Automatic modelling of heterotypic tunnel structures via NURBS-based meshfree method

Abstract

• A NURBS-based meshfree method is proposed for the automatic modelling of heterotypic tunnel structures. • The proposed method unifies continuous-discontinuous analysis in a NURBS-meshfree framework. • A premier integral cell generation approach free of boundary integral points discarding is developed, which improves the robustness of meshfree interpolation. • The proposed method eliminates the barrier between numerical theories and applied modelling in tunnel engineering. For heterotypic tunnel structures with complex geometries and diverse components, a meshfree (MF) method outperforms the finite element method in terms of modelling interfaces, cracks, and discontinuities. This paper proposes a nonuniform rational B-spline (NURBS)-based MF method (NURBS-MF) to analyze such structures. The proposed NURBS-MF combines the merits of both the NURBS representation and MF approach. By mapping the NURBS surface onto a canonical parametric domain, MF nodes in the NURBS-MF method can be generated, regardless of the geometries and discontinuities. An MF interpolation is implemented directly based on the MF nodes within this mapping domain, which creates a set of integral cells completely conforming with the geometry boundary. The integral cells along the boundaries do not split, and thus the discarding of invalid integral points is avoided. Under this framework, by simply inputting material parameters and a discretized grid size, a numerical tunnel model is automatically established based on the tunnel design model represented by NURBS in computer-aided design. Further, the modelling cost and difficulty of complex heterotypic tunnel structures are significantly reduced. Therefore, automatic modelling and calculation are possible with one click, which also eliminates the barrier between numerical theories and applied modelling in tunnel engineering. The proposed method is proven to be novel and efficient for practical engineering problems through several numerical tests.