Thermal analysis of two-dimensional piezoelectric decagonal quasicrystal plates within a symplectic framework

The present study focuses on a two-dimensional decagonal quasicrystal (QC) plate under simply supported boundary conditions, and investigates its thermal elastic response under thermal loading applied to its top surface. Firstly, a Hamiltonian system is established based on the variational principle, from which the analytical expression of the extended displacement–traction vector is derived. Subsequently, through systematic parameter analysis, the individual effects of phonon-phason coupling elasticity, pyroelectric coefficient, and load amplitude are evaluated respectively. The proposed method not only controls that the relative error between the reference solution and the three-dimensional finite element results within 0.5%, but also significantly reduces the computational time by nearly two orders of magnitude. These results provide an efficient tool for the accurate design and optimization of QC composite structures. Furthermore, the analytical solutions obtained through derivation can serve as a benchmark for numerical algorithms such as finite integral transform and finite element method. On the other hand, they provide a theoretical foundation for precise analysis and optimal design of QC-based composites.