A size-dependent Kirchhoff micro-plate model is developed based on the strain gradient elasticity theory. The model contains three material length scale parameters, which may effectively capture the size effect. The model can also degenerate into the modified couple stress plate model or the classical plate model, if two or all of the material length scale parameters are taken to be zero. The static bending, instability and free vibration problems of a rectangular micro-plate with all edges simple supported are carried out to illustrate the applicability of the present size-dependent model. The results are compared with the reduced models. The present model can predict prominent size-dependent normalized stiffness, buckling load, and natural frequency with the reduction of structural size, especially when the plate thickness is on the same order of the material length scale parameter.
The work is supported by the National Natural Science Foundation of China ( 50928601 and 10572077 ), Specialized Research Fund for the Doctoral Program of Higher Education of China ( 20060422013 ), Natural Science Fund of Shandong Province of China ( Y2007F20 ), WCU (World Class University) program through the National Research Foundation of Korea ( R32–2008–000–20042–0 ), International cooperation project of Tsinghua University ( 20091081236 ), National Science Foundation ( CMMI-0643726 ), China Scholarship Council , and Changjiang Scholar Program from Ministry of Education of China .
- Size effect
- Strain gradient elasticity