Haidar A. Rational design of reinforced concrete and polymer concrete buildings with dry friction dampers using the particle swarm optimization.

The dissertation is devoted to the prediction of rational locations of friction dampers in multi-storey buildings to enhance their resistance to seismic and dynamic loads using the methods of swarm intelligence. The method of particle swarm optimization is further developed in application to the tasks of rational design of buildings and structures. The explicit formulas for evaluation of the particles positions in the solution space are presented. Restriction conditions are specified so that to define the search area. Different types of boundary conditions governing the behavior of a particle when its coordinates fall outside the solution space are analyzed. Criteria for the termination of the search process are formulated. For a practical verification of the method of particle swarm optimization, some benchmark functions are considered. A comparative analysis of the particle swarm optimization procedure and the genetic algorithm is presented. Numerical models of multi-storey buildings with dry friction dampers are further developed. The simulations were performed using the FEM package LIRA-SAPR. Modal analysis determines the frequencies and periods of natural vibrations. The seismic analysis is performed and the maximum horizontal displacements of the top of the frame are determined. The problem of the rational location of friction dampers is studied in a case of periodic load applied horizontally to the foundation of the structure. The load frequency is assumed to be equal to the fundamental frequency of the first normal mode, which ensures the most dangerous case of the resonance. The objective function is the displacement amplitude of the top of the frame. The problem of the rational location of friction dampers is solved by the method of particle swarm optimization. Dynamic properties of the polymer concrete frame building are studied and the seismic analysis is performed using the FEM package in LIRA-SAPR. Analytical models describing the dynamic behavior of multi-storey frame buildings with dry friction dampers are further developed. The calculation model is adopted in a form of a vertical cantilever rod with lumped masses. The governing system of differential equations of motion is introduced and futher integrated numerically by the Runge-Kutta method. In order to justify the applicability of the proposed analytical model, its natural frequencies are compared with the results of the modal analysis of the original structure performed in LIRA-SAPR. The problem of a rational location of friction dampers in the six-storey frame building using the proposed lumped mass model is considered. There are two types of objective functions that need to be minimized: 1) the maximal displacements of the floors and 2) the maximal inter-storey drifts. The case of a periodic load with a frequency equal to the fundamental frequency of the structure is considered. The rational locations of the dampers are. The same solution is obtained for the both objective functions implying the installation of the all three dampers at the floor 1. The seismic acceleration is simulated by a stochastic Gaussian process as a superposition of harmonic waves with discrete frequencies and random phases. The spectral energy density of the earthquake is described by the empirical Kanai-Taimi model. Based on the proposed model, accelerograms for different types of soils are developed. Non-stationary vibrations of the six-storey frame building under the seismic load are investigated. The minimal displacements are achieved installing the dampers at the floors 1, 3, 4, whereas the minimal inter-storey drifts require installation of the dampers at the floors 1, 2, 3. The latter solution provides also the minimal accelerations of the building. The dynamic properties and the natural frequencies of a six-storey polymer concrete building are studied. The floors displacements, the inter-storey drifts and the accelerations of the floors are determined. A comparative analysis of the obtained results for the reinforced concrete and the polymer concrete buildings is presented. The developed dynamic models and the methods of simulation of buildings with friction dampers can be used in the design of houses and structures with enhanced resistance to seismic and dynamic impacts, as well as for the reconstruction of existing buildings to increase their seismic protection.