Interval Based Methods for Uncertainty in Computer Aided Analysis

这笔赠款为设计和分析工具的开发提供了资源，这些工具包括不确定因素，并将针对各种制造产品。与以前处理设计中不确定性的概率方法不同，所开发的方法将根据以常规公差表示的可能值来处理不确定性。将要开发的方法和工具以模糊集合论为基础，这使得公式具有坚实的数学基础，并对所开发的方法进行了严格的分析。这项工作最初将解决机械部件静应力分析问题中载荷不确定性和载荷组合的处理问题。然后，开发的方法和软件将扩展到处理材料属性和部件几何的不确定性。在开发分析方法的同时，还将编写实现模糊几何的网格生成器等所需的软件工具。对基于模糊的计算结果的评估将在可能的情况下与组合解进行比较。然后将这些方法推广到时间相关问题。这项研究的结果将提供方法和软件工具，通过传统公差将不确定性包含在部件的应力分析中。以公差表示不确定度将允许设计工程师使用熟悉的概念在分析中包含不确定度。虽然这些方法是专门为固体力学开发的，但将适用于任何基于有限元的工程分析(传热学、流体力学、电场和磁场)。该软件工具将包括求解稀疏、基于模糊的方程组和积分单元刚度矩阵的方法，并将允许将开发的方法整合到现有的商业有限元程序中。当这些方法被包括在商业分析和设计程序中时，设计师将能够在设计决策中例行公事地考虑几何、材料和环境载荷的不确定性的影响。因此，使用这些工具进行产品设计的可靠性将得到提高。

This grant provides resources for the development of design and analysis tools that include uncertainties and that will address a variety of manufactured products. Unlike previous probabilistic methods for treating uncertainties in design, the developed method will treat uncertainties in terms of possible values expressed as conventional tolerances. The methods and tools that will be developed have their foundation in fuzzy set theory, which allows the formulation to have a strong mathematical base with rigorous analysis of the developed methods. The work will initially address the treatment of load uncertainty and loading combinations in problems of static stress analysis of mechanical components. The methods and software developed will then be expanded to treat uncertainty of material properties and component geometry. Along with developing the analysis methods, software tools will be written that are needed for implementations such as mesh generator for fuzzy geometry. Evaluation of results of the fuzzy based calculations will be compared to combinatorial solutions when possible. The methods will then be extended to time dependent problems. The results of this research will provide both the methods and software tools to include uncertainties in the stress analysis of components via conventional tolerances. The expression of uncertainties in terms of tolerances will allow design engineers to include uncertainties in analysis using a familiar concept. The methods, while developed explicitly for solid mechanics, will be applicable to any finite element based engineering analysis (heat transfer, fluid mechanics, electric and magnetic fields). The software tools will include methods for solving a sparse, fuzzy based system of equations and integrating element stiffness matrices and will allow the developed methods to be incorporated into existing commercial finite element programs. When such methods are included in commercial analysis and design programs, designers will be able to routinely consider the effects of uncertainties in geometry, materials, and environmental loading in design decisions. Hence, the reliability of product designs using these tools will be improved.