Isogeometric bending and free vibration analyses of carbon nanotube-reinforced magneto-electric-elastic microplates using a four variable refined plate theory

The classical continuum mechanics theory is inadequate for modeling the mechanical responses of the microstructures due to its failure to account for size effects. Instead, modified strain gradient theory (MSGT) is considered as one of the most accurate theories due to its ability to adjust three length scale parameters (LSPs). Isogeometric approach (IGA) is a computational technique that is capable of accurately solving complex problems. For those reasons, the size-dependent analysis of carbon nanotube-reinforced magneto-electric-elastic microplates based on the MSGT are firstly proposed. The present approach uses the refined plate theory (RPT) with four variables, the MSGT and IGA. The magnetic and electric potentials are assumed to be a combination of a half-cosine and linear variation to satisfy Maxwell's equations. Different types of functionally graded carbon nanotubes (CNTs) including UD, FG-X, FG-O and FG-V are reinforced in the magneto-electric-elastic matrix of the microplates. Governing equations are derived using the extended virtual work principle and then solved by IGA to determine the deflection and natural frequency of the microplates. The influence of the LSPs, CNT distributions, CNT's volume fraction, matrix's volume fraction, magnetic potential, electric voltage and geometry on the deflection and natural frequency of the microplates are studied and discussed.