A quadratic element for upper bound limit analysis Available to Purchase

This paper presents a new finite element formulation of the upper bound theorem. The formulation uses a six‐noded linear strain triangular element. Each node has two unknown velocities and each corner of a triangle is associated with a specified number of unknown plastic multiplier rates. The major advantage of using a linear strain element, rather than a constant strain element, is that the velocity field can be modelled more accurately. In addition, the incompressibility condition can be easily satisfied without resorting to special arrangements of elements in the mesh. The formulation permits kinematically admissible velocity discontinuities at specified locations within the finite element mesh. To ensure that finite element formulation of the upper bound theorem leads to a linear programming problem,the yield criterion is expressed as a linear function of the stresses. The linearized yield surface is defined to circumscribe the parent yield surface so that the solution obtained is a rigorous upper bound. During the solution phase, an active set algorithm is used to solve the resulting linear programming problem. Several numerical examples are given to illustrate the capability of the new procedure for computing rigorous upper bounds. The efficiency and accuracy of the quadratic formulation is compared with that of the 3‐noded constant strain formulation in detail.