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Developing a Reduced-order Model of Hysteretic Shear Building by a Modal Transformation Method based on Mathematical Expansions

Barati, Mohammad Bagher | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53143 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Rahimzadeh Rofouei, Fayyaz
  7. Abstract:
  8. With the advent of virtual memory machines and parallel processing, there has been a considerable shift toward computer-aided design and nonlinear analysis of structures. But increasing the size of computer memory or increasing the number of processing units are not the only ways to achieve a satisfactory solution to a large, complex problem. Another useful method is to reduce the size of the problem so that the reduced model is small enough to be solved at an appropriate processing level, and yet the important engineering behavior of the model is preserved in the reduced problem.Reduced models as an alternative, have gained considerable attention throughout the years in order to meet the challenges such as providing accurate and reliable predictions of the structure’s future behavior while widening their span of applicability. Linear modal analysis is undoubtedly one of most used methods in structural analysis that uncouples the equations of motion by projecting the equations of motion on linear normal modes and helps to avoid time-consuming and costly methods, e.g., direct integration, that solves a set of coupled differential equations. However, following some circumstances in nonlinear systems, the equations of motion might not become fully-decoupled upon using linear modal analysis. A possible solution is removing the terms causing the coupling as it happens in linearization methods; however, the decision is not rational if those terms are of importance or including the nonlinear behavior. An approach that does not project the nonlinear system on a reduced basis, e.g., linear modes, is nonlinear normal modes which, later, its definition was established as a low-dimensional, invariant manifold in the phase space. According to invariant manifolds approach, coordinates of the system are described as “Master and Slave” and relations between them is constructed using mathematical expansions such as Taylor series etc.The overall aim of this work is the creation of an algorithm that allows obtaining the solution of a conservative and hysteretic shear building model under ground motion while considerably reducing the computational effort, taking into account the hysteretic behavior of the system. The proposed algorithm is employed to transform the original structure into a geometrically nonlinear system and removes the possible coupling through defining the slave modes based on master modes. Therefore, considering the observations resulted from the implementation of the proposed method upon a 2D shear building with hysteretic and un-damped configuration, it can be said that the approach rather meets the expectations and provides avenues for further developments to expand its scope of applicability
  9. Keywords:
  10. Reduced Order Model ; Hysteretic Shear Building ; Nonlinear Normal Modes ; Invariant Manifolds ; Hysteresis Behavior

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