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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2015012015
pages 265-280

EXACT BOUNDARY CONDITIONS FOR BUCKLING ANALYSIS OF RECTANGULAR MICRO-PLATES BASED ON THE MODIFIED STRAIN GRADIENT THEORY

Meisam Mohammadi
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
Majid Fooladi
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
Hossein Darijani
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

ABSTRACT

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.