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

摘要

Analysis of static bending, free vibration and buckling behaviours offunctionally graded microplates is investigated in this study. The main idea isto use the isogeometric analysis in associated with novel four-variable refinedplate theory and quasi-3D theory. More importantly, the modified couple stresstheory with only one material length scale parameter is employed to effectivelycapture the size-dependent effects within the microplates. Meanwhile, thequasi-3D theory which is constructed from a novel seventh-order sheardeformation refined plate theory with four unknowns is able to consider bothshear deformations and thickness stretching effect without requiring shearcorrection factors. The NURBS-based isogeometric analysis is integrated toexactly describe the geometry and approximately calculate the unknown fieldswith higher-order derivative and continuity requirements. The convergence andverification show the validity and efficiency of this proposed computationalapproach in comparison with those existing in the literature. It is furtherapplied to study the static bending, free vibration and buckling responses ofrectangular and circular functionally graded microplates with various types ofboundary conditions. A number of investigations are also conducted toillustrate the effects of the material length scale, material index, andlength-to-thickness ratios on the responses of the microplates.