Size-Dependent Flexural Analysis of Thick Microplates Using Consistent Couple Stress Theory

Among various continuum mechanics approaches, size-dependent theories have gained significant attention for their ability to model these effects in micro- and nanostructures. This study presents an exact solution for the flexural analysis of thick microplates based on consistent couple stress theory. Unlike conventional plate theories, such as the Kirchhoff and first-order shear deformation theories, this work employs three-dimensional elasticity theory to accurately model the mechanical response of thick microplates. The governing equations are derived within the framework of couple stress theory, incorporating length-scale effects, and solved under simply supported boundary conditions. The results demonstrate significant reductions in both in-plane and out-of-plane displacements, approximately 24% and 36%, respectively, compared to classical elasticity predictions. These findings highlight the critical role of size effects in accurately predicting the mechanical behavior of microscale structures. The insights gained from this study are particularly relevant to the design and analysis of polymeric and composite microstructures, where small-scale mechanical phenomena influence performance and reliability.