Constrained Structural Optimisation

University of Sheffield

Department of Civil and Structural Engineering

Project Description

The Constrained Force Density Method (CFDM) improves upon the original tried and tested Force Density Method (FDM), which uses member force densities (forces divided by lengths) to define the internal stress state in a structural form-finding process. The FDM has been applied to various strut and tie like structures such as trusses, gridshells and also as thrust network models for representing shell structures (particularly in the area of membrane-only forces). To date, it has been used in a generally unconfined and prescribed format, where the force densities are given manually by the user, and the free vertices allowed to move without limit in all spatial directions. The CFDM improves in this regard from the original FDM by optimising the distribution of internal force densities for design and fabrication objectives, such as minimum volume or construction-related objectives, and for allowing different types of geometric and force driven controls.

This research project aims at extending the CFDM to include a greater set of constraints, applications, objectives, and to explore the design space for a range of different structural forms. Such as: constraining or optimising along or to target surfaces, solving self-weight and load combinations, promoting symmetry, using machine learning methods for design space exploration, additional practical fabrication constraints and targets, investigating joint complexity, evaluating the importance of patterning and the topology of the structure, and the inclusion of local and global stability in analysis. It will also consider the use of other forms of structural analysis and form-finding algorithms (Surface Stress Density Method, Layout Optimisation, Dynamic Relaxation, to name a few) as comparative or alternative methods to meet this end. Such constrained structural optimisation methods help engineers to better use our construction material more responsibly and design/analyse more efficient structural forms.

Optimisation methods to utilise include constrained linear, quadratic and general non-linear programming, and potentially also heuristic methods (such as evolutionary methods). Thus this project involves a confidence to learn, or a current high ability in mathematical and programming methods. The use of Computer Aided Design and modelling software is also key, using Rhinoceros and/or Blender to interface with numerical methods.

Funding Information

This position is for a PhD student working full-time, after the successful award of a departmental EPSRC Doctoral Training Partnerships (DTP), or through a self-funded / scholarship placement.

Eligibility Requirements

The successful applicant is likely to have a first degree in engineering or mathematics. He/she will also have sound computer programming skills, to enable them to take full advantage of state-of-the-art mathematical optimisation and form-finding methods. Hands-on experience of CAD software is desirable but not compulsory.

Application Process

To apply please send a two-page CV and covering letter to [email protected].

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