Limit and shakedown isogeometric analysis of structures based on Bézier extraction

An effective numerical approach is proposed for calculating limit and shakedown load multipliers of structures. The key idea is to integrate isogeometric analysis (IGA) based on Bézier extraction into an associated primal-dual algorithm. Such an associated primal-dual algorithm based upon the von Mises yield criterion and a Newton-like iteration is used to compute simultaneously both quasi-lower and upper bounds of the collapse multiplier. The method requires a low number of degrees of freedom for the desired accuracy of solutions. Numerical results of this method demonstrate the efficiency, and show the better accuracy and convergence than several finite element solutions.