Computation of collapse states with von Mises type yield condition

A new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested. The problem is solved using the exact convex yield condition and the general case of unbounded yield set, corresponding to unrestricted hydrostatic pressure, is treated. The discretization by the nite element method is based on an analysis of the duality between the static principle and the kinematic principle of limit analysis. Also the solution method for the discrete optimization problem is new and exploits this duality. The method simultaneously computes approximations to the elds of stresses and ow in the collapse state. The software used for the optimization problem is independent of continuum mechanics, but has been developed with applications in limit analysis as a primary objective. The e ciency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model: approximately 90 000 nite element nodes with 3 stress components and 2 velocity components at each node. In two space dimensions this may be overkill, but it shows that we are able to solve problems in three space dimensions