定常温度热弹性板的精化理论

A REFINED THEORY OF THERMOELASTIC PLATES UNDER STEADY TEMPERATURE

本文首先给出了定常温度热弹性 Ｂｉｏｔ［１］通解的一种新的简化形式，它看起来与各向同 性弹性力学的Ｐａｐｋｏｖｉｃｈ－Ｎｅｕｂｅｒ 通解十分相象，而后由此出发，由一般的各向同性弹性板推 广到本文的热弹性板问题，研究了热弹性板的问题，在没有任何预先假设的前提下，应用Ｌｕｒ’ｅ 算子法，证明了此通解不失一般性，导出了热弹性板精化理论的控制微分方程。

In this paper a new simplified form of Biot's general solution for the steady thermoelastic plates is given first. It looks like the famous Papkovich-Neuber's general solution of isotropic elastic mechanics. Generalized from problems of isotropic elastic plates, the problems of thermoelastic plates are focused A new refined plate theory is derived by using Lur'e operator from the Biot's general solution given above without any prior hypothesis. In the meantime, the proof that the Biot's general solution does not lose any generality is given.