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资源，这些工具包括不确定性，并将解决各种制造产品。与以往的概率方法处理设计中的不确定性，所开发的方法将不确定性的可能值表示为传统的公差。 将开发的方法和工具有其基础模糊集理论，这使得制定有一个强大的数学基础与严格的分析开发的方法。 这项工作将首先解决机械部件的静态应力分析问题中的载荷不确定性和载荷组合的处理。 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。 沿着分析方法的开发，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，将基于模糊计算的结果评估与组合解决方案进行比较。 然后将该方法扩展到时间相关的问题。 这项研究的结果将提供方法和软件工具，包括通过传统的公差组件的应力分析的不确定性。 公差方面的不确定性的表达将允许设计工程师使用熟悉的概念在分析中包括不确定性。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）。 该软件工具将包括用于求解稀疏的、基于模糊的方程组和集成单元刚度矩阵的方法，并将允许将所开发的方法并入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，设计人员将能够在设计决策中常规地考虑几何形状、材料和环境载荷的不确定性的影响。 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.