Unified Finite Element Method for Engineering Systems with Hybrid Uncertainties

Abstract

The finite element method (FEM) is established as one of the most popular and powerful tools in analysis and design of engineering systems. However, the method can only be used at an advanced (or detail) design stage when a designer has developed sufficient confidence in the design scheme. In the early (or conceptual/ preliminary) design phase, the method can not be used directly due to the existence of uncertainties of various types. In this work, a procedure is proposed for the FEM to handle engineering systems in the presence of hybrid uncertainties that are characterized by randomness (or stochastic uncertainty) and fuzziness (or design imprecision). The proposed scheme utilizes the techniques of stochastic and fuzzy FEMs in a unified manner to investigate the effects of both input random and fuzzy uncertainties on the output system response. Interpretations of the generated solution space and guidelines in selection of an appropriate solution, according to specific design requirements, are discussed. Two numerical examples are presented to illustrate the computational aspects of the proposed scheme. The current procedure is expected to enhance the understanding of designers regarding the effects of uncertainties in an evolutionary design process, especially in the conceptual or preliminary design phase.