scholarly journals Topology Optimization of Micro-Structured Materials Featured with the Specific Mechanical Properties

2019 ◽  
Vol 17 (03) ◽  
pp. 1850144 ◽  
Author(s):  
Jie Gao ◽  
Hao Li ◽  
Zhen Luo ◽  
Liang Gao ◽  
Peigen Li
Keyword(s):  
Mechanical Properties ◽  
Level Set ◽  
Effective Properties ◽  
Homogenization Method ◽  
Material Microstructure ◽  
Structured Materials ◽  
Level Set Function ◽  
Elasticity Property ◽  
Specific Material ◽  
Set Function

Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to optimize the topologies and shapes of these porous material microstructures. Firstly, the energy-based homogenization method (EBHM) is applied to evaluate the material effective properties based on the topology of the material cell, where the effective elasticity property is evaluated by the average stress and strain theorems. Secondly, a parametric level set method (PLSM) is employed to optimize the microstructural topology until the specific mechanical properties can be achieved, including the maximum bulk modulus, the maximum shear modulus and their combinations, as well as the negative Poisson’s ratio (NPR). The complicated topological shape optimization of the material microstructure has been equivalent to evolve the sizes of the expansion coefficients in the interpolation of the level set function. Finally, several numerical examples are fully discussed to demonstrate the effectiveness of the developed method. A series of new and interesting material cells with the specific mechanical properties can be found.

scholarly journals An Image Segmentation Method Based on Improved Regularized Level Set Model

2018 ◽  
Vol 8 (12) ◽  
pp. 2393 ◽  
Author(s):  
Lin Sun ◽  
Xinchao Meng ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Energy Functional ◽  
External Energy ◽  
Regularization Term ◽  
Level Set Function ◽  
New Energy ◽  
Segmentation Approach ◽  
Set Function ◽  
Distance Regularization

When the level set algorithm is used to segment an image, the level set function must be initialized periodically to ensure that it remains a signed distance function (SDF). To avoid this defect, an improved regularized level set method-based image segmentation approach is presented. First, a new potential function is defined and introduced to reconstruct a new distance regularization term to solve this issue of periodically initializing the level set function. Second, by combining the distance regularization term with the internal and external energy terms, a new energy functional is developed. Then, the process of the new energy functional evolution is derived by using the calculus of variations and the steepest descent approach, and a partial differential equation is designed. Finally, an improved regularized level set-based image segmentation (IRLS-IS) method is proposed. Numerical experimental results demonstrate that the IRLS-IS method is not only effective and robust to segment noise and intensity-inhomogeneous images but can also analyze complex medical images well.

A Method for Tracking a Solid Body in a Fluid Field in Immersed Boundary Methods

2018 ◽  
Author(s):  
Guangfa Yao
Keyword(s):  
Level Set ◽  
Solid Body ◽  
Volume Fraction ◽  
Transformation Matrix ◽  
The Body ◽  
New Method ◽  
Immersed Boundary ◽  
Body Interaction ◽  
Level Set Function ◽  
Set Function

Immersed boundary method has got increasing attention in modeling fluid-solid body interaction using computational fluid dynamics due to its robustness and simplicity. It usually simulates fluid-solid body interaction by adding a body force in the momentum equation. This eliminates the body conforming mesh generation that frequently requires a very labor-intensive and challenging task. But accurately tracking an arbitrary solid body is required to simulate most real world problems. In this paper, a few methods that are used to track a rigid solid body in a fluid domain are briefly reviewed. A new method is presented to track an arbitrary rigid solid body by solving a transformation matrix and identifying it using a level set function. Knowing level set function, the solid volume fraction can be derived if needed. A three-dimensional example is used to study a few methods used to represent and solve the transformation matrix, and demonstrate the presented new method.

Low-Dimensional Components of Flows With Large Free/Moving-Surface Motion

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Yi Zhang ◽  
Solomon C. Yim
Keyword(s):  
Flow Field ◽  
Level Set ◽  
Wave Impact ◽  
Moving Surface ◽  
Surface Motion ◽  
Level Set Function ◽  
Highly Nonlinear ◽  
Flow Systems ◽  
Low Dimensional ◽  
Set Function

Flow systems with highly nonlinear free/moving surface motion are common in engineering applications, such as wave impact and fluid-structure interaction (FSI) problems. In order to reveal the dynamics of such flows, as well as provide a reduced-order modeling (ROM) for large-scale applications, we propose a proper orthogonal decomposition (POD) technique that couples the velocity flow field and the level-set function field, as well as a proper normalization for the snapshots data so that the low-dimensional components of the flow can be retrieved with a priori knowledge of equal distribution of the total variance between velocity and level-set function data. Through numerical examples of a sloshing problem and a water entry problem, we show that the low-dimensional components obtained provide an efficient and accurate approximation of the flow field. Moreover, we show that the velocity contour and orbits projected on the space of the reduced basis greatly facilitate understanding of the intrinsic dynamics of the flow systems.

A topology optimization algorithm based on topological derivative and level-set function for designing phononic crystals

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rolando Yera ◽  
Luisina Forzani ◽  
Carlos Gustavo Méndez ◽  
Alfredo E. Huespe
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Algorithm ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Lagrangian Function ◽  
Topological Derivative ◽  
Content Type ◽  
Level Set Function ◽  
Set Function

PurposeThis work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approachThe resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.FindingsThe description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.Originality/valueThe original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

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.

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