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The numerical fracture analysis of non-homogeneous rock or concrete dowels subjected to shear and compression is described in detail. The method of analysis allows the consideration of scale and rate effects due to material non-homogeneity and fracture. The proposed approach is verified by comparing numerical predictions with experimental results reported in the literature for a series of small rock samples, since experimental evidence for large bodies is not yet available (2007). Results generated by Monte Carlo simulation using the so-called discrete element method to model the dowels suggest that a simple three parameters law can be used to predict the relationship between tangential stress at the base and lateral distortion. It is observed that the larger the size of the cubes, the smaller both the peak tangential stress and the rupture distortion. Size effects are also evaluated in samples with vertical restraint. The influence of loading rate is likewise numerically assessed for two sample sizes. The effect is compatible with experimental evidence available for concrete using small samples.

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This paper presents an efficient single-stage scheme for the global optimization of multiple tuned mass dampers subjected to seismic excitations. To take into account the oscillators' vertical and horizontal distribution, the use of the ground structure concept is proposed. This procedure is very useful because it avoids the pre-definition of the tuned mass dampers number and their placement. Because the multiple tuned mass dampers optimization problem is nonconvex and multimodal, this paper presents a novel hybrid stochastic/deterministic algorithm. The Firefly algorithm is used in the stochastic part, that is, to locate the global solution region and to provide a starting point to the local optimizer. The Nelder-Mead algorithm is then used as a local optimizer. Global search restarts are applied after convergence of the local search, allowing convergence to the global solution. In addition, because the structural response is obtained in the frequency domain, the scheme becomes very robust and requires considerably less computational effort than time history analysis. For illustration purposes, a numerical example on a ten-story shear building is demonstrated. In the studies previously cited, the optimization procedure sought the spring and damping constants of each device for pre-defined locations and total number of TMDs. In other words, the location and number of TMDs should be fixed a priori by the designer. To generalize the seismic performance of the single TMD and the two MTMD scenarios, determined through the proposed methodology, the ten-story building structure is subjected to three measured acceleration records during distinct earthquakes. The uncontrolled and each described scenario have been tested under Loma Prieta, El-Centro, and Caucete earthquakes. Tables III-VIII and Figures 3-8 show that the maximum and rms displacements are successfully reduced for all seismic excitations and all scenarios assessed. Figure 9 shows the displacements responses for the uncontrolled structure and for the Scenario 2 (solution 1) under the three seismic signals. Only one MTMD configuration response Figure 3. Peak displacements with respect to ground for a single tuned mass damper.7. Uniform distribution of TMDs in the top floor presented slightly worse results, around 1.2% and 4% inferior for the maximum and rms responses reduction, respectively. 8. The best vertical distribution was achieve with one oscillator placed in the fifth, seventh, eighth, and tenth stories, totalizing four TMDs. The efficiency loss was not as severe as it could be expected, being around 9% and 6.5% for the maximum and rms responses reduction, respectively. In this case, each TMD presented a specific tuning, varying between f opt = 0.90 to 1.05. Figure 8. Root mean square displacements with respect to ground for vertical distribution of tuned mass dampers.