Concurrent Optimization of Structure Topology and Infill Properties With a Cardinal-Function-Based Parametric Level Set Method

2018 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Peng Wei
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Material Property ◽  
Kernel Function ◽  
Basis Function ◽  
Nonlinear Problems ◽  
Structural Topology ◽  
Distance Information ◽  
Level Set Function ◽  
Level Set Approach

In this paper, a parametric level-set-based topology optimization framework is proposed, to concurrently optimize structural topology at the macroscale as well as the infill material properties at the mesoscale. With the parametric level set framework, both the boundary evolution and the material property optimization during the optimization process are driven by the Method of Moving Asymptotes (MMA) optimizer, which is more efficient than the PDE-driven level set approach when handling nonlinear problems with multiple constraints. Rather than using a radial basis function (RBF) for the level set parameterization, a new type of cardinal basis function (CBF) was constructed as the kernel function for the proposed parametric level set approach. With this CBF kernel function, the bounds of the design variables can be defined explicitly, which is a great advantage compared with the RBF-based level set method. A variational approach was conducted to regulate the level set function to be a distance-regularized shape for a better material property interpolation accuracy and higher design robustness. With the embedded distance information from the level set model, boundary layer and the infill can be naturally discriminated.

Parametric Shape and Topology Optimization: A New Level Set Approach Based on Cardinal Kernel Functions

2017 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Xiangmin Jiao
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Material Property ◽  
Kernel Function ◽  
Level Set Methods ◽  
Level Set Function ◽  
Set Function ◽  
Distance Regularization ◽  
Parametric Level Set Method

The parametric level set method is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, conventional levels let methods can be easily coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Furthermore, the parametric level set scheme not only can inherit the original advantages of the conventional level set methods, such as clear boundary representation and high topological changes handling flexibility but also can alleviate some un-preferred features from the conventional level set methods, such as needing re-initialization. However, in the RBF-based parametric level set method, it was difficult to determine the range of the design variables. Moreover, with the mathematically driven optimization process, the level set function often results in significant fluctuations during the optimization process. This brings difficulties in both numerical stability control and material property interpolation. In this paper, an RBF partition of unity collocation method is implemented to create a new type of kernel function termed as the Cardinal Basis Function (CBF), which employed as the kernel function to parameterize the level set function. The advantage of using the CBF is that the range of the design variable, which was the weight factor in conventional RBF, can be explicitly specified. Additionally, a distance regularization energy functional is introduced to maintain a desired distance regularized level set function evolution. With this desired distance regularization feature, the level set evolution is stabilized against significant fluctuations. Besides, the material property interpolation from the level set function to the finite element model can be more accurate.

Generative Design of Multi-Material Hierarchical Structures via Concurrent Topology Optimization and Conformal Geometry Method

2019 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Xianfeng David Gu
Keyword(s):  
Topology Optimization ◽  
Conformal Mapping ◽  
Level Set ◽  
Basis Function ◽  
Material Properties ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Signed Distance ◽  
Level Set Function ◽  
Set Function

Abstract Topology optimization has been proved to be an automatic, efficient and powerful tool for structural designs. In recent years, the focus of structural topology optimization has evolved from mono-scale, single material structural designs to hierarchical multimaterial structural designs. In this research, the multi-material structural design is carried out in a concurrent parametric level set framework so that the structural topologies in the macroscale and the corresponding material properties in mesoscale can be optimized simultaneously. The constructed cardinal basis function (CBF) is utilized to parameterize the level set function. With CBF, the upper and lower bounds of the design variables can be identified explicitly, compared with the trial and error approach when the radial basis function (RBF) is used. In the macroscale, the ‘color’ level set is employed to model the multiple material phases, where different materials are represented using combined level set functions like mixing colors from primary colors. At the end of this optimization, the optimal material properties for different constructing materials will be identified. By using those optimal values as targets, a second structural topology optimization is carried out to determine the exact mesoscale metamaterial structural layout. In both the macroscale and the mesoscale structural topology optimization, an energy functional is utilized to regularize the level set function to be a distance-regularized level set function, where the level set function is maintained as a signed distance function along the design boundary and kept flat elsewhere. The signed distance slopes can ensure a steady and accurate material property interpolation from the level set model to the physical model. The flat surfaces can make it easier for the level set function to penetrate its zero level to create new holes. After obtaining both the macroscale structural layouts and the mesoscale metamaterial layouts, the hierarchical multimaterial structure is finalized via a local-shape-preserving conformal mapping to preserve the designed material properties. Unlike the conventional conformal mapping using the Ricci flow method where only four control points are utilized, in this research, a multi-control-point conformal mapping is utilized to be more flexible and adaptive in handling complex geometries. The conformally mapped multi-material hierarchical structure models can be directly used for additive manufacturing, concluding the entire process of designing, mapping, and manufacturing.

scholarly journals Real-Time Runway Detection for Infrared Aerial Image Using Synthetic Vision and an ROI Based Level Set Method

