Optimisation of Discrete Structures with Multiple Mechanical Constraints and Geometric Complexity Control

Abstract

Discrete structures, including trusses, frames, and grid structures, are renowned for their lightweight nature and ability to span long distances while providing unobstructed interior space. Despite their widespread use in engineering, significant challenges remain in the design process, particularly in simultaneously addressing mechanical constraints and controlling geometric complexity. The flexibility of joint connections in these structures allows for efficient design by enabling the configuration of structural members where necessary. However, this design freedom also leads to numerous combinations of nodal positions and member connectivity, complicating the formulation of optimisation problems that concurrently consider mechanical performance, manufacturability, and cost-effectiveness.

Extensive research has explored the layout optimisation of discrete structures, often focusing on specific mechanical performance metrics such as structural compliance, displacement, stress, or stability. There remains a notable scarcity of comprehensive methods that systematically integrate these practical mechanical constraints to ensure overall structural integrity and safety, especially for large-scale structures with expansive design space and numerous candidate elements. Furthermore, direct results from layout optimisation typically exhibit intricate geometric features, including a large number of elements and overlapping, interconnected members, which significantly hinder manufacturability if not simplified. These challenges are particularly pronounced in grid structures, where member configurations and load-bearing mechanisms extend into 3D, presenting further complexities compared to the predominantly 2D operational structural systems of trusses and frames.

To tackle these challenges, this thesis investigates the layout optimisation of frames and grid structures, simultaneously addressing multiple mechanical constraints and controlling geometric complexity. The proposed methods aim to produce optimal discrete structures that exhibit satisfactory mechanical performance, economic efficiency, and practical manufacturability. The mechanical constraints considered include displacement, stress, and both local and global stability. Geometric complexity control is achieved through three distinct approaches: simplification, regularisation, and diversification. These optimisation frameworks are developed based on the ground structure method, where initial designs are formulated by connecting nodes within prescribed domains. Numerous constraints related to mechanical performance metrics and geometric complexity control are consolidated into unified global expressions to streamline sensitivity analysis and optimisation in the gradient-based optimiser{---}the Method of Moving Asymptotes.

The effectiveness of the proposed methods is evaluated through case studies, confirming their efficiency in generating optimal layouts characterised by desirable mechanical performance, minimal material usage, and manufacturable geometric features. In frame structures, the resulting designs generally present minimal low-stiffness elements, while achieving simplified complexity in member connectivity by reducing the number of elements. Meanwhile, for grid structures, the optimal layouts are regularised with modular structural units and diversified with varying element arrangements. Overall, this thesis advances the field of layout optimisation for discrete structures, facilitating the creation of optimal designs that excel in mechanical performance, construction feasibility, and economic efficiency.

Date of Award	13 Nov 2024
Original language	English
Awarding Institution	Department of Architecture & Civil Engineering
Supervisor	Paul Shepherd (Supervisor) & Jie Wang (Supervisor)