Symplectic approach for accurate buckling analysis in decagonal symmetric two-dimensional quasicrystal plates

Abstract

This study employs a symplectic approach to investigate the buckling behavior of decagonal symmetric two-dimensional quasicrystal plates. The symplectic approach, known for its high flexibility and broad applicability, has become an essential tool in elasticity theory for addressing complex boundary conditions and material characteristics. Quasicrystalline materials exhibit unique elastic responses due to their quasiperiodic structures, which pose challenges that traditional semi-inverse methods often cannot handle. In contrast, the symplectic approach simplifies the analytical process of high-order differential equations without requiring additional potential functions, making variable separation and eigenfunction expansion more efficient. To effectively apply the symplectic approach, this study transforms the governing equations into Hamiltonian dual equations, enabling precise solutions to the eigenvalue problem to identify critical buckling loads and analyze buckling modes under six typical boundary conditions. The results are validated through comparison with existing literature, further demonstrating the reliability and accuracy of the symplectic approach in such problems. Additionally, this study systematically explores the effects of geometric parameters (such as aspect ratio and thickness-to-width ratio), coupling constants, and their influence on phason field elastic constants, revealing their critical roles in the buckling modes of quasicrystal plates. This research provides a new theoretical perspective on the stability analysis of quasicrystal plates, showcasing the unique advantages of the symplectic approach in the analysis of complex structures and materials.