In a virtual prototyping context the importance of physical uncertainty modelling has become more evident. The increased computational performance over the last years enlarges the potential in the use of large models (more DOF’s) and in the application of more advanced numerical methods. This results in more accurate models from the numerical point of view. Realistic numerical modelling however, besides flawless numerical modelling, requires high-fidelity from the physical point of view.
The method of Fuzzy FEM is appropriate to deal with the different physical parameter uncertainties as dimensional tolerances, scatter in material properties, structural design parameters. Interval analysis applied with the alfa-cut strategy is the basis for a fuzzy analysis. Main concern in the proposed interval analysis methods is to obtain conservative interval results using reasonable computational time. The fuzzy framework is applicable in different mechanical disciplines as e.g. dynamic analysis, static analysis. In the fuzzy analysis, the focus is on the investigation of the influence of different uncertainty model parameters on important performance measures.
This paper presents the application of the fuzzy principle on the static analysis of an industrial sized finite element model. The problem stated for the fuzzy frame is of black-box type, with inputs the uncertain parameters, and outputs the displacements and stresses. The proposed problem is used to compare and discuss different methods for interval analysis. On the one hand the classical implementations are considered: the vertex method and the global optimisation approach. On the other hand, two newly proposed techniques are used: the reduced optimisation, and the reduced response surface method. Furthermore the use of the fuzzy analysis technique is demontstrated as a large-scale design sensitivity tool.
