Isogeometric analysis for functionally graded microplates based on modified couple stress theory

TL;DR

This paper develops an advanced isogeometric analysis method using modified couple stress and refined plate theories to accurately model size-dependent behaviors of functionally graded microplates under various conditions.

Contribution

It introduces a novel computational framework combining isogeometric analysis with a modified couple stress theory and a quasi-3D plate model for microplate analysis.

Findings

Validated the method's accuracy and efficiency through convergence tests.

Analyzed effects of material length scale and geometry on microplate responses.

Provided insights into static, vibrational, and buckling behaviors of microplates.

Abstract

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.