Material Interpolation in Multi-Material Topology Optimization for Magnetic Device Design

2019 ◽  
Vol 55 (11) ◽  
pp. 1-4
Author(s):  
Youngsuk Jung ◽  
Seungjae Min
Keyword(s):  
Topology Optimization ◽  
Device Design ◽  
Magnetic Device ◽  
Material Interpolation

scholarly journals NODAL COSINE SINE MATERIAL INTERPOLATION IN MULTI OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE GLOBAL CRITERIA METHOD FOR LINEAR ELASTO STATIC, HEAT TRANSFER, POTENTIAL FLOW AND BINARY CROSS ENTROPY SHARPENING

2021 ◽  
Vol 1 ◽  
pp. 2247-2256
Author(s):  
Martin Denk ◽  
Klemens Rother ◽  
Mario Zinßer ◽  
Christoph Petroll ◽  
Kristin Paetzold
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Potential Flow ◽  
Cross Entropy ◽  
Objective Criterion ◽  
Multi Objective ◽  
Material Interpolation ◽  
Continuous Material ◽  
Mean Compliance ◽  
Transfer Potential

AbstractTopology optimization is typically used for suitable design suggestions for objectives like mean compliance, mean temperature, or model analysis. Some modern modeling technics in topology optimization require a nodal based material interpolation. Therefore this article is referred to a continuous material interpolation in topology optimization. To cover a smooth and differentiable density field, we address trigonometric shape functions which are infinitely differentiable. Furthermore, we extend a so-known global criteria method with a sharpening function based on binary cross-entropy, so that sharper solutions results. The proposed material interpolation is applied to different applications such as heat transfer, elasto static, and potential flow. Furthermore, these different objectives are together optimized using a multi-objective criterion.

scholarly journals Topology Optimization of Passive Constrained Layer Damping with Partial Coverage on Plate

2013 ◽  
Vol 20 (2) ◽  
pp. 199-211 ◽  
Author(s):  
Weiguang Zheng ◽  
Yingfeng Lei ◽  
Shande Li ◽  
Qibai Huang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Objective Function ◽  
Optimization Procedure ◽  
Constrained Layer Damping ◽  
Flat Plates ◽  
Modal Strain Energy ◽  
Partial Coverage ◽  
Material Interpolation ◽  
Passive Constrained Layer Damping

The potential of using topology optimization as a tool to optimize the passive constrained layer damping (PCLD) layouts with partial coverage on flat plates is investigated. The objective function is defined as a combination of several modal loss factors solved by finite element-modal strain energy (FE-MSE) method. An interface finite element is introduced to modeling the viscoelastic core of PCLD patch to save the computational space and time in the optimization procedure. Solid isotropic material with penalization (SIMP) method is used as the material interpolation scheme and the parameters are well selected to avoid local pseudo modes. Then, the method of moving asymptote (MMA) is employed as an optimizer to search the optimal topologies of PCLD patch on plates. Applications of two flat plates with different shapes have been applied to demonstrate the validation of the proposed approach. The results show that the objective function is in a steady convergence process and the damping effect of the plates can be enhanced by the optimized PCLD layouts.

Topology Optimization of Electrostatically Actuated Micromechanical Structures With Accurate Electrostatic Modeling of the Interpolated Material Model

2006 ◽  
Author(s):  
Aravind Alwan ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Electrostatic Force ◽  
Material Model ◽  
Optimality Criteria ◽  
Electrostatically Actuated ◽  
Optimality Criteria Method ◽  
Material State ◽  
Material Interpolation ◽  
New Formulation ◽  
Electrostatic Modeling

In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.

Application of Topological Optimization on Aluminum Alloy Automobile Wheel Designing

2012 ◽  
Vol 562-564 ◽  
pp. 705-708
Author(s):  
Zhi Jun Zhang ◽  
Hong Lei Jia ◽  
Ji Yu Sun ◽  
Ming Ming Wang
Keyword(s):  
Topology Optimization ◽  
Lightweight Design ◽  
Optimization Method ◽  
Variable Density ◽  
Topological Optimization ◽  
Optimal Topology ◽  
Element Analysis ◽  
Material Interpolation ◽  
Strength And Stiffness

Topology optimization method based on variable density and the minimum compliance objective function was used on designing the wheel spokes. SIMP material interpolation model was established to compensate these deficiencies of variable density method. Considering manufacturing process and stress distribution, five bolt wheels was chose to topology optimization. The percentage of material removal of the optimal topology 40% was reasonable. Finite element analysis was used to test the strength and stiffness of the structure of the wheel, the result meets the requirements after wheel topology optimization, and reduces the quality of wheels to 7.76kg, achieve the goals of lightweight design.

