Stress recovery algorithm for reduced order models of mechanical systems in nonlinear dynamic operative conditions

Nonlinear forced response analyses of mechanical systems in the presence of contact interfaces are usually performed in built-in numerical codes on reduced order models (ROM). Most of the cases these derive from complex finite element (FE) models, resulting from the high accuracy the designers require in modeling and meshing the components in commercial FE software. In the technical literature several numerical methods are proposed for the identification of the nonlinear forced response in terms of a kinematic quantity (i.e. displacement, velocity and acceleration) associated either to the master degrees-of-freedom retained in the ROM, or to the slave ones after having expanded the reduced response through the reduction matrix. In fact, the displacement is the quantity usually adopted to monitor the nonlinear response, and to evaluate the effectiveness of a partially loose friction interface in damping vibrations, with respect to a linear case where no friction interfaces exist and no energy dissipation can take place. However, when a ROM is used the engineering quantities directly involved in the mechanical design, i.e. the strains and stresses, cannot be retrieved without a further data processing. Moreover, in the case of a strong nonlinear behavior of the mechanical joints, the distributions of the nonlinear strains and stresses over the structure is likely different than the one obtained as a superposition of linear mode shapes whose definition require a-priori assumptions on the boundary conditions at the contact interface. This means that the mentioned approximation cannot be used to predict the safety margins of a structure working in real (nonlinear) operative conditions. This paper addresses this topic and presents a novel stress recovery algorithm for the identification of the strains and stresses resulting from a nonlinear forced response analysis on a ROM. The algorithm is applied to a bladed disk with friction contacts at the shroud joint, which make the behavior of the blades nonlinear and non-predictable by means of standard linear analyses in commercial FE software.