A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets

This paper presents a three-variable high order shear deformation plate theory (THSDT) for free vibration, buckling and instability analysis of functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs). The underlying approach only uses three primal variables in the same way as numerically solving three-dimensional (3D) solids. It fulfills the classical plate theory (CPT), the first-order shear deformation theory (FSDT) and the higher-order shear deformation theory (HSDT). THSDT has only three variables like CPT but unlike CPT, it takes into account the shear effect without requiring a shear correction factor. It gives a significant advantage in numerical computational aspects such as reducing the computational cost of plate problems using isogeometric analysis (IGA). This new form of the displacement field requires the high continuity with Ck where k⩾3 approximately. IGA can be prioritized as the best candidate for discrete approximations with the arbitrary smoothness of high-order derivatives in a differential weak form of asymmetric fourth order. Numerical validations are given for free vibration, buckling and instability of FGP-GPL plates in order to prove the reliability and accuracy of present method.