Level set band method: A combination of density-based and level set methods for the topology optimization of continuums

Abstract

The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

Topology Optimization for Steady-State Navier-Stokes Flow Based on Parameterized Level Set Based Method

“…In this way, the fluid-solid results can be obtained without intermediate materials. Wei et al [64] proposed a new method, called the level set band method, combining the density method and the level set method, to improve the continuity of objective and constraint functions. This method can deal with the problem of permeability distribution optimization well and is a promising research direction.…”

Automatic Segmentation of the Retinal Nerve Fiber Layer by Means of Mathematical Morphology and Deformable Models in 2D Optical Coherence Tomography Imaging

“…By contrast, in the implicit models [ 63 , 64 ], also called geometric deformable models, contours and surfaces are implicitly represented as level-sets of a scalar function of higher dimensions. The evolution of these implicit models is based on the theory of curve evolution, which allows their adaptation even to concave shapes and topology changes [ 63 , 65 ]. Since the retinal layers to be segmented in this work show a smooth shape and no change in topology, one-dimensional parametric models, also called active contours or snakes [ 61 ], are used in this work.…”

Open-Source Codes of Topology Optimization: A Summary for Beginners to Start Their Research

“…The level set approach employs the zero-contours of high-dimensional implicit functions to describe structural design boundaries [60] Around 2003, Wang et al [10] and Allaire et al [11] first adopted the sensitivity analysis method based on shape derivatives. They applied the LSM to the field of TO, opening up a new research direction [19].…”