Numerical Modeling of Complex Geometry Thin Composite Structures under Vibrational Testing

Stepan A. Lavrenkov; Ivan E. Smirnov; Dmitrii A. Kravchenko; Katerina A. Beklemysheva; Alexey V. Vasyukov

doi:10.14529/jsfi240402

Authors

Stepan A. Lavrenkov Moscow Institute of Physics and Technology, Dolgoprudny, Russia https://orcid.org/0009-0009-2562-3371
Ivan E. Smirnov Moscow Institute of Physics and Technology, Dolgoprudny, Russia https://orcid.org/0009-0009-9590-7257
Dmitrii A. Kravchenko Moscow Institute of Physics and Technology, Dolgoprudny, Russia; Keldysh Research Center, Moscow, Russia https://orcid.org/0000-0003-1341-6075
Katerina A. Beklemysheva Moscow Institute of Physics and Technology, Dolgoprudny, Russia https://orcid.org/0000-0003-2769-6688
Alexey V. Vasyukov Moscow Institute of Physics and Technology, Dolgoprudny, Russia https://orcid.org/0000-0003-0513-1395

DOI:

https://doi.org/10.14529/jsfi240402

Keywords:

inverse problem, vibrational testing, automatic differentiation, openmp, jax

Abstract

This paper considers the inverse problem of material elastic properties identification from vibrational testing data. The present work aims to describe the approach that uses different kinds of optimizations to allow fast inverse problem solution using single modern multicore CPU or GPU. This includes choosing the model that allows to minimize the computational cost still reproducing the experimental results with good quality. The model for mid-surface symmetric isotropic and composite plates that are moving in vibrational stand is provided. The inverse problem is formulated in terms of the loss function minimization and the solution is computed with stochastic global optimization algorithm and second-order local optimization algorithm, which uses automatic differentiation of the forward problem solver to compute the derivatives. The paper describes parallelization for CPU and GPU and also the approach to reduce RAM usage to fit into single server RAM or single GPU VRAM. The numerical experiments presented in the paper demonstrate the solutions for complex rheologies and geometries: laminated composite plates, isotropic materials with frequency dependent elastic properties, perforated samples.

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