fracture problem of functionally graded materials, express the failure index as a quadratic function, and give quantitative trustworthiness of its exact solution. This kind of method is new in computational mechanics; it can be used to handle the quantitative trustworthiness of the exact linear and quadratic outputs. A paper published in IJNME (International Journal for Numerical Methods in Engineering) in 2010 has been cited 7 times by foreign researchers in 2011.

英文关键词： Trustworthiness; Output; Scale; Adaptivity; Fracture