圆板的热后屈曲分析

Legendre Polynomial Applied to Thermal Postbuckling of Circular Plate

用Ｒｉｔｚ法对各向同性圆板在周边转动弹性约束下的热后屈曲进行了研究。挠度试函数用Ｌｅｇｅｎｄｒｅ多项式构成，径向位移则由所设抗度用精确的微分方程求出。与ＦＥＭ结果比较可以看出：该方法用于圆板热后屈曲分析，精度高、收敛快，有关结果可供设计圆板参考。

The thermal postbuckling of circular plate has been investigated by using Ritz method.Legendres polynomial, in the form of eq. (5), is used as a trial function of denection.Radial displacement is exactly solved from the partial differential equation and can be computed with eq. (8). Postbuckling thermal load parameter λNL is non-linear and can be computed with eq. (10)' γ=λNL/λL, where λL is linear thermal load parameter, becomes non dimensional and can be computed with eq. (12).Tables 1 and 2 show computed values of γ for simply supported and clamped circular plates respectively. The FEM results are taken from Ref. [4], and they show FEM method gives good conversence. Our Legendre polynomial as given in eq. (5) is the simplest possible and it already gives results very close to those of FEM method and thus taking Legendre polynomial as trial function leads to fast convergence.Table 3 gives thermal postbuckling results for elastically restrained edges. These results, to our best knowledge, have not appeared in the literature.