article · Mechanics of Advanced Materials and Structures
Analytical modelling reveals how heat, moisture, and size-dependent mechanical forces influence the performance of functionally graded microplates supported by elastic foundations. By combining a trigonometric four-variable plate theory with modified couple stress theory, the behaviour of microplates with material properties graded exponentially across their thickness can be assessed under linearly varying temperature and moisture. The mathematical solutions determine key structural responses, including deflection, stress distribution, natural vibration frequencies, and the critical thresholds for mechanical and thermal buckling. Findings show that accounting for small-scale size effects or elastic foundation support predicts a stiffer microplate. Consequently, these structural models demonstrate reduced bending deflection alongside elevated natural frequencies and buckling resistance. Furthermore, the influence of size effects diminishes significantly as plate thickness increases, matching conventional classical mechanics in thicker structures.
Understanding how miniature structural components respond to heat, moisture, and physical loads is essential for developing reliable microscale systems. This theoretical framework provides analytical tools to predict bending, vibration, and structural stability in microplates with graded material properties, offering engineering insights into how microscopic scale factors alter the mechanical behaviour of materials operating under varying environmental conditions.
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In this paper, the effects of hygrothermal conditions on various behaviors, such as bending, free vibration, mechanical and thermal buckling, of exponentially graded microplates lying on two-parameter elastic foundations are investigated. The trigonometric four-variable plate theory incorporated to the modified couple stress theory (MCST) is employed to derive the equations of motion. The present MCST contains an internal material length scale parameter, thus it can capture the size effect. The microplate is assumed to be subjected to a temperature rise and moisture concentration which are varied linearly through the thickness of the plate. Based on an exponential law, the material properties of the microplate are graded only in z direction. The equations of motion are solved analytically to obtain the displacements, stresses, eigenfrequencies and critical buckling load and temperature of the microplates. The present results are validated by comparing them with those previously published. The numerical examples reveal that considering the size effect and/or the elastic foundations leads to an increment in plate stiffness and thereby leads to a decrement in the deflection and an increment in eigenfrequency and buckling loads. It is also shown that the size effect is negligible for the thicker plate.
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DOI: 10.1080/15376494.2018.1499986
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