A meshless numerical method for optimised design of buried structures in elastic medium

Performance-based design is critical to examine how changes in design parameters influence the safety and stability of the examined structural systems, ensuring optimised performance under varying conditions. Traditional approaches such as finite element method, require careful domain meshing and mesh-sensitivity studies, which are often computationally expensive and, in some cases, mathematically challenging for certain types of problems. Meshless approaches provide efficient and accurate prediction models to address this problem effectively. In this paper, a two-dimensional singular boundary method combined with the method of fundamental solutions is formulated in conjunction with the direct differentiation method to perform design sensitivity-based optimisation of structures embedded in elastic medium under harmonic point loads. The proposed formulation is employed to overcome the non-uniqueness solution problem arising in the singular boundary method when dealing with exterior elastic problems. The accuracy and effectiveness of the proposed approach is assessed in the framework of two analytical examples: a cylindrical cavity subjected to pulsating pressure under Neumann boundary condition and a cavity with a five-cusped hypocycloid boundary under Dirichlet boundary condition. Additionally, the method is assessed in an application of a horseshoe-shaped tunnel embedded in full-space medium and subjected to Neumann boundary conditions. The results indicate that the proposed approach is both accurate and robust for performing sensitivity analysis on complex geometries in elastic media, particularly when compared to the classical singular boundary method. Furthermore, the application case study demonstrates that the method can be effectively used for optimising the shape of underground structures to minimise the impact of geometry on deformations of the surrounding soil. This methodology offers several advantages: it is truly meshless, integration-free, mathematically simple, and easy to implement, providing a valuable tool for decision-making in the design of buried structures within elastic media.