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The minimum volume design problem of elastic perfectly plastic finite element structures subjected to a combination of fixed and perfect cyclic loads is studied. The design problem is formulated in such a way that incremental collapse is certainly prevented. The search for the structural design with the required limit behaviour is effected following two different formulations, both developed on the grounds of a statical approach: the first one operates below the elastic shakedown limit and is able to provide a suboptimal design; the second one operates above the elastic shakedown limit and is able to provide the/an optimal design. The Kuhn–Tucker conditions of the two problems provide useful information about the different behaviour of the obtained structures. An application concludes the paper; the comparison among the designs is effected, pointing out the different behaviour of the obtained structures as well as the required computational effort related to the numerical solutions

A class of thin vaults, the so-called "bòvedas tabicadas", which represent one of the most common Spanish traditional building techniques at the end of XIX century are studied here, treating the relevant analysis problem through a numerical, as well as an experimental, approach. At first the problem is studied by searching for the behaviour of the material effecting suitable experiments. Once the constitutive behaviour of the materials and the structural elements are experimentally characterized, a semi inverse method for the identification of the optimum mechanical parameters to assign to an equivalent homogeneous ideal material through analysis reproducing the executed experimental tests is adopted on the grounds of finite element analysis. Moreover, other tests are processed on a real structure in order to determine the mechanical and geometric response to assigned loads. These results, compared to the related numerical analyses, can be utilized in order to propose some useful simple criteria in the reinforcing design of the referenced structures.

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