%0 Journal Article
%A Mohammadi, Meisam
%A Fooladi, Majid
%A Darijani, Hossein
%D 2015
%I Begell House
%K Kirchhoff plate theory, modified strain gradient, buckling analysis, adjacent equilibrium criterion
%N 3
%P 265-280
%R 10.1615/IntJMultCompEng.2015012015
%T EXACT BOUNDARY CONDITIONS FOR BUCKLING ANALYSIS OF RECTANGULAR MICRO-PLATES BASED ON THE MODIFIED STRAIN GRADIENT THEORY
%U http://dl.begellhouse.com/journals/61fd1b191cf7e96f,2906a3f51d153722,12ded47631b1f6c6.html
%V 13
%X A size-dependent Kirchhoff plate model is developed for determining the exact boundary conditions and pre-buckling forces for buckling analysis of rectangular micro-plates. Modified strain gradient theory with three length scale parameters is considered for better capturing the effects of micro-structures. Also, it can be reduced to the couple stress theory or the classical plate theory by setting two or all length scale parameters to zero, respectively. Using the variational approach and the adjacent equilibrium criterion, all possible boundary conditions (consisting of simply supported, free, and clamped) in addition to the governing equations are derived. In order to complete the boundary conditions, a detailed explanation for determining the pre-buckling forces of micro-plates is presented. Finally, the stability equations are solved analytically for some typical cases of boundary conditions to determine the critical buckling loads of micro-plate. Consequently, the effects of length scale parameters and dimensions on the governing equations, boundary conditions, and also critical buckling loads are investigated in detail.
%8 2015-05-21