微纳米尺度下考虑表面效应的圆形薄板的位移解

Displacement Solution of a Circular Thin Plate with Surface Effects at Micro / nanoscale

基于Gurtin的表面弹性理论,综合考虑板的表面弹性和残余表面应力的影响,建立了微纳米尺度下薄板承受横向分布载荷的力学模型.然后以周边固支的圆板承受横向均布载荷为例,求得了残余表面应力为零、取正值和取负值时的挠曲线.最后对板的位移解进行了分析,阐明了残余表面应力对于其变形的影响.这些计算和分析丰富了传统固体力学的研究范畴,并且为研制微型传感器、微机电系统等提供了一定的参考.

Based upon Gurtin＇ s theory of surface elasticity, the surface elasticity and residual surface stresswere both considered. As a result, the mechanical model of a thin plate under the action of the transverse dis-tributed load at micro/nanoscale was established. As a typical example, a circular plate under the action of thetransverse distributed load was analyzed, and the delfection curves when the redisual surface stress is zero, pos-itive and negative were solved respectively. Finally, these displacement solutions were discussed in detail, andthe effect of the residual surface stress on the deformation was addressed. These calculations and analyses haveenriched the scople of classical solid mechanics, and provided some references for the design of microsensorsand MEMS, etc.