Symplectic Method Analysis of the Thermal Buckling Behavior of Graphene Origami-Reinforced Composite Beams

This study constructs a buckling analysis model integrating Euler–Bernoulli beam theory and Hamiltonian formulation to clarify the buckling characteristics of graphene origami (GOri)-reinforced beams and systematically explore the structural stability of graded composite beams. Under the symplectic space framework, the thermal buckling issue of GOri composite beams is converted into a zero-eigenvalue problem, where critical thermal buckling loads and corresponding buckling modes correspond to the symplectic eigenvalues and eigenfunctions of the Hamiltonian system. Taking the through-thickness continuity of GOri fillers into consideration, analytical expressions of buckling modes and critical buckling loads are derived using bifurcation criteria and normalization operations. Afterwards, parametric investigations are conducted to reveal how GOri content, spatial distribution, ambient temperature and folding degree affect beam buckling responses. Numerical results demonstrate that GOri distribution exerts a dominant influence on the structural buckling performance; critical thermal buckling loads tend to decline with rising folding degree and temperature. Reasonable optimization of GOri layout can significantly strengthen the mechanical capacity of composite beams, which lays solid theoretical guidance for their structural design and mechanical property enhancement.