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We analyze the frequency response of structural dynamic systems with uncertainties in load and material properties. We introduce uncertainties in the system as interval numbers, and use Interval Finite Element Method (IFEM). Overestimation due to dependency is reduced using a new decomposition for the stiffness and mass matrices, as well as for the nodal equivalent load. In addition, primary and derived quantities are simultaneously obtained by means of Lagrangian multipliers that are introduced in the total energy of the system. The obtained interval equations are solved by means of a new variant of the iterative enclosure method resulting in guaranteed enclosures of relevant quantities. Several numerical examples show the accuracy and efficiency of the new formulation.

We present a new interval-based formulation for the static analysis of plane stress/strain problems with uncertain parameters in load, material and geometry. We exploit the Interval Finite Element Method (IFEM) to model uncertainties in the system. Overestimation due to dependency among interval variables is reduced using a new decomposition strategy for the structural stiffness matrix and the nodal equivalent load vector. Primary and derived quantities follow from minimization of the total energy and they are solved simultaneously and with the same accuracy by means of Lagrangian multipliers. Two different element assembly strategies are introduced in the formulation: one is Element-by-Element, and the other resembles conventional assembly. In addition, we implement a new variant of the interval iterative enclosure method to obtain outer and inner solutions. Numerical examples show that the proposed interval approach guarantees to enclose the exact system response.

In order to ensure the safety of a structure, adequate strength for structural elements must be provided. In addition, the catastrophic deformations such as buckling must be prevented. In most buckling analyses, structural properties and applied loads are considered certain. Using the linear finite element method, the deterministic buckling analysis is done in two main steps. First, a static analysis is performed using an arbitrary ordinate of applied load. Using the obtained element axial forces, the geometric stiffness of the structure is assembled. Second, performing an eigenvalue problem between the structure's elastic and geometric stiffness matrices yields the structure's critical buckling loads. However, these deterministic approaches disregard uncertainty in the structure's material and geometric properties. In this work, an interval formulation is used to represent the uncertainty in the structure's parameters such as material characteristics.