A displacement-based dislocation map has been used to build the eigenstress stress, which is the base of the structure’s limit analysis. The limit load has been calculated as the upper bound of any equilibrated stress that respects the compatibility inequalities by means of a linear optimization program. The eigenstress stress nodal parameters were assumed as the design variables, and the compatibility inequalities have been obtained from the Mises–Schleicher criterion, assuming that the stress belongs to the corresponding plastic domain. The numerical application has considered a linear secant representation of the domain, with a penalty factor on stresses, to correct the linearization error. Examples concerning a simply supported cantilever beam, a pipe section, and a plate with a circular hole highlighted the accuracy of the procedure with respect to the established literature. Moreover, the procedure has been applied to investigate plane structure examples. A square plate with variable elliptic holes has been analyzed, and the influence of ellipticity on the collapse load has been shown. The effects of porosity and heterogeneity of the structure with respect to the collapse load are shown considering the porous cantilever and representative volume element. The evaluation of the limit load along different element directions envisaged a point-wise calculation of the compatibility domain of the porous material to be used in the macro-scale analysis of the structures made of porous micro-cells.
