Раціональне проектування залізобетонних і полімербетонних будівель із демпферами сухого тертя за допомогою методів ройового інтелекту

Abstract

UK: Розвинуто метод рою частинок для визначення місць раціонального розташування демпферів сухого тертя у багатоповерхових каркасних будівлях для підвищення їх сейсмічної стійкості. Досліджено вплив значень параметрів методу рою частинок на його практичну збіжність при пошуку екстремумів тестових функцій. Виконано порівняльний аналіз методу рою частинок та генетичного алгоритму. Виконано чисельне динамічне моделювання багатоповерхового каркасного будинку у ПК ЛІРА-САПР. Визначено раціональне розташування демпферів, яке забезпечує найшвидше згасання коливань. Виконано порівняльний аналіз динамічних характеристик каркасних будівель, виготовлених із залізобетону та полімербетону. Розроблено аналітичну динамічну модель багатоповерхового каркасного будинку із демпферами сухого тертя. Розроблено математичну модель сейсмічного навантаження. Досліджено нестаціонарні коливання будинку під дією періодичних і сейсмічних навантажень. Одержано чисельні розв’язки нелінійних динамічних рівнянь за допомогою методу Рунге-Кутти. Визначено місця раціонального розташування демпферів сухого тертя. Досліджено динамічні характеристики будинків, каркас яких виготовлено із залізобетону та полімербетону. Результати дисертації можуть використовуватись при розробці проектів будинків і споруд із підвищеною стійкістю до сейсмічних і динамічних навантажень.

EN: 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. The proper magnitudes of the weight coefficients are determined ensuring the minimal computational costs required to detect the global extrema. A comparative analysis of the particle swarm optimization procedure and the genetic algorithm is presented. The both methods allow determination of the global extrema of the benchmark functions at approximately the same computational costs. However, the particle swarm optimization procedure provides a gradual slowing down of all particles and their stopping in the vicinity of the extremum. Instead, in the considered variant of the genetic algorithm, the particles continue moving stochastically around the extremum, which can complicate the decision to terminate the search process. According to the results of the analysis, in the dissertation the particle swarm method is employed to determine the places of rational locations of friction dampers. Numerical models of multi-storey buildings with dry friction dampers are further developed. A 2D model of a ten-storey reinforced concrete frame building is considered. 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. A design solution with three friction dampers installed as braces in the central span of the building is considered. 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 load amplitude is determined in such a way that the displacement of the top of the frame should be equal to the displacements obtained before by the seismic analysis. A periodic load is applied during a specified period of time, after which free vibrations of the building occur. The objective function is the displacement amplitude of the top of the frame after a certain time after removing the load. The problem of the rational location of friction dampers is solved by the method of particle swarm optimization. A population of 8 particles is employed. The rational locations of the dampers are determined at the floors 2, 5 and 6, which provide the fastest attenuation of the vibrations of the structure. 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. A 2D model of a six-storey reinforced concrete frame building is considered. 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. Let us note that the presence of dry friction dampers involves a significant nonlinearity into the input dynamical equations. Further, the governing equations of motions are 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 obtained analytical and numerical solutions are in a good agreement. The analysis of the displacement patterns of the lowest six normal modes evaluated in LIRA-SAPR confirms the validity of the basic physical assumptions of the lumped mass model. The problem of a rational location of friction dampers in the six-storey frame building using the proposed lumped mass model is considered. A design solution with three dampers installed as braces in the central span of the building is adopted. 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 predicted using the method of particle swarm optimization with a population of 16 particles. The same solution is obtained for the both objective functions implying the installation of the all three dampers at the floor 1. Mathematical models of seismic loads are further developed. 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. Using the method of particle swarm optimization, the population of 16 particles is employed to predict the rational locations of friction dampers. 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 response of the polymer concrete structure to periodic and seismic loads is investigated. 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.