Study on MLS meshless method for linear bending and free vibration of piezolaminated stiffened plates
摘要
Stiffened piezoelectric laminated plates integrate piezoelectric functionality and enhanced structural performance, yet their accurate analysis is urgently in need of reliable methodological support, which constitutes the core motivation of this study. Based on the linear elastic piezoelectric constitutive relationship, this study proposes a Moving Least-squares (MLS) meshless Galerkin method for the linear bending and free vibration analysis of stiffened piezoelectric laminated plates. The method employs the MLS technique to construct the displacement field, incorporates electric potential degrees of freedom, and combines the First-order Shear Deformation Theory (FSDT). By superimposing the energy functionals of the plate and stiffeners to satisfy displacement compatibility, the governing equations are derived using the principle of minimum potential energy and Hamilton’s principle, respectively, while boundary conditions are handled via the full transformation method. To verify the accuracy, numerical simulations are conducted under different lamination schemes, load conditions, and boundary conditions, with results compared against ABAQUS finite element solutions and existing literature data. Findings show that compared to unstiffened plates, stiffeners significantly enhance local stiffness, reduce deformation, and increase natural frequencies. The proposed meshless method provides a reliable tool for the accurate analysis of stiffened piezoelectric laminated plates, and the optimal design of stiffeners can meet the demands of lightweight and high-stiffness smart structures in aerospace, marine, and other fields.