Related papers: Shell topology optimization based on level set met…
For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…
Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how…
The work provides an exhaustive comparison of some representative families of topology optimization methods for 3D structural optimization, such as the Solid Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional…
We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
Shell structures with a high stiffness-to-weight ratio are desirable in various engineering applications. In such scenarios, topology optimization serves as a popular and effective tool for shell structures design. Among the topology…
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…
Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior…
This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…
The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit…
Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e. components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…
This paper presents a density-based topology optimization approach to design structures under self-weight load. Such loads change their magnitude and/or location as the topology optimization advances and pose several unique challenges,…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…