Equivalence of Refined Theory and Decomposed Theorem of Thermoelastic Beams under Steady Temperature
Gao Yang(1),Wang Minzhong(2)
(1 China Agricultural University, Beijing 100083) (2 Peking University, Beijing 100871)

Abstract: The decomposition theorem of thermoelastic beams without transverse surface loadings is proposed, and that the general state of stress of beams can be decomposed into three parts, ie., the interior state, thermal state and Papkovi ch-Fadle state (shortened form the P-F state) is concluded. Based on thermoelas ticity theory, the refined theory of thermoelastic beams is derived by using the rmoelastic solution and Lur'e method without adhoc assumptions, and the exact equations for the beam without transverse surface loadings consist of three gover ning differential equations: the fourth-order equation, temperature equation and transcendental equation. It is then proved that the refined beam theory and the decomposed beam theorem are equivalent—the fourth-order equation, tempera ture equation and transcendental equation are equivalent to the interior state, thermal state and P-F state respectively.
Keywords: thermoelasticity, rectangular beams, the refined theory, the decomposed theorem, equivalence.