Fractional order models for the homogenization and wave propagation analysis in periodic elastic beams

Meccanica - The advancement of manufacturing techniques has led to a rapid increase in the design and fabrication of periodic and architectured materials for a variety of dynamics and wave...     

Modeling vibratory damage with reduced-order models and the generalized finite element method

This paper investigates a coupled computational analysis framework that uses reduced-order models and the generalized finite element method to model vibratory induced stress near local defects. The application area of interest is the life prediction of thin gauge structural components exhibiting nonlinear, path-dependent dynamic response. Full-order finite element models of these structural components can require prohibitively large amounts of processor time. Recent developments in nonlinear reduced-order models have demonstrated efficient computation of the dynamic response. These models are relatively insensitive to small imperfections. Conversely, the generalized finite element method provides the ability to model local defects without geometric dependency on the mesh. A more robust version of the method, with numerically built enrichment functions, provides a multiple-scale modeling capability through direct coupling of global and local finite element models. Replacing the component finite element model with a reduced-order model allows for efficient computation of dynamic response while providing the necessary information to drive local, solid analyses which can zoom in on regions containing stress risers or cracks. This paper describes the coupling of these approaches to enable fatigue and crack propagation predictions. Numerical/experimental examples are provided.