Isogeometric analysis of functionally graded plates with a logarithmic higher order shear deformation theory: Fid-Bau Portal

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

Zhu, Yaqiao / Shi, Peng / Kang, Yongtao / Cheng, Baofa

Abstract 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 C¹-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.

Highlights • A new logarithmic higher order shear deformation theory without the requirement of shear correction factor is developed. • The present theory is assessed with the isogeometric analysis for the static bending, free vibration and buckling responses of FG plates in thermal environment. • Different plate geometries, boundary conditions, FG material combinations, temperature change conditions, volume fraction indices of FG plates are considered. • The present theory is highly effective and accurate for the static bending, free vibration and buckling analysis of FG plates by comparing the present results to those obtained by various plate theories and solving methods.