基于新修正偶应力理论的Tmoshenko梁热稳定性与尺度效应分析

Thermal buckling analysis of composite laminated Tmoshenko beam founded in the new modified couple stress theory

基于新修正偶应力理论,首次提出了机械载荷与热载荷共同作用下的微尺度Tmoshenko层合梁热稳定性模型,该模型只需引入一个材料尺度参数。依据虚功原理推导了模型的控制方程和边界条件,以简支梁为例,通过使用纳维叶方法进行模型的热稳定性分析得到解析解。结果表明:所建模型可以捕捉到尺度效应。材料尺度参数越大,达到屈曲临界载荷时的温度越高,尺度效应越明显;随着屈曲临界温度的增高,屈曲临界载荷的数值不断增大,体现出温度对屈曲临界载荷的影响;增大梁的几何尺度参数到一定数值后,该模型退化为宏观经典模型。

Based on the new modified couple stress theory,the thermal stability model of micro-scale laminated Tmoshenko beam under mechanical load and thermal load was proposed for the first time.The model only needed to introduce a material scale parameter.According to the principle of virtual work,the governing equations and boundary conditions of the model could be derived.In this paper,the simply supported beam was taken as an example,the Navier method was used to analyze the thermal stability of the model and calculated the analytical solution.The results show that the model can obviously capture the scale effect.The larger the value of the material scale parameter is,the higher the temperature at the critical load of buckling is,and the more obvious the scale effect is;With the increase of the critical temperature,the value of the critical mechanical load increases continuously,thereby reflecting the effect of temperature on the critical load of buckling;When the scale parameter is used,the model can be degraded to the macroscopic classical model.