Isogeometric evaluation of higher-order shear deformation theories for functionally graded magneto-electro-elastic nanoplates under nonlocal strain gradient elasticity

We are happy to announce that Dr. Thai Hoang Chien and colleagues recently published their work entitled "Isogeometric evaluation of higher-order shear deformation theories for functionally graded magneto-electro-elastic nanoplates under nonlocal strain gradient elasticity" trên tạp chí Engineering Analysis with Boundary Elements.

Abstract:

The coupled influence of higher-order shear deformation theories (HSDTs) and nonlocal strain gradient theory (NSGT) on free vibration of functionally graded magneto-electro-elastic (FG-MEE) nanoplates has not been comprehensively examined. To bridge this gap, the present study develops a unified isogeometric analysis (IGA) framework to systematically evaluate and compare three HSDTs: the four-variable C¹, five-variable C¹ and seven-variable C⁰ formulations. The NSGT provides a powerful theoretical foundation for simultaneously capturing nonlocal softening and strain-gradient stiffening size effects. However, its weak-form implementation requires third- or fourth-order derivatives, which are incompatible with traditional finite element formulations when combined with the HSDTs. This limitation is overcome in the proposed approach by employing the IGA, where the high-order continuity of NURBS basis functions enables direct implementation without mixed formulations. The C^p-1 continuity of NUBRS easily satisfy the requirements for third-order and fourth-order derivatives inherent in C⁰ and C¹ theories. The numerical results show two key findings. First, the HSDT choice significantly affects the frequency predictions under the NSGT with this effect becoming stronger at the nanoscale compared to classical theories. Second, softening-to-stiffening transitions depend on NSGT parameters. While, HSDT models converge to identical predictions under the pure nonlocal theory, noticeable discrepancies emerge when strain-gradient effects are incorporated, indicating that the divergence originates exclusively from the gradient contribution. Ultimately, these results highlight the importance of HSDT selection in nanoscale multi-physics modelling. The proposed unified approach provides an efficient computational tool for the accurate analysis and design optimization of MEE nanodevices.