A Model Updating Method for Plate Elements Using Particle Swarm Optimization (PSO), Modeling the Boundary Flexibility, Including Uncertainties on Material and Dimensional Properties

Abstract

It is a well-known fact that, in a real engineering situation, fixtures are not ideally stiff, so numerical simulations using them are unlikely to present results that are consistent with the experimental ones. The present paper intends to describe a model updating methodology inserting translational and rotational springs in order to better represent the real clamping. For that purpose, the PSO stochastic optimization method will be used to determine the spring stiffness in an iterative way. In addition, uncertainties regarding the material properties, such as density and Young's Modulus, as well as workpiece dimensions, will also be taken into account in the optimization algorithm. Once the experimental natural frequencies and the geometry of the studied parts are known, the algorithm automatically updates the model, approximating the natural frequencies obtained from the numerical model to the experimentally obtained ones as closely as possible. In addition, the modal shapes of the updated simulation will be compared to the experimental data and to a rigid boundary simulation. Results will demonstrate that the proposed methodology efficiently represents the fixturing flexibility: both natural frequencies and mode shapes found were close to the real dynamic system.

Preface to the special issue of the International Symposium on Solid Mechanics (MecSol 2017)

“…• New Developments and Applications: beam-column (Hortencio and Falcón, 2018) and bolted (Vilela et al, 2018) connection design, assessment of flexible fixtures (Negri et al, 2018), and hydride formation and growth in metals (Souza et al, 2018).…”

Estimation of structural stiffness with the use of Particle Swarm Optimization

“…Moreover, the number of stiffness coefficients estimated may be too high to apply analytical optimization techniques. Due to these problems, the FEM update method was developed based on various forms of Artificial Intelligence (AI) techniques (Maia and Silva, 1997;Levin and Lieven, 1998;Marwala, 2010;Park et al, 2017;Negri et al, 2018;Bartilson et al, 2019;Bianconi et al, 2020;Kang et al, 2020;Naranjo-Pérez et al, 2020;Zhang and Sun, 2020). The main difference of the proposed method is that the computation of the cost function is not based on the modal sensitivity analysis (Fox and Kapoor, 1968;Adhiakri, 1999), but on the low dimensional eigenvalue problem.…”