Level set based shape optimization using trimmed hexahedral meshes

A novel adaptive mesh refinement scheme for the simulation of phase‐field fracture using trimmed hexahedral meshes

“…TH meshes showed a good performance for solving structural problems with nonlinear materials, 21 complex composite domains, 22 and shape optimization. 23 Recently, explicit shape functions for TH elements 24 have been developed to reduce the computational cost for building the stiffness matrix of TH elements. Adaptively refined TH meshes created from octree background meshes can effectively resolve the length scale in phase-field fracture models.…”

“…TH meshes consist of TH elements (polyhedral elements) on the domain boundary and regular hexahedral elements inside the domain. TH meshes showed a good performance for solving structural problems with nonlinear materials, 21 complex composite domains, 22 and shape optimization 23 . Recently, explicit shape functions for TH elements 24 have been developed to reduce the computational cost for building the stiffness matrix of TH elements.…”

A novel formulation for the explicit discretisation of evolving boundaries with application to topology optimisation

“…While this method provides an explicit discretization of the boundary at every time-step, it becomes inefficient, as the geometry gets larger and more complex, to recreate the mesh at every time-step [1,10]. With remeshing, complex data-structure handling schemes are often required to handle the mesh changes [27]. From the point of view of implementation in a typical FEM package, this approach requires changing the input file of the analysis at every iteration.…”

“…An alternative strategy to represent explicitly an evolving boundary, presented by Nguyen and Kim [27], consists of trimming hexahedral meshes. This element-trimming approach relies on a background mesh of regular hexahedral elements, and on the information provided by the zero-level isosurface of the LS function, to break the hexahedral elements into multiple polyhedral elements.…”

“…This element-trimming approach relies on a background mesh of regular hexahedral elements, and on the information provided by the zero-level isosurface of the LS function, to break the hexahedral elements into multiple polyhedral elements. The polyhedral elements provide good accuracy for complex-geometry parts, but they also require complex schemes to obtain the shape functions, often requiring the division into simpler (tetrahedral) sub-domains [27]. Furthermore, the marching cubes algorithm used requires changing element connectivities -and, consequently, the analysis input file [27].…”