Probabilistic finite element analysis using ANSYS

Driven by stiff competition, industrial manufacturers find themselves under growing pressure to optimize apparently conflicting technical and financial goals in an environment of ever increasing product complexity. In addition, this challenge is to be met under the existence of randomness and uncertainty, which the products are subjected to. Consequently, finding the right balance between conflicting goals under the existence of uncertainties requires the use of probabilistic tools. To achieve this, ANSYS Inc. has released two tools, namely the ANSYS Probabilistic Design System and the ANSYS DesignXplorer. This paper describes the problems that can be addressed, the underlying algorithms implemented and methodologies of these methods in both tools. A special topic of the paper is the discussion and explanation of the Variational Technology, which is offered in both tools. Variational Technology is a highly efficient method to provide accurate, high-order response surfaces based on a single finite element analysis. The capabilities, strengths and weaknesses of these methods are discussed. The possibility to reduce the execution time using parallel computing is discussed. Different measures to assess the accuracy and validity of the results obtained with the different probabilistic methods are given special attention. Various capabilities to post-process the probabilistic results are mentioned. The methods and the capabilities to optimize multiple and possibly conflicting goals are highlighted. Finally, the application of the software is illustrated using various industrial example problems. (c) 2005 Elsevier Ltd. All rights reserved.