Elastoplastic thermal buckling of functionally graded material beams

Elastoplastic thermal buckling characteristics of ceramic-metal functionally graded material (FGM) beams subjected to transversely non-uniform temperature rise are investigated by symplectic method in Hamiltonian system. Based on TTO model, the linear hybrid hardening elastoplastic model is used to simulate the elastoplastic material properties and establish thermal elastoplastic constitutive equations of FGM beams. Then, the canonical equations are established to transform critical loads and buckling modes into symplectic eigenvalues and eigensolutions in symplectic space. The main contributions of this study are that complete buckling mode space and critical thermal axial forces for elastoplastic thermal buckling of the FGM beams are obtained by analytical solutions; meanwhile, buckling temperatures and elastoplastic interfaces of the bucked FGM beams are obtained by inverse solutions. Numerical examples of buckling behaviors varying with thermal load, slenderness ratio and power law index are presented. The effects of elastoplastic material properties on critical temperatures and plastic zone are analyzed and discussed.