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Along with the applicability of optimization algorithms, there are lots of features that can affect the functioning of the optimization techniques. The main purpose of this paper is investigating the significance of boundary constraint handling (BCH) schemes on the performance of optimization algorithms. To this end, numbers of deterministic and probabilistic BCH approaches are applied to one of the most recent proposed optimization techniques, named interior search algorithm (ISA). Apart from the implementing different BCH methods, a sensitivity analysis is conducted to find an appropriate setting for the only parameter of ISA. Concrete cantilever retaining wall design as one of the most important geotechnical problems is tackled to declare proficiency of the ISA algorithm, on the one hand, and benchmark the effect of BCH schemes on the final results, on the contrary. As results demonstrate, various BCH approaches have a perceptible impact on the algorithm performance. In like manner, the essential parameter of ISA can also play a pivotal role in this algorithm's efficiency.

In this work, we propose an inertial amplified resonator (IAR) as a building block of a tunable locally resonant metasurface. The IAR consists in a mass-spring resonator coupled with two inerters, realized by two inclined rigid links connected to an additional mass. The IAR has a static behaviour equivalent to that of a standard mass-spring oscillator whereas its dynamic response can be controlled by means of the geometrical configuration and mass of the inerters. We derive the dynamic amplification factor and the base force of the IAR for an imposed harmonic motion and perform a parametric study to unveil its peculiar dynamics. Next, we use an effective medium approach to derive the closed-form dispersion law of a metasurface consisting of IARs coupled to a semi-infinite elastic substrate. We show that the IAR enriches the dynamics of the metasurface providing the ability (1) to shift its bandgap frequency spectrum without changing the mass and stiffness of the resonators, (2) to design single frequency or multifrequency (metawedges) metasurfaces, (3) to obtain a high-frequency behavior typical of an added dead mass layer (i.e., non-resonant), which confers to the metasurface additional filtering properties.

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Inertial flow in porous media, governed by the Forchheimer equation, is affected by domain heterogeneity at the field scale. We propose a method to derive formulae of the effective Forchheimer coefficient with application to a perfectly stratified medium. Consider uniform flow under a constant pressure gradient $$\Delta P/L$$ Δ P / L in a layered permeability field with a given probability distribution. The local Forchheimer coefficient $$\beta$$ β is related to the local permeability k via the relation $$\beta =a/k^c$$ β = a / k c , where $$a>0$$ a > 0 being a constant and $$c\in [0,2]$$ c ∈ [ 0 , 2 ] . Under ergodicity, an effective value of $$\beta$$ β is derived for flow (i) perpendicular and (ii) parallel to layers. Expressions for effective Forchheimer coefficient, $$\beta _e$$ β e , generalize previous formulations for discrete permeability variations. Closed-form $$\beta _e$$ β e expressions are derived for flow perpendicular to layers and under two limit cases, $$F\ll 1$$ F ≪ 1 and $$F\gg 1$$ F ≫ 1 , for flow parallel to layering, with F a Forchheimer number depending on the pressure gradient. For F of order unity, $$\beta _e$$ β e is obtained numerically: when realistic values of $$\Delta P/L$$ Δ P / L and a are adopted, $$\beta _e$$ β e approaches the results valid for the high Forchheimer approximation. Further, $$\beta _{e}$$ β e increases with heterogeneity, with values always larger than those it would take if the $$\beta - k$$ β - k relationship was applied to the mean permeability; it increases (decreases) with increasing (decreasing) exponent c for flow perpendicular (parallel) to layers. $$\beta _{e}$$ β e is also moderately sensitive to the permeability distribution, and is larger for the gamma than for the lognormal distribution.