Nonlinear elastodynamic material identification of heterogeneous isogeometric Bernoulli-Euler beams

2025-06-05

AI Summary

This study addresses the material parameter identification problem for heterogeneous Bernoulli–Euler beams undergoing nonlinear large deformations. A two-stage isogeometric model updating framework is proposed: first, the spatially varying elastic modulus distribution is inverted from quasi-static displacement fields; second, the density distribution is reconstructed using low-frequency modal data. Innovatively, a rotation-free isogeometric beam formulation, B2M1 membrane-locking-free elements, and a triple independent discretization strategy—separately for finite element modeling, experimental measurements, and material parameter representation—are adopted to achieve decoupled identification of elastic modulus and density. The method integrates trust-region optimization, analytical gradient computation, and Tikhonov regularization, ensuring robustness under 4% high noise levels and yielding high reconstruction accuracy for both parameters. Validation covers complex heterogeneous distributions and fine material grids, and the framework naturally extends to shell and 3D continuum structures.

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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.

Problem

• Identify heterogeneous material distributions in beams
• Determine density from modal data and elastic properties
• Minimize error between experiments and numerical model

Innovation

• Isogeometric FEM for material identification
• Multi-step elastic and density determination
• Trust-region optimization with analytical derivatives