Abstract
The analysis of wave propagation has been extensively used as a tool for non destructive evaluation of structural components. The numerical analysis of wavefield in damaged media can be useful to investigate the problem theoretically and to support the interpretation of experimental measurements. A finite element analysis of non homogeneous media can be computationally very expensive, especially when a fine mesh is required to properly model the geometric and/or material discontinuities that are characteristic of the damaged areas. The computational cost associated with wave propagation simulations motivates the development of the simplified damage models presented in Chaps. 6 and 7. This chapter presents a different approach whereby the computational cost is reduced through a multi-scale analysis. A coarse mesh is employed to capture the macroscopic behavior of the structure, and a refined mesh is limited to the small region around the discontinuity. The co-existence of two scales in the model is handled through the application of proper bridging relations between the two scales, and the generation of interaction forces at the interfaces according to the Bridging Scales Method. This technique allows a coarse description of the global behavior of the structure while simultaneously obtaining local information regarding the interaction of propagating waves with a localized discontinuity in the domain. Time and frequency domain formulations of the Bridging Scales Method are illustrated through examples on simulations of 1D and 2D waveguides.
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References
Gonella S, Ruzzene M (2008) Bridging scales analysis of wave propagation in heterogeneous structures with imperfections. Wave Motion 45:481–497
Kadowaki H, Liu WK (2004) Bridging multi-scale method for localization problems. Comput Methods Appl Mech Eng 193(30–32):3267–3302
Liu WK, Chen Y, Chang C, Belytschko T (1996) Advances in multiple scale kernel particle methods. Comput Mech 18(2):73–111
Liu WK, Karpov E, Park H (2006) Nano mechanics and materials. Theory, multiscale methods and applications. Wiley, New York
Liu WK, Park HS, Qian D, Karpov EG, Kadowaki H, Wagner GJ (2006) Bridging scale methods for nanomechanics and materials. Comput Methods Appl Mech Eng 195(13–16):1407–1421
McVeigh C, Vernerey F, Liu WK, Brinson LC (2006) Multiresolution analysis for material design. Comput Methods Appl Mech Eng 195(37–40):4291–4310
Park HS, Liu WK (2004) An introduction and tutorial on multiple-scale analysis in solids. Comput Methods Appl Mech Eng 193(17–20):1733–1772
Wagner G, Liu W (2003) Coupling of atomistic and continuum simulations using a bridging scale decomposition. J Comput Phys 190(1):249–274
Weeks W (1966) Numerical inversion of laplace transforms using laguerre functions. J Assoc Comput Mach 13(3):419
Weideman J (1999) Algorithms for parameter selection in the weeks method for inverting the laplace transform. SIAM J Sci Comput 21(1):111–128
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© 2011 Springer-Verlag London Limited
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Gopalakrishnan, S., Ruzzene, M., Hanagud, S. (2011). Bridging Scales Analysis of Wave Propagation in Heterogeneous Structures with Imperfections. In: Computational Techniques for Structural Health Monitoring. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-284-1_8
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DOI: https://doi.org/10.1007/978-0-85729-284-1_8
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