Multi-Material Topology Optimization using a Reconciled Level-Set Method

Topology optimization exploiting the reconciled level-set method is used for multi-material problems. Each material is being represented by a single level-set function and evolves separately utilizing the Merriman-Bence-Osher (MBO) operator. The proposed method has been applied into designing 2D and 3D metamaterials with tailored effective properties.

Integrated Topology Optimization and Additive Manufacturing

Modeling and Simulation of Additive Manufacturing

Modeling and simulation of metal based additive manufacturing in micro scale by using level-set method. The heat transportation and the movement of surface is studied. By applying the level set method, the complex geometry changes of particles and the interface of (phases) captured with high fidelity.

 

Practical algorithms and a MATLAB-based open source framework are developed to seamlessly integrate the level-set-based topology optimization procedure with additive manufacturing process. The optimization result is converted to an STL (STereoLithography) file, which is the de facto standard format for 3D printing.

Parametric Structural Shape & Topology Optimization with a Variational Distance Regularized Level Set Methods

In this work, a double-well potential functional is employed for distance regularization within the structural topology optimization loop, which can ensure the signed-distance property of the level set function within a narrow band along the structural boundaries while keeping the level set function flat in the rest area of the computational domain. The Radial Basis Function (RBF) based parameterization techniques is combined with mathematical programming to improve the performance of the proposed method in handling topology optimization problems with non-convex objective functions and multiple constraints. The flatness of the level set function in the material region also enables easier creation of new holes in the topology optimization process. 

Multiphysics  Topology Optimization of Smart Energy Harvesters

The proliferation of Micro-Electro-Mechanical Systems (MEMS), portable electronics and wireless sensing networks has raised the need for a new class of devices with self-powering capabilities. Vibration-based piezoelectric energy harvesters provide a very promising solution, as a result of their capability of converting mechanical energy into electrical energy through the direct piezoelectric effect. The reconciled level set (RLS) method is employed to solve multi-material shape and topology optimization problems, using the Merriman–Bence–Osher (MBO) operator. Designs with both single and multiple materials are presented, which constitute improvements with respect to existing energy harvesting designs.

Designing Metasurfaces with Topology Optimization and Conformal Mapping Theory

A computational framework for computational design and additive manufacturing of free-form periodic metasurfaces is explored. The proposed scheme rests on the level-set based topology approach and the conformal mapping theory. A metamaterial with pre-specified performance is created using a level-set based topology optimization method. The achieved unit cell is further mapped to the 3D quad meshes on a free-form surface by applying the conformal mapping method which can preserve the local shape and angle when mapping the 2D design to a 3D surface.

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

In the conventional RBF-based parametric level set method, it is difficult to find out the range of the design variables. Besides, the parametric level set function often suffers large fluctuations during the optimization process. These issues cause difficulties both in numerical stability control and in material property mapping. To solve those issues, a unique Cardinal Basis Function (CBF) is constructed based on the Radial Basis Function (RBF) partition of unity collocation method. Additionally, a distance regularization energy functional is introduced to stabilize the parametric level set evolution and ensure the accuracy of the material property mapping from the level set model to the finite element analysis model.

Multi-Material Topology Optimization of Structures Infilled with Conformal Metamaterials

Different from existing work, we propose an alternative way of mapping the metamaterial microstructures to irregular domains by employing the conformal mapping theory. Each group of metamaterials is bounded by a thin layer of material to guarantee structural connectivity between different microstructures and smooth external boundaries.

Extended Level Set Methods (X-LSM) for Shape and Topology Optimization on Manifolds

We propose a new method to systematically address the issue of structural shape and topology optimization on free-form surfaces. By combining the conformal mapping theory with the level set framework, the topology optimization problem on the manifold embedded in the 3D space can be recast as an equivalent 2D topology optimization problem in the Euclidean space. Compared with other approaches which need project the Euclidean differential operators to the manifold, the proposed method can not only reduce the computational cost but also preserve all the advantages of conventional level set methods.

Concurrent Optimization of Structural Topology and Material Properties with a Cardinal Basis Function Based Parametric Level Set Method

A concurrent structural topology optimization is utilized for generating the optimal structural topology and the optimal material properties simultaneously. The structure is modeled via the shell-infill level set model. A separate topology optimization is carried out to determine the actual metamaterial layouts. An isotropic constraint is imposed in the metamaterial design to ensure the consistency of the material properties with the help of the angle-preserving conformal mapping. Multiple control points are introduced to the mapping to preserve the designed material property with  minimized distortion.

