Solução de problemas dinâmicos envolvendo a interação solo-estrutura pelo método de espaço de estados

Abstract

With the advancement of construction technologies, population density, and land scarcity, buildings have become increasingly tall and slender, and seismically active regions are being inhabited. The analysis of the dynamic behavior in the structure, considering the effects of soil-structure interaction (SSI), is important to avoid erroneous estimates in the previous analysis of the project and to guarantee the safety and structural stability. However, the study involves the use of complex language and methods that demand high computational cost, such as the use of finite element and boundary element methods. In the present work, the generalized state-space solution method for N floors was used, considering only the bending effect as a response to the vibration arising from the coupled soil-structure problem and seismic excitation. The study basically consists of four phases, all applied to two-dimensional metallic structures. The first is intended to validate the state-space model implemented in this research. The second phase consists of the application of a seism acting directly on the first mass of the two-dimensional metallic structure with three floors and comparing the algorithm with the solution using the 4th-order precision Runge-Kutta method. The third phase is the generalization of the state-space method for coupled problems involving SSI. The last phase is the comparison between the structure (i) being excited directly in the structure and (ii) considering the coupled SSI problem. The calculations were implemented in the commercial Matlab software and the results are presented in the time and frequency domain. The results obtained by the state-space method, when validated and compared, had an excellent agreement with the analytical solution and with the Runge-Kutta method, respectively