A Simple Non-Conforming Isogeometric Formulation with Superior Accuracy for Free Vibration Analysis of Thin Beams and Plates

Abstract

A set of non-conforming quadratic basis functions is introduced to formulate the mass and stiffness matrices that enable a superior frequency accuracy for isogeometric free vibration analysis of thin beams and plates. The non-conforming basis functions are expressed as a simple combination of the original basis functions and their second-order derivatives with an adjustable parameter. By construction, these quadratic non-conforming basis functions only affect the mass matrices and do not alter the stiffness matrices. The adjustable parameter arising from the non-conforming basis functions are determined through optimizing the frequency accuracy. In the case of thin beams, the proposed non-conforming isogeometric formulation leads to an increase of frequency accuracy order or superconvergence. For thin plates, the frequency error of the proposed method is guaranteed to be no larger than that of the standard isogeometric approach. Numerical results for thin beams and plates consistently verify that the proposed formulation with non-conforming basis functions is quite robust and produces very favorable frequency accuracy for both uniform and non-uniform meshes.