The full-section asphalt concrete waterproof layer (FACWL) has garnered significant attention for its outstanding ability to reduce frost heave and thaw-related weakening in railway track beds, particularly in seasonally frozen regions. To explore the dynamic properties of the FACWL, a fractional-order constitutive model was utilized to characterize the viscoelastic behavior of asphalt concrete. Additionally, a vehicle–track coupled finite element (FE) model and the numerical approach incorporating the fractional-order constitutive model were developed and validated via experimental and field testing. Simulation results indicate that applying the FACWL reduces the vertical dynamic response of each structural layer, vertical peak accelerations across the subgrade surface layer exhibited reductions exceeding 30% in both positive and negative directions. Moreover, the tensile strain at the bottom of the FACWL remained relatively low, less than 100 με. Compared with conventional waterproof sealing layers, the viscoelastic nature of the FACWL facilitates energy dissipation, effectively decreasing the overall vibrational amplitude and vertical deformation within the track structure by more than 20%. Consequently, the FACWL plays a crucial role in ensuring the long-term stability of the subgrade and minimizing vibrations in the track system.

In this paper, a deep learning framework combined with isogeometric analysis (IGA for short) called IGA-Reuse-Net is proposed for efficient reuse of numerical simulation on a set of topology-consistent models. Compared with previous data-driven numerical simulation methods only for simple computational domains, our method can predict high-accuracy PDE solutions over topology-consistent geometries with complex boundaries. UNet3+ architecture with interlaced sparse self-attention (ISSA) module is used to enhance the performance of the network. In addition, we propose a new loss function that combines a coefficients loss and a numerical solution loss. Several training datasets with topology-consistent models are constructed for the proposed framework. To verify the effectiveness of our approach, two different types of Poisson equations with different source functions are solved on three datasets with different topologies. Our framework can achieve a good trade-off between accuracy and efficiency. It outperforms the physics-informed neural network (PINN for short) model and yields promising results of prediction.

Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with similar semantic features. Given a template domain, B-spline based consistent volumetric parameterization is first constructed for a set of models with similar semantic features. An efficient quadrature-free method is investigated in our framework to compute the entries of stiffness matrix by Bézier extraction and polynomial approximation. In our approach, evaluation on the stiffness matrix and imposition of the boundary conditions can be pre-computed and reused during IGA on a set of CAD models. Examples with complex geometry are presented to show the effectiveness of our methods, and efficiency similar to the computation in linear finite element analysis can be achieved for IGA taken on a set of models.