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Modelling analysis of surface stress on a rectangular cantilever beam

2004; Institute of Physics; Volume: 37; Issue: 15 Linguagem: Inglês

10.1088/0022-3727/37/15/014

1361-6463

Yin Zhang, Quan Ren, Ya‐Pu Zhao,

Mechanical and Optical Resonators

Three models of surface stress on a rectangular cantilever beam are presented. The surface stress is modelled as a corresponding concentrated moment at the beam free end, a corresponding concentrated moment plus a corresponding concentrated axial load at the beam free end, and a corresponding uniformly distributed axial stress plus bending moment per unit length along the beam span, respectively. The results of the three models are compared under three different loading scenarios. We also present an analysis of the error source, when using Stoney's formula to predict the surface stress, by comparing the kinematic and loading assumptions of the three models. The surface stress effects on structure deflection are usually modelled as bending moments applied at structure free edge(s)/end(s). Modelling the surface stress effect along the beam neutral axis is presented and compared with modelling its effect at free edge(s)/end(s). The stiffening effect of tensile surface stress is also studied.