scholarly journals An explicit topology optimization method using moving polygonal morphable voids (MPMVs)

2020 ◽  
Vol 23 (2) ◽  
pp. 536-540 ◽  
Author(s):  
Hoang Van-Nam
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Density Field ◽  
Optimization Approach ◽  
Design Variables ◽  
Mesh Independence ◽  
Gradient Based ◽  
Element Density ◽  
Optimization Solvers

Introduction: Conventional topology optimization approaches are implemented in an implicit manner with a very large number of design variables, requiring large storage and computation costs. In this study, an explicit topology optimization approach is proposed by movonal morphable voids whose geometry parameters are considered as design variables. Methods: Each polygonal void plays as an empty-material zone that can move, change its shapes, and overlap with its neighbors in a design space. The geometry eters of MPMVs consisting of the coordinates of polygonal vertices are utilized to render the structure in the design domain in an element density field. The density function of the elements located inside polygonal voids is described by a smooth exponential function that allows utilizing gradient-based optimization solvers. Results & Conclusion: Compared with conventional topology optimization approaches, the MPMV approach uses fewer design variables, ensure mesh-independence solution without filtering techniques or perimeter constraints. Several numerical examples are solved to validate the efficiency of the MPMV approach.

scholarly journals Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

2021 ◽  
Author(s):  
Atul Kumar Sharma ◽  
Gal Shmuel ◽  
Oded Amir
Keyword(s):  
Topology Optimization ◽  
Electric Fields ◽  
Computational Cost ◽  
Optimization Method ◽  
Phononic Crystals ◽  
Frequency Bands ◽  
Design Variables ◽  
Gradient Based ◽  
Soft Dielectrics ◽  
Design Freedom

Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable. To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider than those obtained from the previous metaheuristics-based method, while the computational cost to identify them is reduced by orders of magnitude.

Coupling Moving Morphable Voids and Components Based Topology Optimization of Hydrogel Structures Involving Large Deformation

2021 ◽  
Vol 89 (1) ◽  
Author(s):  
Yisong Qiu ◽  
Shuaiqi Zhang ◽  
Weisheng Zhang ◽  
Hongfei Ye ◽  
Hongwu Zhang ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Large Deformation ◽  
Optimization Design ◽  
Density Field ◽  
Adjoint Sensitivity ◽  
Topology Optimization Problem ◽  
Strain Energy Density Function ◽  
Design Variables ◽  
Component Approach ◽  
Gradient Based

Abstract A coupling of moving morphable void and component approach for the topology optimization of hydrogel structures involving recoverable large deformation is proposed in this paper. In this approach, the geometric parameters of moving morphable voids and components are set as design variables to respectively describe the outline and material distribution of hydrogel structures for the first time. To facilitate the numerical simulation of large deformation behavior of hydrogel structures during the optimization process, the design variables are mapped to the density field of the design domain and the density field is then used to interpolate the strain energy density function of the element. Furthermore, the adjoint sensitivity of the optimization formulation is derived and combined with the gradient-based algorithm to solve the topology optimization problem effectively. Finally, two representative numerical examples of the optimization of isotropic hydrogel structures are used to prove the effectiveness of the proposed method, and the optimization design of an anisotropic bionic hydrogel structure is presented to illustrate the applicability of the method. Experimental results are also presented to demonstrate that the explicit topologies obtained from the method can be directly used in the manufacture of hydrogel-based soft devices.

Topology Optimization of Planar Gear-Linkage Mechanisms

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Neung Hwan Yim ◽  
Seok Won Kang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Mechanism Synthesis ◽  
Gear Design ◽  
Linkage Design ◽  
Gradient Based ◽  
Mechanical Elements ◽  
Topology Optimization Method

Topology optimization for mechanism synthesis has been developed for the simultaneous determination of the number and dimension of mechanisms. However, these methods can be used to synthesize linkage mechanisms that consist only of links and joints because other types of mechanical elements such as gears cannot be simultaneously synthesized. In this study, we aim to develop a gradient-based topology optimization method which can be used to synthesize mechanisms consisting of both linkages and gears. For the synthesis, we propose a new ground model defined by two superposed design spaces: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks, each of which is assumed to rotate as an output gear, while the linkage design space is discretized by zero-length-spring-connected rigid blocks. Another set of zero-length springs is introduced to connect gear blocks to rigid blocks, and their stiffness values are varied to determine the existence of gears when they are necessary to produce the desired path. After the proposed topology-optimization-based synthesis formulation and its numerical implementation are presented, its effectiveness and validity are checked with various synthesis examples involving gear-linkage and linkage-only mechanisms.

Synthesis of Gear-Linkage Mechanisms by Topology Optimization

2018 ◽  
Author(s):  
Neung Hwan Yim ◽  
Seok Won Kang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Synthesis Method ◽  
Variable Stiffness ◽  
Optimization Methods ◽  
Optimization Method ◽  
Planar Mechanisms ◽  
Gear Design ◽  
Linkage Design ◽  
Gradient Based

This work is concerned with a new mechanism synthesis method for the simultaneous determination of the type, number and dimension of mechanisms by topology optimization. Earlier topology optimization methods can synthesize linkage mechanisms that consist only of links and joints. The proposed synthesis method is a gradient-based topology optimization method useful for the synthesis of planar mechanisms consisting of linkages and gears. To formulate the topology optimization based method, we propose two superposed design spaces as a ground structure: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks while the linkage design space by rigid blocks. The zero-length springs with variable stiffness are used to control the connectivity of blocks, which in turns determines the configuration of the synthesized mechanism. After the proposed topology-optimization-based synthesis formulation is presented, its effectiveness and validity are checked with various synthesis examples.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

scholarly journals A new stress-based topology optimization approach for finding flexible structures

