Shikui Chen

Design of Multimaterial Compliant Mechanisms Using Level-Set Methods

A monolithic compliant mechanism transmits applied forces from specified input ports to output ports by elastic deformation of its comprising materials, fulfilling required functions analogous to a rigid-body mechanism. In this paper, we propose a level-set method for designing monolithic compliant mechanisms made of multiple materials as an optimization of continuum heterogeneous structures. Central to the method is a multiphase level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure. Combined with the classical shape derivatives, the level-set method yields an Eulerian computational system of geometric partial differential equations, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. The proposed method is demonstrated for single-input and single-output mechanisms and illustrated with several two-dimensional examples of synthetics of multimaterial mechanisms of force inverters and gripping and clamping devices. An analysis on the formation of de facto hinges is presented based on the shape gradient information. A scheme to ensure a well-connected topology of the mechanism during the process of optimization is also presented.

Shape feature control in structural topology optimization

A variational approach to shape feature control in topology optimization is presented in this paper. The method is based on a new class of surface energies known as higher-order energies as opposed to the conventional energies for problem regularization, which are linear. In employing a quadratic energy functional in the objective of the topology optimization, non-trivial interactions between different points on the structural boundary are introduced, thus favoring a family of shapes with strip-like (or beam) features. In addition, the quadratic energy functional can be seamlessly integrated into the level set framework that represents the geometry of the structure implicitly. The shape gradient of the quadratic energy functional is fully derived in the paper, and it is incorporated in the level set approach for topology optimization. The approach is demonstrated with benchmark examples of structure optimization and compliant mechanism design. The results presented show that this method is capable of generating strip-like (or beam) designs with specified feature width, which have highly desirable characteristics and practical benefits and uniquely distinguish the proposed method.

Compliant Mechanism Optimization: Analysis and Design with Intrinsic Characteristic Stiffness

Abstract This article focuses on design formulation of compliant mechanisms posed as a topology optimization problem. With the use of linear elasticity theory, a single-input, single-output compliant mechanism is represented by the stiffness matrix of its structure with respect to the input–output ports. It is shown that the stiffness model captures the intrinsic stiffness properties of the mechanism. Furthermore, in order for the optimization problem to be properly defined, it is necessary that the stiffness matrix of the mechanisms structure must be guaranteed to be always positive definite. An exploratory design formulation is then presented based on this necessary condition. Numerical examples are provided to illustrate the potential benefits of using the intrinsic stiffness properties for compliant mechanism design with topology optimization techniques.

Topology optimization of multi-material negative Poisson’s ratio metamaterials using a reconciled level set method

Metamaterials are defined as a family of rationally designed artificial materials which can provide extraordinary effective properties compared with their nature counterparts. This paper proposes a level set based method for topology optimization of both single and multiple-material Negative Poissons Ratio (NPR) metamaterials. For multi-material topology optimization, the conventional level set method is advanced with a new approach exploiting the reconciled level set (RLS) method. The proposed method simplifies the multi-material topology optimization by evolving each individual material with a single level set function and reconciling the result level set field with the MerrimanBenceOsher (MBO) operator. The NPR metamaterial design problem is recast as a variational problem, where the effective elastic properties of the spatially periodic microstructure are formulated as the strain energy functionals under uniform displacement boundary conditions. The adjoint variable method is utilized to derive the shape sensitivities by combining the general linear elastic equation with a weak imposition of Dirichlet boundary conditions. The design velocity field is constructed using the steepest descent method and integrated with the level set method. Both single and multiple-material mechanical metamaterials are achieved in 2D and 3D with different Poissons ratios and volumes. Benchmark designs are fabricated with multi-material 3D printing at high resolution. The effective auxetic properties of the achieved designs are verified through finite element simulations and characterized using experimental tests as well. A multi-material topology optimization approach exploiting the reconciled level-set method.The boundary of each individual material is evolved with a single level set function.Multiple level set functions are reconciled with the MerrimanBenceOsher (MBO) operator.Both 2D and 3D multi-material designs were obtained and used for validate the proposed method.

