A time-domain approach for the simulation of three-dimensional seismic wave propagation using the scaled boundary finite element method

A direct time-domain approach to simulate seismic wave propagation in three-dimensional unbounded media is proposed based on the Scaled Boundary Finite Element Method (SBFEM). A domain of interest is commonly partitioned into a far field and a near field. The far field is modelled by the semi-analytical SBFEM satisfying rigorously the radiation conditions at infinity. Separate scaled boundary finite elements are employed to reach a balance between computational efficiency and accuracy. The near field is discretized into arbitrarily-shaped scaled boundary finite elements without the occurrence of hanging nodes. This advantage of the SBFEM in mesh generation is leveraged by incorporating the automatic octree-based meshing technique. By exploiting the geometrical similarity of both bounded and unbounded SBFE subdomains the computational cost is reduced. Inspired by the Domain Reduction Method (DRM), seismic waves are introduced to the system via a single layer of elements in the near field. This formulation of seismic input is mathematically convenient as it avoids the direct participation of the formulation of the far field. The proposed approach is attractive in a reliable simulation of the far field, flexible mesh generation of the near field and simple formulation of the seismic excitations. These merits are demonstrated through numerical simulations of seismic wave propagation in a free field and different examples featuring complex geometries in the near fields

Three-dimensional image-based numerical homogenisation using octree meshes

The determination of effective material properties of composites based on a three-dimensional representative volume element (RVE) is considered in this paper. The material variation in the RVE is defined based on the colour intensity in each voxel of an image which can be obtained from imaging techniques such as X-ray computed tomography (XCT) scans. The RVE is converted into a numerical model using hierarchical meshing based on octree decompositions. Each octree cell in the mesh is modelled as a scaled boundary polyhedral element, which only requires a surface discretisation on the polyhedron's boundary. The problem of hanging (incompatible) nodes – typically encountered when using the finite element method in conjunction with octree meshes – is circumvented by employing special transition elements. Two different types of boundary conditions (BCs) are used to obtain the homogenised material properties of various samples. The numerical results confirm that periodic BCs provide a better agreement with previously published results. The reason is attributed to the fact that the model based on the periodic BCs is not over-constrained as is the case for uniform displacement BCs

An Open-Source ABAQUS Implementation of the Scaled Boundary Finite Element Method to Study Interfacial Problems Using Polyhedral Meshes

The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis pipeline in the standard finite element method (FEM). In this paper, we implement polyhedral elements based on the SBFEM into the commercial finite element software ABAQUS. To this end, user elements are provided through the user subroutine UEL. Detailed explanations regarding the data structures and implementational aspects of the procedures are given. The focus of the current implementation is on interfacial problems and therefore, element-based surfaces are created on polyhedral user elements to establish interactions. This is achieved by an overlay of standard finite elements with negligible stiffness, provided in the ABAQUS element library, with polyhedral user elements. By means of several numerical examples, the advantages of polyhedral elements regarding the treatment of non-matching interfaces and automatic mesh generation are clearly demonstrated. Thus, the performance of ABAQUS for problems involving interfaces is augmented based on the availability of polyhedral meshes. Due to the implementation of polyhedral user elements, ABAQUS can directly handle complex geometries given in the form of digital images or stereolithography (STL) files. In order to facilitate the use of the proposed approach, the code of the UEL is published open-source and can be downloaded from https://github.com/ShukaiYa/SBFEM-UEL.Comment: 34 pages, 34 figure

Dynamic non-local damage analysis using an octree pattern-based massively parallel explicit solver

This paper presents the development of a massively parallel explicit solver based on the central difference method (CDM) for the dynamic analysis of damage processes. In this context, the material degradation is incorporated using an integral-type non-local isotropic damage model. A fully automatic preprocessing is enabled by following the octree-based mesh generation paradigm. To handle neighbouring elements with different sizes and to avoid hanging nodes in the generated mesh, polyhedral elements are implemented within the framework of the scaled boundary finite element method (SBFEM). A pre-computation approach is advocated to develop a highly efficient solver, where the limited number of master cells in a balanced octree grid are exploited. The parallelisation is carried out using a mesh-partitioning technique and message-passing-interface (MPI) directives, which is highly complementary to the use in high-performance computing (HPC) facilities. In order to showcase the performance of the proposed solver, a problem of practical interest is selected, featuring the analysis of an XCT image-based model of concrete containing about 1 billion voxels. The simulated results have been obtained within minutes by exploiting the computational power of approximately 12k cores