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Hung Nguyen-Xuan, Chien Hoang Thai, Jeremy Bleyer, Phu Vinh Nguyen; Upper bound limit analysis of plates using a rotation-free isogeometric approach; Asia Pacific Journal on Computational Engineering, Vol. 1 (2014), doi:10.1186/s40540-014-0012-5 (Journal Paper).



This paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending.


The formulation relies on the kinematic (or upper bound) theorem and namely B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers.

Results and conclusions

Several numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.


Plate bending; Limit analysis; Rigid-perfect plasticity; NURBS; Isogeometric analysis; Second-order cone programming