Interval Based Methods for Uncertainty in Computer Aided Analysis

这项拨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性，并将处理各种制造产品。与以往处理设计不确定性的概率方法不同，所开发的方法将根据表示为常规公差的可能值来处理不确定性。将开发的方法和工具以模糊集合理论为基础，这使得该公式具有强大的数学基础，并对所开发的方法进行了严格的分析。这项工作将首先解决载荷不确定性和载荷组合在机械部件的静态应力分析问题的处理。开发的方法和软件将扩展到处理材料特性和部件几何形状的不确定性。随着分析方法的发展，将编写实现所需的软件工具，如模糊几何的网格生成器。在可能的情况下，将模糊计算结果的评价与组合解决方案进行比较。然后将这些方法扩展到时间相关问题。本研究的结果将提供方法和软件工具，包括不确定因素的应力分析，通过传统的公差。用公差表示不确定性将允许设计工程师使用熟悉的概念在分析中包含不确定性。这些方法虽然是为固体力学而开发的，但也适用于任何基于有限元的工程分析（传热、流体力学、电场和磁场）。软件工具将包括求解稀疏、模糊方程组和集成单元刚度矩阵的方法，并将允许开发的方法纳入现有的商业有限元程序。当这些方法被纳入商业分析和设计程序时，设计师将能够在设计决策中常规地考虑几何、材料和环境负荷等不确定性的影响。因此，使用这些工具的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.