Fuzzy finite elements: Combination of Guyan reduction and a new method to solve linear fuzzy system

In practice it is sometimes very difficult and in many cases even impossible to define correct and unique input data for structural mechanics applications. Fuzzy numbers can represent the uncertain input for those cases. As a consequence fuzzy arithmetic, based on the extension principle can be applied to solve finite element problems with uncertain parameters. Application of fuzzy arithmetic directly to the traditional techniques for the numerical solution of finite elements however turns out to be impracticable, especially solving systems of linear equations. Here we present a new method to solve systems of linear fuzzy equations combined with Guyan Reduction. Our conclusions are confirmed by a simple static problem.