Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory

Abstract

The nonlinear static bending analysis of microplates resting on imperfect Pasternak elastic foundations is carried out in this paper. The finite element method based on the modified couple stress theory is used to derive the nonlinear finite element formulations. The present theory and mathematical model are validated by comparisons of this work’s results with those of other reputable publications, which show a very good agreement. The influences of length-scale parameter, nonlinearity, elastic foundation parameters, imperfect foundations, and boundary conditions on the nonlinear static bending response of microplates are then explored. The computed data of this study is very intriguing, particularly the interaction of the microplate with the imperfect elastic foundation, and this helps us better understand the mechanical behavior of this structure.

Keywords

• Imperfect elastic foundations
• Nonlinearity
• Static bending
• Microplates
• Modified couple stress
• Imperfect elastic foundations