Combined Axial and Bending Stiffness in Interval Finite-Element Methods

This paper presents a new approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Parameter uncertainties are introduced as interval numbers. Interval arithmetic is applied to finite-element method to analyze the structural responses due to uncertain loading, axial and bending stiffness. However, a naïve use of interval arithmetic in the formulation of finite-element method, i.e., replacing the deterministic parameters with corresponding interval ones, will result in meaningless wide results due to the so-called dependency problem. In the present approach, an element-by-element technique is used to reduce the overestimation and compatibility conditions are ensured by a penalty method. With the newly developed overestimation control, most sources of overestimation are eliminated and a very sharp enclosure for the system response is obtained. A number of numerical examples are introduced.