Designing Distributed Compliant Mechanisms with Characteristic Stiffness

A novel method is proposed in this paper to address the cutting-edge problem of topology optimization of distributed compliant mechanisms, which requires the design to possess both large output displacements and evenly distributed compliance simultaneously. The design is represented by a level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. Existing techniques for eliminating de facto hinges in the design are reviewed. Further, the intrinsic deficiencies in the widely used “spring model” are discussed and a new formulation considering the “characteristic stiffness” of the mechanism is proposed. The proposed method is demonstrated with benchmark examples of compliant mechanism optimization. The result is a design with evenly distributed compliance and a more desirable characteristic, which uniquely distinguishes our method.Copyright

Optimal Synthesis of Compliant Mechanisms Using a Connectivity Preserving Level Set Method

We present a level set based method for optimal design of compliant mechanisms. The focus of the investigation is on how to preserve the structural connectivity in the optimization process of the level set method. By introducing an extra constraint using the connected components labeling technique, the structural connectivity of the design is well maintained during the topology optimization process.Copyright

An Open Source Framework for Integrated Additive Manufacturing and Level-Set-Based Topology Optimization

Panagiotis Vogiatzis Computational Modeling, Analysis and Design Optimization Research Laboratory Department of Mechanical Engineering State University of New York at Stony Brook Stony Brook, NY, 11794 Email: Panagiotis.Vogiatzis@stonybrook.edu Shikui Chen Computational Modeling, Analysis and Design Optimization Research Laboratory Department of Mechanical Engineering State University of New York at Stony Brook Stony Brook, NY, 11794 Email: Shikui.Chen@stonybrook.edu

GEOMETRIC WIDTH CONTROL IN TOPOLOGY OPTIMIZATION USING LEVEL SET METHOD AND A QUADRATIC ENERGY FUNCTIONAL

A variational approach to geometric width control in topology optimization is presented in this paper. Different from conventional topology optimization approaches which only consider optimizing performance-describing objective functions, a quadratic energy functional governing the feature characteristic of geometric width is employed. In this manner, the geometric feature of the designed structure as well as its functional performance is accounted for. In addition, the quadratic energy function can be seamlessly integrated into the level set model that represents the geometry of the structure implicitly. The approach is demonstrated with benchmark examples of structure optimization and compliant mechanism optimization. The preliminary results show that this method is capable of generating strip-like (or beam) designs with specified feature width, which is a highly desirable characteristic and uniquely distinguishes the proposed method.Copyright

A Level-Set-Based Multistage Metamodeling Approach for Design Optimization

A level-set-based multistage metamodeling approach is developed for design optimization. Different from the existing objective-oriented sequential sampling methods, where the design objective and constraints have to be combined into a single response of interest, our method offers the flexibility of building metamodels for multiple responses (objective/constraints) simultaneously. Uncertainty quantification (UQ) is introduced for each metamodel to represent the confidence interval due to the lack of sufficient samples at the early stages of metamodeling. Based on the extreme values of the optimal solution identified within the confidence interval, the level set method (LSM), together with a series of Boolean operations, is used to identify the region(s) of interests with arbitrary topologies. Introducing LSM facilitates region manipulations, representation of disconnected regions of interest, and visualization for design exploration. Through mathematical benchmark examples and an engineering design problem, we demonstrate that the proposed method possesses a superior efficiency in design exploration to the conventional sequential sampling strategy and allows the use of multiple samples at each sampling stage. As the metamodeling process moves on, the region of interests is progressively reduced, and the optimal design is asymptotically approached. Our results are compared with those from one-stage metamodeling using the Optimal Latin Hypercubes (OLH) experiments. Our study shows that the proposed method can effectively capture the region of interests with any shape/topology and locate the optimum design with improved efficiency.

On Design of Mechanical Metamaterials Using Level-Set Based Topology Optimization

Recently, engineered metamaterials have aroused considerable interests in many fields, due to their distinctive characteristics different from conventional materials. This paper proposes a level-set based topological optimization method for design of the mechanical metamaterials with negative Poisson’s ratio. The strain energy method is employed to predict the effective properties of the periodic microstructure. The adjoint variable method is applied to calculate the shape sensitivity, which is further used to construct the design velocity field. Finally, the level set method is applied to achieve shape evolution and topological changes of the microstructure until the desired materials properties like negative Poisson’s ratios are achieved.Copyright