Automatic image‐based stress analysis by the scaled boundary finite element method

Abstract

SUMMARYDigital imaging technologies such as X-ray scans and ultrasound provide a convenient and non-invasive way to capture high-resolution images. The colour intensity of digital images provides information on the geometrical features and material distribution which can be utilised for stress analysis. The proposed approach employs an automatic and robust algorithm to generate quadtree (2D) or octree (3D) meshes from digital images. The use of polygonal elements (2D) or polyhedral elements (3D) constructed by the scaled boundary finite element method avoids the issue of hanging nodes (mesh incompatibility) commonly encountered by finite elements on quadtree or octree meshes. The computational effort is reduced by considering the small number of cell patterns occurring in a quadtree or an octree mesh. Examples with analytical solutions in 2D and 3D are provided to show the validity of the approach. Other examples including the analysis of 2D and 3D microstructures of concrete specimens as well as of a domain containing multiple spherical holes are presented to demonstrate the versatility and the simplicity of the proposed technique.

A novel scaled boundary finite element formulation with stabilization and its application to image‐based elastoplastic analysis

“…The effect of the jagged boundary in the stress obtained from the elastic analysis is highly localized at the small elements along the jagged boundaries. The stresses away from the jagged boundaries remain close to the stresses obtained using geometry‐based meshes …”

“…This method typically produces a large number of elements leading to excessive computational burden. A more efficient approach is to utilize quadtree (2D) or octree (3D) algorithms to process digital image data . This approach avoids the generation of a large number of elements compared with the pixel‐based approach, since the quadtree and octree decompositions are able to allow the transition between the geometrical features of different scales efficiently.…”

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

“…Recourse is always made to some type of mathematical model, usually a set of partial differential equations (PDEs). The resulting problem is solved numerically using a wide variety of discretisation methods including finite element methods [22][23][24][25][26], finite differences, meshfree methods [27], isogeometric approaches [28,29], geometry independent field approximation [30,31], scaled-boundary finite elements [32][33][34][35][36], boundary element approaches [37], enriched boundary elements [38] or combinations thereof [39][40][41].…”

A scaled boundary finite element formulation for poroelasticity

“…Recently, with the introduction of scaled boundary shape functions, the application of the SBFEM has expanded to include more complex fields in engineering such as heterogeneous media, elastoplasticity, and geometric and material nonlinearity . The flexibility of the SBFEM allows seamless implementation with quadtree‐ and octree‐meshes,() leading to full automation of the engineering analysis with minimal human interaction. In this paper, the application of the SBFEM will be further extended for coupled‐field problems in engineering.…”

“…A balanced quadtree decomposition() is adopted to discretise the images. Quadtree meshes avoid the generation of a large number of elements due to their ability to rapidly transition between geometrical features of different scales() compared with pixel‐ or voxel‐based approaches, eg, the works of Hollister and Kikuchi and Huang and Li based on the FEM. The mesh generation process is fully automatic and significantly reduces the time and human effort required to convert an image into a mesh.…”