Computation of limit and shakedown loads for pressure vessel components using isogeometric analysis based on Lagrange extraction

This paper presents an isogeometric finite element method based on Lagrange extraction in combination with a primal-dual algorithm for estimating limit and shakedown loads of pressure vessel components. The primal-dual algorithm is used to determinate simultaneously both upper and quasi-lower bounds of the limit load multiplier. The Lagrange extraction is integrated into isogeometric analysis. This way, which directly connects a C Lagrange basis with smooth NURBS basis and offers an alternative implementation of isogeometric analysis in the standard finite element method code, allows computations in the same manner as the standard finite element, but the present approach possesses the distinguishing advantages of using higher-order basis approximations. Numerical results of plane and axisymmetric problems are compared with analytical or other available solutions to prove the reliability and efficiency of the present approach. The application of shakedown analysis in pressure vessel engineering is illustrated by some examples.