Upper bound limit analysis using the weak form quadrature element method

Limit analysis is a useful tool for design and safety assessment of structures in civil and geotechnical engineering. In the present study, a newly developed high order algorithm-the weak form quadrature element method is reformulated for upper bound limit analysis. The dual formulations of the kinematic theorem are employed with the nodal stresses chosen as the optimization variables. The weak form equilibrium constraint is numerically integrated by Lobatto integration and then the nodal derivatives are approximated by differential quadrature analogue. The resulting optimization problem is formulated as a standard second-order cone programming problem and solved by the optimization toolbox Mosek. This paper aims to improve the efficiency of the existing numerical limit algorithms especially for problems with singularities such as cracked structures and to overcome the well-known volumetric locking occurred for incompressible materials. Some numerical tests are given to show the accuracy and efficiency of the present method.