Highly Accurate Isogeometric Free Vibration Analysis Of Curved Euler-Bernoulli Beams And Kirchhoff-Love Cylindrical Shells

Isogeometric analysis unifies the computer aided geometry design and finite element analysis through using the same set of high order smooth basis functions for geometric modeling and structural analysis.The smooth basis functions in isogeometric analysis lead to significant accuracy superiority compared with the finite element structural vibration analysis with C0 basis functions.In this thesis,the frequency accuracy measures for the isogeometric free vibration analysis of curved EulerBernoulli beams and Kirchhoff-Love cylindrical shells are proposed.With the aid of the proposed accuracy measures,highly accurate isogeometric methods are then developed to improve the frequency accuracy for the free vibration analysis of curved beams and cylindrical shells.Firstly,the frequency accuracy measure for the isogeometric free vibration analysis of curved beams is established.Based upon this frequency accuracy measure,the frequency errors for the isogeometric formulation with various basis order combinations of axial and radial displacement approximations are investigated.As the result,the matching relationship between the axial and radial displacement approximations using different order basis functions is disclosed.Meanwhile,since a cylindrical shell can be obtained by taking the cross product of a straight beam and a curved beam,the frequency accuracy measure for curved beams is then rationally generalized to construct an effective frequency accuracy measure for cylindrical shells.Subsequently,these frequency accuracy measures serve a foundation to optimize the frequency accuracy through re-designing the quadrature rules used for the numerical integration of isogeometric stiffness and mass matrices.As a result,highly accurate isogeometric formulations with optimized quadrature rules are presented to elevate the accuracy of free vibration analysis of curved Euler-Bernoulli beams and KirchhoffLove cylindrical shells.It is also shown that the highly accurate isogeometric formulation for curved beams can reduce to a superconvergent isogeometric algorithm for straight beam free vibration analysis.The effectiveness of the proposed methods is systematically demonstrated by numerical results.