Topology Optimization Design of Structures Based on Eigenfrequency Matching

2021 ◽  
Author(s):  
Daniel Giraldo-Guzmán ◽  
Clifford Lissenden ◽  
Parisa Shokouhi ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Optimization Design ◽  
Programming Algorithm ◽  
Optimization Approach ◽  
Resonator Design ◽  
Linear Programming Algorithm ◽  
Target Values ◽  
Material Interpolation ◽  
Optimization Parameters ◽  
Analytical Sensitivities

Abstract We demonstrate the design of resonating structures using a density-based topology optimization approach, which requires the eigenfrequencies to match a set of target values. To develop a solution, several optimization modules are implemented, including material interpolation models, penalization schemes, filters, analytical sensitivities, and a solver. Moreover, common challenges in topology optimization for dynamic systems and their solutions are discussed. In this study, the objective function is to minimize the error between the target and actual eigenfrequency values. The finite element method is used to compute the eigenfrequencies at each iteration. To solve the optimization problem, we use the sequential linear programming algorithm with move limits, enhanced by a filtering technique. Finally, we present a resonator design as a case study and analyze the design process with different optimization parameters.

An Adaptive Material Interpolation for the Reconstruction of P-Wave Velocity Models with Sharp Interfaces using the Topology Optimization Method

2021 ◽  
pp. 2150016
Author(s):  
Juliano F. Gonçalves ◽  
Emílio C. N. Silva
Keyword(s):  
Topology Optimization ◽  
Wave Velocity ◽  
Optimization Problem ◽  
Material Model ◽  
Optimization Method ◽  
P Wave ◽  
Velocity Models ◽  
P Wave Velocity ◽  
Material Interpolation ◽  
Sharp Interfaces

A topology optimization (TO) approach is used to reconstruct P-wave velocity models with sharp interfaces. The concept of material model (interpolation), usually applied in TO to design structures and multi-physics devices, is explored in this work to solve this inverse problem. An adaptive interpolation rule is proposed to deal with the reconstruction problem as a transition from a single- to a multi-material approach combining the Solid Isotropic Material with Penalization (SIMP) and peak function material models. Data collected during the optimization process is used to find material candidates by means of a curve fitting strategy based on generalized simulated annealing (GSA), if this information is not available. The numerical analysis is carried out using a finite element (FE) approach in the frequency domain. Both forward and adjoint problems are solved aided by an open source Domain-Specific Language (DSL) framework and automated derivation tool, while the optimization problem is solved by using a BFGS algorithm. Numerical results for 2D examples demonstrated that proposed material interpolation can lead to solutions with sharper interfaces and improved resolution without including any type of regularization or extra constraint in the optimization problem.

Topology Optimization of Multi-Material Lattices for Maximal Bulk Modulus

2019 ◽  
Author(s):  
Hesaneh Kazemi ◽  
Ashkan Vaziri ◽  
Julián Norato
Keyword(s):  
Topology Optimization ◽  
Bulk Modulus ◽  
Ground Structure ◽  
Cubic Symmetry ◽  
Optimization Constraints ◽  
Design Variables ◽  
Material Interpolation ◽  
Parametric Description ◽  
High Level ◽  
Geometry Projection

Abstract In this paper, we present a method for multi-material topology optimization of lattice structures for maximum bulk modulus. Unlike ground structure approaches that employ 1-d finite elements such as bars and beams to design periodic lattices, we employ a 3-d representation where each lattice bar is described as a cylinder. To accommodate the 3-d bars, we employ the geometry projection method, whereby a high-level parametric description of the bars is smoothly mapped onto a density field over a fixed analysis grid. In addition to the geometric parameters, we assign a size variable per material to each bar. By imposing suitable constraints in the optimization, we ensure that each bar is either made exclusively of one of a set of a multiple available materials or completely removed from the design. These optimization constraints, together with the material interpolation used in our formulation, make it easy to consider any number of available materials. Another advantage of our method over ground structure approaches with 1-d elements is that the bars in our method need not be connected at all times (i.e., they can ‘float’ within the design region), which makes it easier to find good designs with relatively few design variables. We illustrate the effectiveness of our method with numerical examples of bulk modulus maximization for two-material lattices with orthotropic symmetry, and for two- and three-material lattices with cubic symmetry.

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