Lower bound limit analysis through discontinuous finite elements and semi-analytical procedures

This work deals with the limit analysis of structures through the lower-bound theorem, using dislocations based finite elements and eigenstress modelling. The lower bound approach is based on the knowledge of the self-equilibrated stresses that constitutes the basis of the domain where the optimal solution should be searched. A twofold strategy can be used to get selfequilibrated stresses, i.e., eigenstresses. The first one pursues the calculation of the selfequilibrated stress through the numerical approximation of the differential equilibrium equation in homogeneous form through an a posteriori discretization that used polynomial representation of finite degree. The second one consists of Finite Element implementation of the self-equilibrated stress calculation by discontinuous finite elements based on Volterra's dislocations theory. Both the formulations are written in terms of the strain and precisely in terms of the strain nodal displacement parameters. Consequently, it is possible to formulate an iterative procedure starting from the knowledge of the dislocation at the incoming collapse, in Melan’s residual sense, and calculate the structural ductility requirement. Several numerical examples are presented to confirm the method's feasibility.