Isogeometric analysis of functionally graded plates with a logarithmic higher order shear deformation theory

This paper presents a new logarithmic higher order shear deformation theory (LHSDT) based on isogeometric analysis (IGA) to study the static bending, free vibration, and buckling behaviors of functionally graded plates. The temperature change conditions are considered. In the LHSDT fashion, shear stresses disappear at the top and bottom surfaces of the plates and shear correction factor vanishes. The requirement for C-1-continuity in terms of the LHSDT is straightforwardly possessed with the aid of inherent high order continuity of non-uniform rational B-spline (NURBS), which serves as basis functions in our IGA formulation. The superior performance and accuracy of the proposed method is demonstrated through extensive numerical examples. The computed results of static bending, vibration and buckling from the proposed theory are in a very good agreement with reference solutions available in literature obtained by various plate theories and different solving method.