A Method for Static Interval Analysis of Uncertain Structures with Interval Parameters

By representing the uncertain parameters as interval numbers, the static linear interval equations about the structural system were obtained in this paper by means of the finite element method. These equations are linear interval equations, for which some solution methods were discussed and a step-dividing method was presented. In this method, the independent uncertain parameters were given the discrete values within each interval, and the linear interval equations were changed into the corresponding certain ones. And then the boundaries of every interval solution components are determined by searching for the maximum and minimum values of the equation solutions. Some mathematical examples were used to examine the correctness and efficiency of the algorithm and which was applied to static interval analysis of engineering problems. Compared with other methods, the calculation results show that the algorithm of this paper is efficient and accurate.

Fuzzy Analysis of Geometric Tolerances Using Interval Method

The quality and performance of any mechanical system are greatly influenced by the GD&T (geometric dimensioning and tolerancing) used in its design. A proper consideration of the various types of tolerances associated with different components could not only satisfy the assembly requirements, but also minimize the manufacturing cost. To satisfy the design and functional specifications, one has to know how various tolerance patterns affect the manufacturability and assemblability of the designed parts. Therefore, a thorough understanding of how different forms of mechanical tolerances interact with each other becomes a must for designers and manufacturers. The effects of form, orientation, and position tolerances on the kinematic features and dimensions of mechanical systems are analysed using a new approach, based on fuzzy logic, in this article. In this approach, the α-cut method is used with the mechanical tolerances concerned as intervals. The proposed approach represents a more natural and realistic way of dealing with uncertain properties like geometric dimensions. A typical mechanical assembly system involving form, orientation, and position tolerances is used as an illustrative example. As the fuzzy approach leads to systems of non-linear interval equations, a modified Newton-Raphson method is developed for the solution of these equations. The current approach is found to be effective, simple, and accurate and can be extended to the analysis and synthesis of any uncertain mechanical system where the probability distribution functions of the uncertain parameters are unknown.