Nonlinear elastodynamic material identification of heterogeneous isogeometric Bernoulli-Euler beams

TL;DR

This paper introduces a finite element model updating framework for identifying heterogeneous material distributions in Bernoulli-Euler beams using isogeometric analysis and modal data, demonstrating accurate results even with noisy measurements.

Contribution

It presents a novel two-step identification process combining static and modal data within an isogeometric finite element framework, including regularization and optimization techniques.

Findings

Accurate material distribution reconstruction with sufficient experimental data.

Robustness against measurement noise up to 4%.

Effective use of regularization for dense material meshes.

Abstract

This paper presents a Finite Element Model Updating framework for identifying heterogeneous material distributions in planar Bernoulli-Euler beams based on a rotation-free isogeometric formulation. The procedure follows two steps: First, the elastic properties are identified from quasi-static displacements; then, the density is determined from modal data (low frequencies and mode shapes), given the previously obtained elastic properties. The identification relies on three independent discretizations: the isogeometric finite element mesh, a high-resolution grid of experimental measurements, and a material mesh composed of low-order Lagrange elements. The material mesh approximates the unknown material distributions, with its nodal values serving as design variables. The error between experiments and numerical model is expressed in a least squares manner. The objective is minimized using local optimization with the trust-region method, providing analytical derivatives to accelerate computations. Several numerical examples exhibiting large displacements are provided to test the proposed approach. To alleviate membrane locking, the B2M1 discretization is employed when necessary. Quasi-experimental data is generated using refined finite element models with random noise applied up to 4%. The method yields satisfactory results as long as a sufficient amount of experimental data is available, even for high measurement noise. Regularization is used to ensure a stable solution for dense material meshes. The density can be accurately reconstructed based on the previously identified elastic properties. The proposed framework can be straightforwardly extended to shells and 3D continua.