LAUSR

Abstract A superconvergent isogeometric formulation is presented to accurately analyze the natural frequencies for elastic continua. This formulation is realized by a set of superconvergent quadrature rules which are designed for the numerical integration of isogeometric mass and stiffness matrices. In order to obtain these quadrature rules, a natural frequency error measure for elastic continua is systematically deduced using the quadratic basis functions, where the mass and stiffness matrices are formulated by the assumed quadrature rules. In contrast to the quadrature-based superconvergent isogeometric formulation for the scalar-valued wave equations, it is shown that herein different quadrature rules are required for the mass and stiffness matrices to achieve the superconvergence of natural frequency computation for the vector-valued elastic continuum problems. Consequently, the superconvergent quadrature rules are established through optimizing the natural frequency accuracy. It turns out that with these quadrature rules, the accuracy of natural frequencies for elastic continua is improved by two orders compared with the standard isogeometric formulation employing the consistent mass matrix. Meanwhile, it is found that the superconvergent quadrature rules involve the wave propagation angle and consequently simplified quadrature rules without the angle dependence are further proposed for straightforward practical applications. Numerical results reveal the superconvergence of the proposed method regarding the natural frequencies for elastic continua.