This investigation presents a comprehensive study of scale-dependent free vibration and static bending behaviors of bio-inspired helicoidal laminated composite (BHLC) microplates using a computational approach that combines refined plate theory (RPT) with isogeometric analysis (IGA). The modified strain gradient theory (MSGT) captures micro-scale effects through three material length-scale parameters (LSPs), while the RPT accurately describes transverse shear deformation without requiring shear correction factors. Bio-inspired configurations are modeled to reproduce the enhanced stiffness-to-weight ratios and improved mechanical performance observed in natural structures, such as mantis shrimp dactyl clubs and fish scales. The governing equations are derived using Hamilton’s principle and discretized through non-uniform rational B-Spline (NURBS)-based IGA to ensure geometric exactness and higher continuity in microplate formulations. Convergence studies are conducted to verify numerical stability and comparisons with available solutions confirm the accuracy and reliability of the proposed approach. Parametric investigations reveal the influences of material gradation, geometric parameters and LSPs on natural frequency and deflection of the BHLC microplates. The results indicate that size effects are significantly amplified as structural dimensions align with the material's intrinsic length scales. Furthermore, the study confirms that BHLC architectures offer superior mechanical performance compared to conventional cross-ply and angle-ply configurations. Moreover, the developed methodology provides an efficient and accurate computational tool for vibration and bending analyses of advanced micro-scale laminated structures, which can be applied for the design and optimization of bio-inspired engineering applications, including micro-electromechanical systems (MEMS), micro-robotics, protective armor systems and other advanced structures.
Hung et al. (Mon,) studied this question.