Accuracy and Convergence Using a Local Interaction Simulation Approach in One, Two, and Three Dimensions

Abstract

Guided waves are utilized in structural health monitoring for identifying damage in material components. Simulations can be used to examine how elastic waves propagate in components to help in selecting measurement and data analysis techniques. In this work, the influence of grid size and the frequency sample rate on the amplitude accuracy and convergence of local interaction simulation approach/sharp interface model (LISA/SIM) numerical simulations are studied as they pertain to guided wave propagation in structural materials. These issues are studied in all three dimensions, and amplitude distortion with respect to the Courant–Friedrich–Lewy criterion is explored. The LISA/SIM enables accurate and fast modeling of localized and sharp changes in material properties across interfaces associated with heterogeneities and/ or boundaries. The validity of the simulation is demonstrated by comparing simulated responses with experimentally measured data. Additionally, Lamb wave dispersion curves are extracted through the course of the convergence study using a broadband pulse and the two-dimensional fast Fourier transform method.

Hybrid Global Matrix/Local Interaction Simulation Approach for Wave Propagation Simulation in Composite Laminates

“…Previous researchers 20 have noted the dependence of LISA results on the in-plane discretization. This dependence is also seen in the present LISA Hybrid results, particularly in the group velocity of the propagating wave.…”

“…Sundararaman and Adams used a three-dimensional LISA formulation to study the effect of simple damage in isotropic and unidirectional orthotropic plates 9 and subsequently examined the effects of grid size. 20 Recently, Nadella and Cesnik 15, 21 extended the approach to simulate wave propagation in arbitrary composite laminates and expanded the 3-D formulation to account for plies in non-principal directions. The resulting iterative equations are used in this work, and they are included for reference in the appendix.…”

Simulation of Guided Wave Propagation in Isotropic and Composite Structures using LISA

“…The parameters (cuboid grid and time step) used in the discretization of the Eqs. (11)- (13) are selected based on the Courant-Friedric-Lewy (CFL) criterion. The CFL criterion is a constraint that bounds the time step and cell size by the relation:…”

Piezoelectric coupled LISA for guided wave generation and propagation

“…Traditional numerical tools such as finite elements (FE) are computationally inefficient because of the small wavelength discretizations required to attain converging results. It has been shown that local interaction simulation approach (LISA) [9,10], a numerical method based on finite difference (FD) transformations is capable of efficiently and accurately modeling GW propagation. This method is based on iterative equations (IE) for "unit cells" that are used to represent/discretize the model.…”

“…LISA employs the sharp interface model (SIM) to address the issue of discontinuities and boundaries, which distinguishes it from the formal FD techniques. LISA has been used to study the wave propagation characteristics [11] [12] and accuracy of simulations [10] in isotropic plates. Furthermore, damage interaction and identification [13] also addressed in 2-D isotropic plates.…”