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Essays of Discrete Structures: Purposeful Design of Grammatical Structures by Directed Stochastic Search

Essays of Discrete Structures: Purposeful Design of Grammatical Structures by Directed Stochastic Search

Year: 1997

Author: Kristina Shea

Supervisor: Prof. Jonathan Cagan

Institution: Carnegie Mellon University

Pages: 1-173

Abstract

This work presents a computational approach to the layout of discrete structures that incorporate practical design goals for routine and challenging design problems. The number of alternatives for the configuration of discrete structures that satisfy multiple design goals is quite large and the competition among design goals can make the relation between form and function unclear. Therefore, the objective of this work is a computational method capable of searching this ill-defined design space to generate innovative design alternatives that enhance creativity and provide insight into form-function relations for multiobjective structural design.
A grammatical approach to structural design is enabled by applying shape annealing, a computational design technique that combines a grammatical formalism (shape grammars) with directed stochastic search (simulated annealing), to the layout of discrete structures. A shape grammar is used to define a language of discrete structures through the specification of spatial design transformations that implicitly represent the relation between form and function in trusses. Two shape grammars, a planar truss grammar and a single-layer space truss grammar, will be presented. In order to generate purposeful designs from this language, an optimization model is presented that incorporates the structural design goals of efficiency, economy, utility and elegance.
Applying a grammatical approach to the design of discrete structures has resulted in the generation of structural essays where an essay of designs explores relations among design criteria and spatial forms in a particular structural design domain. Structural essays are presented for planar trusses, towers, pseudo-tensegrities, and single-layer space trusses that form domes and complex roof shapes. The purpose in generating structural essays is to provide the designer with a set of functionally feasible and optimally directed designs that explore the relation between form and function in the context of the design application. Additionally, presenting alternative design styles could enhance the creativity of a designer in conceiving a novel solution. Four main contributions result from this work: (1) a grammatical approach to structural design, (2) a computational design method for the generation of essays of innovative, discrete structures that reflect practical design goals, (3) a stochastic, discrete method for structural topology, shape and sizing optimization, and (4) a proof-of-concept of the shape annealing method as an effective method for design configuration problems.

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