Computation of collapse states with von Mises type yield condition

A new computational approach to the problem of limit analysis with quadrati c yield condition is developed and tested. The problem is solved using the exact convex yield condition and the general case of unbounded yield set, c orresponding to unrestricted hydrostatic pressure, is treated. The discretization by the finite element method is based on an analysis of the duality between the static principle and the kinematic principle of lim it analysis. Also the solution method for the discrete optimization problem is new and exploits this duality. The method simultaneously computes appro ximations to the fields of stresses and flow in the collapse state. The sof tware used for the optimization problem is independent of continuum mechani cs, but has been developed with applications in limit analysis as a primary objective. The efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model: app roximately 90 000 finite element nodes with 3 stress components and 2 veloc ity 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. Copyright (C) 1999 John Wiley & Sons, Ltd.