A computationally efficient method for the first order step-by-step limit analysis of space frames is presented. The incremental non-holonomic analysis is based on the generalized plastic node method. The non-linear yield surface is approximated by a multi-faceted surface, thus avoiding the iterative formulation at each load step. In order to prevent the occurrence of very small load steps a second internal and homothetic to the initial yield surface is implemented which creates a plastic zone for the activation of the plastic modes. This implementation reduces substantially the computational effort of the procedure without affecting the value of the final load. The solution of the linear equilibrium equation at each load step is obtained with the preconditioned conjugate gradient method. Special attention is paid to the fact that the overall stiffness matrix changes gradually with the successive formation of plastic nodes. The application of the conjugate gradient method is based on some recent developments on improved matrix handling techniques and efficient preconditioning strategies. A number of test problems have been performed which show the usefulness of the proposed approach and its superiority in respect to efficient direct methods of solution in both storage requirements and computing time.
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