A Plasticity-based Topology Optimisation (PTO) Method and its Applications to Geostructure Design

Conventional topology optimisation frameworks in structural and geotechnical engineering have predominantly relied on elastic analysis, often overlooking the nonlinear characteristics and collapse behaviour of materials. To address this limitation, this thesis develops a plasticity-based topology optimisation framework for the design of continuous structures, particularly geostructures, where material failure is explicitly incorporated into the design formulation. The proposed numerical framework integrates mixed limit analysis within a density-based topology optimisation approach. Penalisation strategies are introduced to achieve black-and-white designs, with the final problem formulated as a standard second-order cone programming (SOCP) problem, which is solved using a primal–dual interior-point algorithm. For enhanced computational efficiency, the smoothed finite element method (S-FEM) is employed, enabling the use of linear tetrahedral elements without volumetric locking issues. Additionally, mesh refinement techniques are employed to further optimise computational performance. The framework is progressively extended from the design of single-material systems to multi-material systems, facilitating the optimal placement of reinforcement materials within weaker domains. This multi-material formulation is particularly advantageous for geotechnical applications, where reinforcement can significantly enhance the stability of geostructures. Case studies presented in this thesis - including plates, beams, bridges, embankments, and shallow foundations - demonstrate superior collapse resistance compared to conventional elasticity-based designs. To bridge the gap between numerical design and practical implementation, a physical model test is conducted. A geo-foundation structure, comprising untreated and biopolymer-treated clay, is fabricated based on the optimised layout and subjected to laboratory testing. The measured collapse load and failure pattern closely align with numerical predictions, thereby verifying the reliability and applicability of the proposed optimisation approach. Overall, this thesis provides a computationally efficient and physically consistent framework for collapse-oriented design, advancing the capabilities of topology optimisation in both structural and geotechnical contexts, with demonstrated potential for practical application in sustainable infrastructure development.