Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

This paper presents a framework for implementing a novel perfectly matching layer and infinite element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain. To achieve this, traditional hexahedral finite elements are used to model wave propagation in the inner domain and IE test functions are implemented in the exterior domain. Two alternative implementations of the PML formulation are studied: the case with constant stretching in all three dimensions and the case with spatially dependent stretching along a single direction. The absorbing ability of the PML+IE formulation is demonstrated by the favourable comparison with the reflection coefficient for a plane wave incident on the boundary achieved using a finite-element-only approach where stress free boundary conditions are implemented at the domain edge. Values for the PML stretching function parameters are selected based on the minimisation of the reflected wave amplitude and it is shown that the same reduction in reflection amplitude can be achieved using the PML+IE approach with approximately half of the number of elements required in the finite-element-only approach.

Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates

An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.

3D Forward Modeling of Seepage Self-potential Using Finite-infinite Element Coupling Method

The streaming potential in porous media is one of the main constituents of the self-potential. It has attracted special attention in environmental and engineering geophysics. Forward modeling of streaming potentials could be the foundation of corresponding data inversion and interpretation, and improving the application effect of the self-potential method. The traditional finite element method has a large subdivision area and computational quantity, and the artificial boundary condition is not suitable for complex models. The Helmholtz-Smoluchowski equation is introduced for evaluating the streaming potential. Then three new shape functions of the multidirectional mapping infinite elements are proposed and the finite-infinite element coupling method is deduced for reducing the subdivision scale and improving both the calculation efficiency and accuracy. The correctness and validity of the new coupled method are verified by a resistive model in homogeneous half-space. Besides, a seepage model with complex terrain and a landfill model with dynamic leakages are modeled using the improved coupled method. The results show that the accuracy of the improved coupled method is superior to the unimproved coupled method, and is better than the finite element method. Also, the coupled method has better adaptability to complex models and is suitable for the accurate simulation of dynamic multi-source seepage models.