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Optimal locations of the actuators for frame active control are investigated in this article. The aim is to minimize the structural drifts by employing several actuators. By utilizing genetic algorithm, the appropriate locations of the actuators are determined. They should be placed in locations where they can minimize the maximum structural drift. To explore the capability of the proposed techniques, the response of a 20-story building is controlled using three suggested methods. Furthermore, two different concepts are considered for comparing the performance of the authors' approaches. One is based on the maximum responses of the structure, and the other is according to the magnitudes of the actuators' forces. All findings prove the efficiency of the recommended strategies.

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In this paper, the effect of angle between predictor and corrector surfaces on the structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the structural equilibrium path’s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was previously found by other researchers, via a different mathematical process. Several benchmark structures, which have geometric nonlinear behavior, are analyzed with the proposed methods. The finite element method is utilized to analyze these problems. The abilities of suggested schemes are evaluated in tracing the complex equilibrium paths. Moreover, comparison study for the required number of increments and iterations is performed. Results reflect the robustness of the authors’ formulations.

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By minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. This new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. Since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. In fact, both linear and nonlinear parts of the frame axial strains are included in the presented formulation. These higher-order terms affect the resulting unbalanced force and also frame tangent stiffness. Moreover, the finite element method, updated Lagrangian description, and arc length scheme are employed in this study. To check the efficiency of the proposed strategy, several numerical examples are solved. The findings indicate that the authors’ technique can accurately trace the structural equilibrium paths having the limit points.

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Reducing waste material plays an essential role for engineers in the current world. Nowadays, recycled materials are going to be used in order to manufacture concrete beams. Previous studies concluded that the currently proposed formulas to predict the flexural and shear behavior of the reinforced concrete beams were not appropriate for those manufactured by recycled materials. This study aims to employ the Particle Swarm Optimization Algorithm to suggest the flexural and shear performance of recycled material reinforced concrete beams. For this purpose, the previous experimental outcomes are utilized, and new equations are established to anticipate both flexural and shear behavior of the recycled material concrete beams. Consequently, all findings are compared with those achieved experimentally. The attained significances of this study show that the proposed formulas have high accuracy for the experimental data.