The conversion between thermal snap-through and bifurcation instabilities of metal foam sandwich beams by refined first-order shear theory

The bending, vibration, and buckling of metal foam structures under thermal loads have consistently attracted significant interest in various engineering applications. However, most theoretical models rely on numerical results, which obscure connections between the system parameters and the system response, and the thermal instability type of metal foam structures has not been clarified. This paper aims to investigates the instability type of metal foam sandwich beams under various temperature fields. The analysis incorporates three models for porosity distribution and two scenarios for temperature fields. Firstly, a nonlinear governing equation for metal foam sandwich beams under uniform and linear temperature fields is formulated by using refined first-order shear theory, Von Karman geometric nonlinearity, and the concept of physical neutral plane. Secondly, an analytical solution to the nonlinear integral-differential boundary value problem for metal foam sandwich beams is obtained by using the Nayfeh’s semi-inverse solution method. Finally, the instability type, post-buckling paths, and corresponding mechanism of metal foam sandwich beams are predicted by the analytical solution and free energy evaluation, respectively. The results indicate that the clamped-supported (CC) metal foam sandwich beam will experience bifurcation instability; however, the instability type of the simply-supported (S-S) metal foam sandwich beam transitions from bifurcation instability to snap-through as the pore distribution and temperature fields vary. Furthermore, the buckling resistance of metal foam sandwich beams can be substantially improved through meticulous optimization of material parameters. These findings are anticipated to provide novel insights and valuable references for the design and regulation of metal foam structures.