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In order to ensure the safety of a structure, adequate strength for structural elements must be provided. Moreover, catastrophic deformations such as buckling must be prevented. Using the linear finite element method, deterministic buckling analysis is completed in two main steps. First, a static analysis is performed using an arbitrary ordinate applied loading pattern. Using the obtained element axial forces, the geometric stiffness of the structure is assembled. Second, an eigenvalue problem is performed between structure's elastic and geometric stiffness matrices, yielding the structure's critical buckling loads. However, these deterministic approaches do not consider uncertainty the structure's material and geometric properties. In this work, a new method for finite element based buckling analysis of a structure with uncertainty is developed. An imprecise probability formulation is used to quantify the uncertainty present in the mechanical characteristics of the structure.

The lightweight seat of a high performance car is designed taking into account a rear impact, i.e. the crash due to an impulse applied from the rear. The basic parameters of the seat structure are derived resorting to simulations of a crash with a test dummy positioned on the seat. The simulations provide the forces acting at the seat structure, in particular the forces applied at the joint between the seat cushion and the seat backrest are taken into account. Such a joint is simulated as a plastic hinge and dissipates some of the crash energy. The simulations are validated by means of indoor tests with satisfactory results. A tool has been developed for the preliminary design of lightweight seats for high performance cars.