2021 ◽  
Author(s):  
Martin Noack ◽  
Arnold Kühhorn ◽  
Markus Kober ◽  
Matthias Firl
Keyword(s):  
Topology Optimization ◽  
Stress State ◽  
Design Space ◽  
Flexible Structures ◽  
Optimization Approach ◽  
Principal Stresses ◽  
Output Displacement ◽  
Design Concepts ◽  
Flexible Designs ◽  
Gauss Points

AbstractThis paper presents a new FE-based stress-related topology optimization approach for finding bending governed flexible designs. Thereby, the knowledge about an output displacement or force as well as the detailed mounting position is not necessary for the application. The newly developed objective function makes use of the varying stress distribution in the cross section of flexible structures. Hence, each element of the design space must be evaluated with respect to its stress state. Therefore, the method prefers elements experiencing a bending or shear load over elements which are mainly subjected to membrane stresses. In order to determine the stress state of the elements, we use the principal stresses at the Gauss points. For demonstrating the feasibility of the new topology optimization approach, three academic examples are presented and discussed. As a result, the developed sensitivity-based algorithm is able to find usable flexible design concepts with a nearly discrete 0 − 1 density distribution for these examples.

Topology Optimization Algorithm for Plates and Shells Subjected to Plastic Deformations

1998 ◽  
Author(s):  
Kohei Yuge ◽  
Nobuhiro Iwai ◽  
Noboru Kikuchi
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Homogenization Method ◽  
Finite Deformations ◽  
Thin Shells ◽  
Plastic Deformations ◽  
Material Tensor ◽  
Design Variables ◽  
Interpolation Technique ◽  
Plates And Shells

Abstract A topology optimization method for plates and shells subjected to plastic deformations is presented. The algorithms is based on the generalized layout optimization method invented by Bendsϕe and Kikuchi (1988), where an admissible design domain is assumed to be composed of microstructures with periodic cavities. The sizes of the cavities and the rotational angles of the microstructures are design variables which are optimized so as to minimize the applied work. The macroscopic material tensor for the porous material is numerically calculated by the homogenization method for the sensitivity analysis. In this paper, the method is applied to two-dimensional elasto-plastic problems. A database of the material tensor and its interpolation technique are presented. The algorithm is expanded into thin shells subjected to finite deformations. Several numerical examples are shown to demonstrate the effectiveness of these algorithms.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

A fast multiobjective optimization approach to S-duct scoop inlets design with both inflow and outflow

2018 ◽  
Vol 233 (9) ◽  
pp. 3381-3394
Author(s):  
Lifang Zeng ◽  
Dingyi Pan ◽  
Shangjun Ye ◽  
Xueming Shao
Keyword(s):  
Multiobjective Optimization ◽  
Total Pressure ◽  
Optimization Method ◽  
Navier Stokes ◽  
Integral Model ◽  
Optimization Approach ◽  
Navier Stokes Equation ◽  
Cross Sectional ◽  
Design Variables ◽  
Computational Fluid Dynamics Analysis

A fast multiobjective optimization method for S-duct scoop inlets considering both inflow and outflow is developed and validated. To reduce computation consumption of optimization, a simplified efficient model is proposed, in which only inflow region is simulated. Inlet pressure boundary condition of the efficient model is specified by solving an integral model with both inflow and outflow. An automated optimization system integrating the computational fluid dynamics analysis, nonuniform rational B-spline geometric representation technique, and nondominated sorting genetic algorithm II is developed to minimize the total pressure loss and distortion at the exit of diffuser. Flow field is numerically simulated by solving the Reynolds-averaged Navier–Stokes equation coupled with k–ω shear stress transport turbulence model, and results are validated to agree well with previous experiment. S-duct centreline shape and cross-sectional area distribution are parameterized as the design variables. By analyzing the results of a suggested optimal inlet chosen from the obtained Pareto front, total pressure recovery has increased from 97% to 97.4%, and total pressure distortion DC60 has decreased by 0.0477 (21.7% of the origin) at designed Mach number 0.7. The simplified efficient model has been validated to be reliable, and by which the time cost for the optimization project has been reduced by 70%.

scholarly journals Microstructural Topology Optimization of Constrained Layer Damping on Plates for Maximum Modal Loss Factor of Macrostructures

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanpeng Fang ◽  
Lei Yao ◽  
Shuxia Tian ◽  
Junjian Hou
Keyword(s):  
Topology Optimization ◽  
Loss Factor ◽  
Strain Energy ◽  
Design Method ◽  
Optimization Method ◽  
Constrained Layer Damping ◽  
Viscoelastic Materials ◽  
Modal Strain Energy ◽  
Design Variables ◽  
Microstructural Topology Optimization

This paper presents microstructural topology optimization of viscoelastic materials for the plates with constrained layer damping (CLD) treatments. The design objective is to maximize modal loss factor of macrostructures, which is obtained by using the Modal Strain Energy (MSE) method. The microstructure of the viscoelastic damping layer is composed of 3D periodic unit cells. The effective elastic properties of the unit cell are obtained through the strain energy-based method. The density-based topology optimization is adopted to find optimal microstructures of viscoelastic materials. The design sensitivities of modal loss factor with respect to the design variables are analyzed and the design variables are updated by Method of Moving Asymptotes (MMA). Numerical examples are given to demonstrate the validity of the proposed optimization method. The effectiveness of the optimal design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to the plates with CLD treatments.

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