Architectural Morphogenesis Through Topology Optimization

Architectural Morphogenesis Through Topology Optimization

Roberto Naboni (Politecnico di Milano, Italy) and Ingrid Paoletti (Politecnico di Milano, Italy)
DOI: 10.4018/978-1-5225-3993-3.ch004

Abstract

This chapter illustrates the main approach for a generative use of structural optimization in architecture. Structural optimization is very typical of sectors like mechanical, automotive engineering, while in architecture it is a less used approach that however could give new possibilities to performative design. Topology Optimization, one of its most developed sub-methods, is based on the idea of optimization of material densities within a given design domain, along with least material used and wasted energy. In the text is provided a description of TO methods and the principles of their utilization. The process of topology optimization of microstructures of cellular materials is represented and illustrated, emphasizing the all-important criteria and parameters for structural design. A specific example is given of the research at ACTLAB, ACB Dept, Politecnico di Milano, of performative design with lattice cellular solid structures for architecture.
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Background On Structural Optimization

In structural engineering, a main goal is developing load-bearing systems which satisfy economically the design performance objectives and safety constraints. Economical consideration is often the main driver for developing a design process that enables the minimization of resource consumption. In doing so, an important concept is the one of optimization, that refers to the selection of the best element from some set of available alternatives (Radman, 2013). Optimality conditions of structural systems have been introduced first in 1901 by Anthony Michell in his theoretical study The Limit of Economy of Material in Frame-Structures” (Michell, 1904). What Michell claimed is a continuous displacement field with equal and opposite principal strains, considered as limit strains of the material in compression and tension. If in a particular problem it is possible to design a structure all of whose members are in tension, or alternatively compression, then the optimum design is achieved, since all the members of a truss are laid along these principal strain lines. Also, the tension and compression members that meet at a node must be orthogonal, since they lie along principal directions with unequal principal strains e and -e.

Figure 1.

Loads in the members of the Michell cantilever due to a unit load at the tip

The work of Michell was remarkable because he achieved these results without any prior work on optimization theory, but largely based on intuition. However, it suffers some limitations: it is limited to planar structures, distributed loads are not included, loads are applied only on the boundary, the manner by which a truss approaches the infinitely refined limit is not addressed, and consequently the exact relationship between the limit and the underlying discrete truss structures is unclear.

Figure 2.

Michell’s optimality analysis of structural systems are based mostly on intuition, with no prior work, but they are applied only on two dimensional structures and considering just loads applied on the boundaries

Wider access to computational work in 1990s justified the development of numerical procedures for the TO of structures, aimed at finding the best layout, configuration and spatial distribution of materials in the design domain of the continuum structure (Bendsøe and Kikuchi, 1988).

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