含弱界面的微纳尺度双层梁的热弹性分析

Thermo-Elastic Analysis of Micro-and Nano-Scaled Bilayer Beams with Weak Interface

众多微尺度实验已经证实了一些材料在微纳尺度下的力学行为具有尺寸效应.这种现象采用经典的弹性理论无法得到合理的解释,因而需要新的理论,修正偶应力理论就是其中一种.采用修正偶应力理论研究微纳尺度下两端自由铁木辛柯双层梁受热载荷后的弯曲响应,考虑两层之间存在弱界面.获得了梁的挠度、曲率以及界面剪力等表达式,并与经典弹性力学的结果进行了比较.通过分析计算可知,采用修正偶应力理论可预测微纳尺度下双层梁的尺寸效应,而当梁的特征尺寸远大于其材料的内禀尺度时,则与经典理论的结果一致.

It is confirmed by many experiments that the mechanical behavior of some materials at micro-and nano-scales is size-dependent. A reasonable explanation of such a phenomenon, giving birth to new theories, including the modified couple stress theory can＇t be given by the classical theory of elasticity. In this paper, a Timoshenko type beam theory based on the couple stress theory was proposed for the analysis of micro- and nano-scaled bilayer beams with free ends and subjected to thermal loading by incorporating the weak interface between the two layers. The expressions for the beam deflection, curvature, and interracial shear force can be obtained explicitly and they were compared with the results of the classical elasticity. The numerical results indicate that, the modified couple stress theory can well predict the size effect of micro-and nano-scaled bilayer beam, while it agrees well with the classical theory when the characteristic size of the beam is much larger than the intrinsic scale length of the material.