Free vibration and buckling analysis of bio-inspired helicoid laminated composite plates resting on Pasternak foundation using the first- order meshfree

This article investigates the buckling and free vibration behavior of bio-inspired helicoid laminated composite (BiHLC) plates resting on a Pasternak foundation (PF) using the meshfree moving Kriging (MK) method for the first time. In this study, the MK method leverages Reddy's first-order shear deformation theory (FSDT) for analysis of the mechanical behavior of plates. The PF is characterized by two stiffness parameters: spring stiffness k1 and shear stiffness k2. A key advantage of the MK interpolation is its Kronecker's delta property, enabling direct enforcement of boundary conditions (BC). Unlike original MK method, this approach does not require pre-defining the correlation parameter, which can influence approximation accuracy. The governing equations are derived using Hamilton's principle. A thorough analysis is conducted to understand how the helicoidal layup scheme, geometrical parameters, BC, and the foundation's stiffness parameters influence the critical buckling loads and natural frequencies of BiHLC plates.