基于新修正偶应力理论的Mindlin层合板热稳定性分析

Thermal buckling analysis of composite laminated Mindlin plate founded in the new modified couple stress theory

以新修正偶应力理论为基础,首次提出了机械载荷与热载荷共同作用下的微尺度Mindlin层合板热稳定性模型,该模型只引入一个材料尺度参数,通过虚功原理推导出了控制方程和边界条件,以四边简支方板为例,进行了热稳定性分析,应用纳维叶解法得到解析解。结果表明,所建模型可以捕捉到尺度效应。材料尺度参数值越大,屈曲临界温度越高;当跨厚比增大时,屈曲临界温度下降;随着板几何参数的增大,模型将退化为宏观模型;温度变化量越大,考虑热载荷作用下的屈曲临界载荷越大,尺度效应体现越显著。

Based on the new modified couple stress theory,a thermal stability model for Mindlin laminated plates under the interaction between mechanical and thermal loads is proposed for the first time.The model introduces only one material-scale parameter and through the principle of virtual work obtains the stability equations and boundary conditions.Using a simply supported square plate as an example,its analytical solution is obtained by using Navier’s method.The results show that the scale effect can be captured by the model.The critical buckling critical temperature goes up when the material scale parameter increases;when the span-thickness ratio increases,the critical temperature decreases;with the increase of the plate geometry parameter,the model will degenerate into a macroscopic model;when the temperature change is lager,the critical buckling load under thermal load becames lager and the scale effect became more obvious.