This paper presents an efficient MATLAB framework for large-scale density-based topology optimization and porous infill optimization in 3D. Besides showing comparable computational efficiency with existing MATLAB implementations at equivalent simulation scales, this framework supports significantly larger models with up to 128 million hexahedral simulation elements on a standard PC equipped with 64 GB RAM. Furthermore, it can handle arbitrary non-cuboid design domains and does not require powers-of-two differences in the elements’ spatial resolutions. To achieve this, the technical contribution concentrates on solving the linear system of static finite element method (FEM). A tailored element-based matrix-free computing stencil is demonstrated to circumvent the vast memory consumption in large-scale FEM. Its computational efficiency is assured by fully leveraging the efficient matrix–vector operations and indexing functionalities in MATLAB. We further improve the computational efficiency and memory consumption of the MATLAB-implemented geometric multigrid method with a non-dyadic Galerkin coarsening and a diagonal relaxation scheme.

Variable thickness sheet and homogenization-based topology optimization often result in spread-out, non-well-defined solutions that are difficult to interpret or de-homogenize to sensible final designs. By extensive numerical investigations, we demonstrate that such solutions are due to non-uniqueness of solutions or at least very flat minima. Much clearer and better-defined solutions may be obtained by adding a measure of non-void space to the objective function with little if any increase in structural compliance. We discuss various alternatives for cleaning up solutions and propose two efficient approaches which both introduce an auxiliary field to control non-void space: one approach based on a cut element based auxiliary field (hybrid approach) and another approach based on an auxiliary element based field (density approach). At the end, we demonstrate significant qualitative and quantitative improvements in variable thickness sheet and de-homogenization designs resulting from the proposed cleaning schemes.

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid–structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance equations. Upon each linearization step, the number of unknowns is strongly decreased by using modal reduction, which leads to a substantial gain in computational efficiency. Through adaptive re-calibration and truncation augmentation whenever a non-dimensional deformation threshold is exceeded, we ensure that the reduced modal basis maintains arbitrary accuracy for small and large deformations. Our novel model is embedded into a partitioned, loosely coupled finite volume–finite element framework, in which the structural interface motion within the Eulerian fluid solver is accounted for by a conservative cut-element immersed-boundary method. Applications to the aeroelastic instability of a flat plate at supersonic speeds, to an elastic panel placed within a shock tube, and to the shock induced buckling of an inflated thin semi-sphere demonstrate the efficiency and accuracy of the method.

This work considers an efficient approach for length scale control in high-resolution three-dimensional level set–based topology optimization. A contrast parameter–based cut element method is employed to ensure a crisp interface representation while working on fixed background hexahedral meshes. This enables the use of efficient multigrid preconditioned Krylov methods in massively parallelized computations. The minimum length scale is controlled using a projection filter without the need for β-continuation. The capabilities of the proposed approach is demonstrated on several numerical examples using more than 62 million hexahedral elements.

Additive manufacturing (AM) and topology optimization (TO) form a pair of complementary techniques in transforming digital models into physical replicas: AM enables a cost-effective fabrication of geometrically complex shapes, while TO provides a powerful design methodology for generating optimized models, which are typically complex from a geometric perspective. The potential of both techniques has recently been explored in graphics, resulting in fantastic applications especially regarding structural and aesthetic properties of fabricated models. In this tutorial, we start from the fundamentals of AM and TO, and proceed to advanced TO techniques which steer the optimization process, i.e., taking into account the manufacturing as well as aesthetic appearance.