The contribution of this work centers on the establishment of a novel topology optimization framework targeted specifically towards the needs of the structural engineering industry. Topology optimization can be used to minimize the material consumption in a structure, while at the same time providing a tool to generate design alternatives integrating architectural and structural engineering concepts. This tool can be an initial step towards the creation of efficient designs and provides an interactive, rational process for a project where architects and engineers can more effectively incorporate each other's ideas. Through the selection of layout constraints, the objection function, and other metrics that might fit the problem being studied, the engineer can then present the architect with a spectrum of solutions based on these parametric studies. This selection process has been shown to provide new ways to look at designs, which in turn inspires the overall design of the structure.To streamline and simplify the design process, the computational framework described throughout this thesis is based on an integrated topology optimization approach involving the concurrent optimization of both continuum (e.g. Q4, polygonal) and discrete (e.g. beam, truss) finite elements to design the structural systems of high-rise buildings. For instance, after the overall shape and location of the perimeter columns of the building are known, topology optimization can be used to design the internal structural system, while concurrently sizing the members. Moreover, while typical topology optimization problems are based on a single objective function (i.e. minimum compliance), in the context of buildings it is important to evaluate and account for potential geometric instabilities as well. Thus, multi-objective optimization, including linearized buckling, has been studied in this context. To handle the large amounts of data associated with a high-rise, this new framework has been written to take advantage of a topological data structure together with object-oriented programming concepts to handle a variety of finite element problems, in an efficient, but generic fashion as demonstrated in this work. Several practical examples and case studies of high-rise buildings and other architectural structures are given to show the importance and relevance of this approach to the structural design industry.Finally, to better understand the geometries derived throughout the thesis, optimal structures are explored in more detail using the notions of graphic statics and reciprocal diagrams. The advantage to using graphic statics for this class of optimal problems is that it provides all of the information needed to determine the total load path in a graphical manner, allowing the engineer and/or architect to gain valuable insight to the problem at hand. Moreover, using the reciprocal form and force diagrams, we describe how in the course of finding one minimum load path structure, a second minimum load path structure is also found. These analytical studies parallel several of the numerical examples derived throughout the thesis to verify the resulting topologies from a different perspective.
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