2018 ◽  
Vol 10 (10) ◽  
pp. 1544 ◽  
Author(s):  
Changjiang Liu ◽  
Irene Cheng ◽  
Anup Basu
Keyword(s):  
Real Time ◽  
Level Set Method ◽  
Level Set ◽  
Infrared Image ◽  
Region Of Interest ◽  
Aerial Image ◽  
Real Time Processing ◽  
Synthetic Vision ◽  
Level Set Function ◽  
Rough Region

We present a new method for real-time runway detection embedded in synthetic vision and an ROI (Region of Interest) based level set method. A virtual runway from synthetic vision provides a rough region of an infrared runway. A three-thresholding segmentation is proposed following Otsu’s binarization method to extract a runway subset from this region, which is used to construct an initial level set function. The virtual runway also gives a reference area of the actual runway in an infrared image, which helps us design a stopping criterion for the level set method. In order to meet the needs of real-time processing, the ROI based level set evolution framework is implemented in this paper. Experimental results show that the proposed algorithm is efficient and accurate.

Kantorovich-Rubinstein misfit for inverting gravity-gradient data by the level-set method

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. G55-G73
Author(s):  
Guanghui Huang ◽  
Xinming Zhang ◽  
Jianliang Qian
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Random Noise ◽  
Magnetic Data ◽  
Gravity Gradient ◽  
Local Minima ◽  
Target Model ◽  
Level Set Function ◽  
Level Set Evolution ◽  
Set Function

We have developed a novel Kantorovich-Rubinstein (KR) norm-based misfit function to measure the mismatch between gravity-gradient data for the inverse gradiometry problem. Under the assumption that an anomalous mass body has an unknown compact support with a prescribed constant value of density contrast, we implicitly parameterize the unknown mass body by a level-set function. Because the geometry of an underlying anomalous mass body may experience various changes during inversion in terms of level-set evolution, the classic least-squares ([Formula: see text]-norm-based) and the [Formula: see text]-norm-based misfit functions for governing the level-set evolution may potentially induce local minima if an initial guess of the level-set function is far from that of the target model. The KR norm from the optimal transport theory computes the data misfit by comparing the modeled data and the measured data in a global manner, leading to better resolution of the differences between the inverted model and the target model. Combining the KR norm with the level-set method yields a new effective methodology that is not only able to mitigate local minima but is also robust against random noise for the inverse gradiometry problem. Numerical experiments further demonstrate that the new KR norm-based misfit function is able to recover deep dipping flanks of SEG/EAGE salt models even at extremely low signal-to-noise ratios. The new methodology can be readily applied to gravity and magnetic data as well.

Numerical Simulation of Breaking Waves Using a Level Set Method

2002 ◽  
Author(s):  
Pablo Go´mez ◽  
Julio Herna´ndez ◽  
Joaqui´n Lo´pez ◽  
Fe´lix Faura
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Study ◽  
Operating Conditions ◽  
Breaking Wave ◽  
Level Set Function ◽  
Set Function ◽  
The Impact

A numerical study of the initial stages of wave breaking processes in shallow water is presented. The waves considered are assumed to be generated by moving a piston in a two-dimensional channel, and may appear, for example, in the injection chamber of a high-pressure die casting machine under operating conditions far from the optimal. A numerical model based on a finite-difference discretization of the Navier-Stokes equations in a Cartesian grid and a second-order approximate projection method has been developed and used to carry out the simulations. The evolution of the free surface is described using a level set method, with a reinitialization procedure of the level set function which uses a local grid refinement near the free surface. The ability of different algorithms to improve mass conservation in the reinitialization step of the level set function has been tested in a time-reversed single vortex flow. The results for the breaking wave profiles show the flow characteristics after the impact of the first plunging jet onto the wave’s forward face and during the subsequent splash-up.

scholarly journals A local solution approach for level-set based structural topology optimization in isogeometric analysis

2020 ◽  
Vol 7 (4) ◽  
pp. 514-526
Author(s):  
Zijun Wu ◽  
Shuting Wang ◽  
Renbin Xiao ◽  
Lianqing Yu
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Isogeometric Analysis ◽  
Iteration Process ◽  
Solid Material ◽  
Optimization Approach ◽  
Structural Topology ◽  
Zero Level ◽  
Solution Approach ◽  
Level Set Function

Abstract This paper develops a new topology optimization approach for minimal compliance problems based on the parameterized level set method in isogeometric analysis. Here, we choose the basis functions as level set functions. The design variables are obtained with Greville abscissae based on the corresponding collocation points. The zero-level set boundaries are derived from the level set function values of the interpolation points in all knot spans. In the optimization iteration process, the whole design domain is discretized into two types of subdomains around the zero-level set boundaries, undesign area with void materials and redesign domain with solid materials. To decrease the size of equations and the computational consumptions, only the solid material area is recalculated and the void material area is discarded according to the high accuracy of isogeometric analysis. Numerical examples demonstrate the validity of the proposed optimization method.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 578-585 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

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