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An innovative strategy for the optimal design of planar frames able to resist to seismic excitations is here proposed. The procedure is based on genetic algorithms (GA) which are performed according to a nested structure suitable to be implemented in parallel computing on several devices. In particular, this solution foresees two nested genetic algorithms. The first one, named "External GA", seeks, among a predefined list of profiles, the size of the structural elements of the frame which correspond to the most performing solution associated to the highest value of an appropriate fitness function. The latter function takes into account, among other considerations, of the seismic safety factor and the failure mode which are calculated by means of the second algorithm, named "Internal GA". The details of the proposed procedure are provided and applications to the seismic design of two frames of different size are described., Comment: 25 pages, 8 figures, 7 tables

Limit analysis is a computationally efficient tool to assess the resistance and the failure mode of structures but does not provide any information on the displacement capacity, which is one of the concepts which most affects the seismic safety. Therefore, since many researchers did not consider limit analysis as a possible tool for the seismic assessment of structures, its widespread employment has been prevented. In this paper this common belief is questioned and the authors show that limit analysis can be useful in the evaluation of the seismic performance of frame structures. In particular, to overcome the limitation on the possibility to evaluate the displacements of a structure based on a limit analysis approach, an approximated capacity curve is reconstructed. The latter is based on a limit analysis strategy, which takes into account the second order effects, and evaluates the displacement capacity considering a post-peak softening branch and a threshold on the allowed plastic rotations. Then, based on this simplified capacity curve, an equivalent single degree of freedom system is defined in order to assess the seismic performance of frame structures. The proposed simplified strategy is implemented in a dedicated software and the obtained results are validated with well-established approaches based on nonlinear static analyses, showing the reliability and the computational efficiency of this methodology, Comment: 27 pages, 9 figures, 5 tables

The structural response of masonry arches is strongly dominated by the arch geometry, the stone block dimensions and the interaction with backfill material or surrounding walls. Due to their intrinsic discontinuous nature, the nonlinear structural response of these key historical structures can be efficiently modelled in the context of discrete element approaches. Smeared crack finite elements models, based on the assumption of homogenised media and spread plasticity, fail to rigorously predict the actual collapse behaviour of such structures, that are generally governed by rocking and sliding mechanisms along mortar joints between stone blocks. In this paper a new Discrete Macro-Element Method (DMEM) for predicting the nonlinear structural behaviour of masonry arches is proposed. The method is based on a macro-element discretization in which each plane element interacts with the adjacent elements through zero-thickness interfaces and whose internal deformability is related to a single degree of freedom only. Both experimental and numerical validations show the capability of the proposed approach to be applied for the prediction of the non-linear response of masonry arch structures under different loading conditions.

In this paper a procedure for the dynamic identification of damage in spatial Timoshenko arches is presented. The proposed approach is based on the calculation of an arbitrary number of exact eigen-properties of a damaged spatial arch by means of the Wittrick and Williams algorithm. The proposed damage model considers a reduction of the volume in a part of the arch, and is therefore suitable, differently than what is commonly proposed in the main part of the dedicated literature, not only for concentrated cracks but also for diffused damaged zones which may involve a loss of mass. Different damage scenarios can be taken into account with variable location, intensity and extension of the damage as well as number of damaged segments. An optimization procedure, aiming at identifying which damage configuration minimizes the difference between its eigen-properties and a set of measured modal quantities for the structure, is implemented making use of genetic algorithms. In this context, an initial random population of chromosomes, representing different damage distributions along the arch, is forced to evolve towards the fittest solution. Several applications with different, single or multiple, damaged zones and boundary conditions confirm the validity and the applicability of the proposed procedure even in presence of instrumental errors on the measured data., Comment: 34 pages, 19 figures

This paper studies the inverse problem related to the identification of the flexural stiffness of an Euler Bernoulli beam in order to reconstruct its profile starting from available response data. The proposed identification procedure makes use of energy measurements and is based on the application of a closed form solution for the static displacements of multi-stepped beams. This solution allows to easily calculate the energy related to beams modeled with arbitrary multi-step shapes subjected to a transversal roving force, and to compare it with the correspondent data obtained through direct measurements on real beams. The optimal solution which minimizes the difference between measured and calculated data is then sought by means of genetic algorithms. In the paper several different stepped beams are investigated showing that the proposed procedure allows in many cases to identify the exact beam profile. However it is shown that in some other cases different multi-step profiles may correspond to very similar static responses, and therefore to comparable minima in the optimization problem, thus complicating the profile identification problem., Comment: 27 pages, 7 figures, 6 tables

This paper presents an automatic approach for the evaluation of the plastic load and failure modes of planar frames. The method is based on the generation of elementary collapse mechanisms and on their linear combination aimed at minimizing the collapse load factor. The minimization procedure is efficiently performed by means of genetic algorithms which allow to compute an approximate collapse load factor, and the correspondent failure mode, with sufficient accuracy in a very short computing time. A user-friendly original software in the agent-based programming language Netlogo, here employed for the first time with structural engineering purposes, has been developed showing its great versatility and advantages. Many applications have been performed both with reference to the classical plastic analysis approach, in which all the loads increase proportionally, and with a seismic point of view considering a system of horizontal forces whose magnitude increases while the vertical loads are assumed to be constant. In this latter case a parametric study has been performed aiming at evaluating the influence of some geometric, mechanical and load distribution parameters on the ultimate collapse load of planar frames., Comment: 35 pages, 20 figures