Topology optimization using a continuous density field and adaptive mesh refinement

Abstract

A new method of topology optimization is introduced in which a continuous material field is combined with adaptive mesh refinement. Using a continuous material field with different analysis and design meshes allows the method to produce optimal designs that are free of numerical artifacts like checkerboard patterns and material islands. Adaptive mesh refinement is then applied to both meshes to precisely locate the optimal boundary of the final structure. A Helmholtz-type density filter is used to prevent the appearance of small topological features as the mesh refinement proceeds. Results are presented for several test problems, including problems with geometrically complex domain boundaries.

A density field parametrization for topology optimization using Bernstein elements

“…In the case of the first‐order Bernstein elements, Figure shows that small holes and structural members can emerge in the refined parts of the mesh as the mesh is refined. This confirms our earlier result and is a consequence of not applying any kind of filter to the density field (the designs produced in our previous work are virtually identical to those shown in Figure ). As a result, the minimum feature size is driven by the mesh size.…”

“…In all other respects, the method described in the previous work is identical to the present method with first‐order Bernstein elements in the design mesh. Figure reproduces results from our previous work for the case of no Helmholtz filter and three mesh refinement steps for the same cantilever beam problem. The optimal topology obtained is clearly different from that shown in Figure .…”

“…One crucial detail of the meshing scheme we use is that the “design” mesh describing the density field and the “analysis” mesh describing the displacement field are coupled. In our previous work, which considered adaptive mesh refinement with first‐order elements in both meshes, we found that taking the analysis mesh to be a global refinement of the design mesh was effective in preventing the appearance of material “islands” described by Rahmatalla and Swan when linear elements were used in both meshes. This is an alternative to using higher‐order elements or nonaligned meshes that is both straightforward to implement and computationally inexpensive to run.…”

“…The volume fraction limit V * is set to 0.3 in all test problems. The computational environment we use is similar to that employed in our previous work, 17 so we only summarize the major details here. The finite element calculations are carried out with the deal.II C++ package.…”

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

“…Since the shell structures are widely used in the engineering domains such as aerospace, vehicle and ship, the ITO for shell structure optimization has a bright prospect for solving engineering problems. Moreover, the IGA has the local refinement ability [Vuong, Giannelli, Jüttler et al (2011); Scott, Li, Sederberg et al (2012); Wu, Huang, Liu et al(2015)], which provides an opportunity to easily implement the topology optimization with adaptive mesh [Lambe and Czekanski (2018); Wang, Kang and He (2013)]. Definitely, the ITO can be also combined with other approaches used in conventional topology optimizations, e.g.…”