Structural design of uncertain mechanical systems using interval arithmetic

This paper deals with a method to analyze the modal characteristics of structures including bounded uncertain parameters. These parameters can be uncertain, variable or not set at a design stage. We will use interval theory to propose a formulation adapted to finite element mechanical problems, taking into account the construction of mass and stiffness matrices. We will consider two kinds of problems: finding the bounds of static problem solutions, and the envelopes for transfer functions. A new numerical method will be used, based on the formulation proposed above. We will emphasize the efficiency of this method on simple mechanical problems. A frame structure will be studied, for which an overlap phenomenon appears on the transfer function envelope.