The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity fields in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady state solution of the partial differential equation.

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Topology Optimization of Compliant Mechanisms

Shikui Chen @ Stony Brook University

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

A concurrent structural topology optimization framework is proposed to simultaneously generate the topology of the multimaterial structure at macroscale and the optimal material properties at mesoscale. The multimaterial structure is modeled by the ‘color level set’ model. The different metamaterials are designed considering an isotropic constraint. The consistency of the designed metamaterial properties is ensured by the angle-preserving conformal mapping. Multiple control points are introduced to the mapping to minimize the area distortion.

Computational Generation and Conformal Fabrication of Woven Fabric Structures by Harmonic Foliation

A framework for computational generation and conformal fabrication of woven thin-shell structures with arbitrary topology is proposed. By solving graph-valued harmonic maps on the input surface, we construct two sets of harmonic foliations perpendicular to each other. The warp and weft threads are created afterward and then manually woven to reconstruct the surface. This method is ideal for weaving surface structures on a variety of engineering applications, including wearable electronics, sheet metal craft, architectural designs, and conformal woven composite parts in the automotive and aircraft industries.

Research

Topology Optimization of Multimaterial Thermoelectric Structures

A SIMP-based topology optimization is applied to the design of thermoelectric structures with multiple thermoelectric materials aiming to maximize the output power or conversion efficiency by optimal distribution of different  materials. Instead of dummy materials, both the P-type and N-type elements are optimally distributed with two different practical thermoelectric materials. Specifically, Bi₂Te₃ and Zn₄Sb₃ are selected for the P-type element while Bi₂Te₃ and CoSb₃ for the N-type element. The maximum conversion efficiency could reach 9.61% and 12.34%, respectively, in the temperature range from 25 ℃ to 400 ℃.

Conformal Topology Optimization of Multi-material Ferromagnetic Soft Structures Using an Extended Level Set Method

The extended level set method (X-LSM) and conformal geometry theory are employed to enable conformal topology optimization of the ferromagnetic soft active structures on free-form surfaces. A magnetic body force is adopted to control the deformation of the ferromagnetic soft active structures. The boundary evolution on a free-form 3D surface can be mapped into a 2D rectangular plane by solving a modified Hamilton-Jacobi equation weighted by conformal factors. The reconciled level set (RLS) method is firstly implemented within the X-LSM framework to enable multi-material conformal topology optimization of ferromagnetic soft active structures on free-form surfaces.Two topologically optimized designs are printed using the functional 3D printing technology, or the so-called 4D printing, to physically realize soft active structures with built-in functionalities.

Topology Optimization of Thermal Cloaks in Euclidean Spaces and Manifolds using an Extended Level Set Method

Thermal cloaks are devices designed to shield an object against thermal detection. This paper proposes to design thermal cloaks using the level-set-based shape and topology optimization in the context of pure heat conduction. The optimized thermal cloaks are free of high anisotropy and non-homogeneity commonly seen in the popular transformation thermotics or scattering cancellation methods. A conformal thermal cloak on the manifold is also topologically optimized using the extended level set method (X-LSM), which has not been reported in the literature. The feasibility and robustness of the proposed method to design thermal meta-devices with cloaking functionality are demonstrated through a number of 2D and 3D (solid and shell) numerical examples with different cloaking regions (circular, human-shaped, spherical, and curved circular). This work may shed light on further exploration of the thermal meta-devices in the heat flux manipulation regime. 

Shape and Topology Optimization of Conformal Thermal Control Structures on Free-form Surfaces: A Dimension Reduction Level Set Method (DR-LSM)

In this paper, the authors propose a dimension reduction level set method (DR-LSM) for shape and topology optimization of heat conduction problems on general free-form surfaces utilizing the conformal geometry theory. Reducing the dimension can not only significantly reduce the computational cost of finite element analysis but also overcome the hurdles of dynamic boundary evolution on free-form surfaces.  The proposed method is applied to the design of conformal thermal control structures on free-form surfaces. Specifically, both the Hamilton–Jacobi equation and the heat equation, the two governing PDEs for boundary evolution and thermal conduction phenomena, are transformed from the manifold in 3D space to the 2D rectangular domain using conformal parameterization. The objective function, constraints, and the design velocity field are also computed equivalently with FEA on the 2D parameter domain with properly modified forms.