Predicting the Benefits of Topology Optimization

2015 ◽  
Author(s):  
Shiguang Deng ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Shape Optimization ◽  
Systematic Method ◽  
Topological Sensitivity ◽  
Numerical Examples ◽  
Initial Design

Topology optimization is a systematic method of generating designs that maximize specific objectives. While it offers significant benefits over traditional shape optimization, topology optimization can be computationally demanding and laborious. Even a simple 3D compliance optimization can take several hours. Further, the optimized topology must typically be manually interpreted and translated into a CAD-friendly and manufacturing friendly design. This poses a predicament: given an initial design, should one optimize its topology? In this paper, we propose a simple metric for predicting the benefits of topology optimization. The metric is derived by exploiting the concept of topological sensitivity, and is computed via a finite element swapping method. The efficacy of the metric is illustrated through numerical examples.

Tracing Pareto-Optimal Frontiers in Topology Optimization

2010 ◽  
Author(s):  
Krishnan Suresh
Keyword(s):  
Fixed Point ◽  
Topology Optimization ◽  
Iteration Scheme ◽  
Stochastic Method ◽  
Pareto Optimal ◽  
Topological Sensitivity ◽  
Fixed Point Iteration ◽  
Numerical Examples ◽  
Multi Objective ◽  
Sensitivity Field

In multi-objective topology optimization, a design is defined to be “pareto-optimal” if no other design exists that is better with respect to one objective, and as good with respect to others. This unfortunately suggests that unless other ‘better’ designs are found, one cannot declare a particular topology to be pareto-optimal. In this paper, we first show that a topology can be guaranteed to be (locally) pareto-optimal if certain inherent properties associated with the topological sensitivity field are satisfied, i.e., no further comparison is necessary. This, in turn, leads to a deterministic, i.e., non-stochastic, method for directly tracing pareto-optimal frontiers using the classic fixed-point iteration scheme. The proposed method can generate the full set of pareto-optimal topologies in a single-run, and is therefore both efficient and predictable, as illustrated through numerical examples.

scholarly journals Two Algorithms for a Class of Elliptic Problems in Shape Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Tian ◽  
Dai Xiaoxia ◽  
Zhang Chengwei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Shape Optimization ◽  
Variational Problem ◽  
Optimization Problem ◽  
Elliptic Boundary ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Elliptic Boundary Value

We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.

Optimum Design of Tractor Clutch PTO Finger by Using Topology and Shape Optimization

2015 ◽  
Author(s):  
O. Dogan ◽  
F. Karpat ◽  
N. Kaya ◽  
C. Yuce ◽  
M. O. Genc ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Topology Optimization ◽  
Shape Optimization ◽  
Optimization Techniques ◽  
Design Parameters ◽  
Agricultural Activities ◽  
Element Analysis ◽  
Design Life ◽  
Topology And Shape Optimization

Tractors are one of the most important agricultural machinery in the world. They provide agricultural activities in challenging conditions by using various agricultural machineries which are added on them. Therefore, there has been a rising demand for tractor use for agricultural activities. During the power transmission, tractor clutches are exposed to high static and cyclic loading directly. Thus, most of clutch parts fail before completing their design life which is under 106 cycles. Especially, because of the high stress, there are a number of fractures and breakages are observed around the pin area of the finger mechanisms. Due to these reasons, it is necessary to re-design these fingers by using modern optimization techniques and finite element analysis. This paper presents an approach for analysis and re-designs process of tractor clutch PTO finger. Firstly, the original designs of the PTO fingers are analyzed by using finite element analysis. Static structural analyses are applied on these fingers by using ANSYS static structural module. The boundary conditions are determined according to the data from the axial fatigue test bench. Afterwards, the stress-life based fatigue analyses are performed with respect to Goodman criterion. It is seem that the original design of the PTO finger, failed before the design life. Hence, the PTO finger is completely re-designed by using topology and shape optimization methods. Topology optimization is used to find the optimum material distribution of the PTO fingers. Topology optimization is performed in solidThinking Inspire software. The precise dimensions of the PTO fingers are determined by using shape optimization and response surface methodology. Two different design parameters, which are finger thickness and height, are selected for design of experiment and 15 various cases are analyzed. By using DOE method three different equations are obtained which are maximum stresses, mass, and displacement depending on the selected design parameters. These equations are used in the optimization as objective and constraint equations in MATLAB. The results indicate that the proposed models predict the responses adequately within the limits of the parameters being used. The final dimensions of the fingers are determined after shape optimization. The new designs of the PTO fingers are re-analyzed in terms of static and fatigue analysis. The new design of the PTO finger passed the analysis successfully. As a result of the study, the finger mass is increased 7% but it is quite small. Maximum Equivalent Von-Misses stress reduction of 25.3% is achieved. Fatigue durability of the PTO finger is improved 53.2%. The rigidity is improved up to 27.9% compared to the initial design. The optimal results show that the developed method can be used to design a durable, low manufacturing cost and lightweight clutch parts.

Design of Phononic Materials Using Multiresolution Topology Optimization

2013 ◽  
Author(s):  
Sandro L. Vatanabe ◽  
Emilio C. N. Silva
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
High Resolution ◽  
Elastic Materials ◽  
Element Mesh ◽  
Computational Framework ◽  
Numerical Examples ◽  
Acoustic Waveguides ◽  
Acoustic Wave Devices ◽  
Multiresolution Topology Optimization

In this work the Multiresolution Topology Optimization (MTOP) scheme is investigated to obtain high resolution designs of phononic (elastic) materials, focusing primarily on acoustic waveguides. We demonstrate via numerical examples that the resolution of the design can be significantly improved without refining the finite element mesh. The first one is the simplest case where one might be interested in maximizing the energy reaching certain parts of the domain. The second and more interesting example is the creation of different propagation patterns for different frequencies, thus creating smart filters. The results demonstrate the power and potential of our computational framework to design sophisticated acoustic wave devices.

scholarly journals Failure analysis of a re-design knuckle using topology optimization

2019 ◽  
Vol 10 (2) ◽  
pp. 465-473 ◽  
Author(s):  
Yung-Chuan Chen ◽  
Hsing-Hui Huang ◽  
Chen-Wei Weng
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Fatigue Life ◽  
Optimization Method ◽  
Fe Model ◽  
Material Distribution ◽  
Systematic Design ◽  
Systematic Method ◽  
Iso 8608 ◽  
Topology Optimization Method

Abstract. In this study, a systematic design process is carried out for the design of the knuckle. A systematic method is proposed for the design and analysis of a lightweight steering knuckle in an electric vehicle. In the proposed approach, a finite element (FE) model of the knuckle is constructed based on an inspection of the suspension and steering requirements of the target vehicle and the results of a kinematic analysis. A two-stage topology optimization method is then applied to refine the material distribution within the FE model in such a way as to minimize the knuckle weight. Finally, FE simulations are performed to evaluate the strength of the knuckle under road impact conditions and to determine the fatigue life of the knuckle for four ISO 8608 road classes (A–D). The results show that the optimized knuckle has a weight of 3.64 kg (approximately 6.2 % lighter than the original knuckle of the same strength and material) and achieves fatigue lives of 2.512×1011, 2.972×108, 5.598×103 and 2.432×101 cycles for road classes A, B, C and D, respectively.

Sensitivity Analysis With the Shape Optimization Program

1990 ◽  
Author(s):  
Erdal Atrek
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Shape Optimization ◽  
Computer Program ◽  
Continuum Structures ◽  
Numerical Examples ◽  
Optimization Program

Abstract SHAPE is an industry oriented commercial finite element based computer program for the shape optimization of continuum structures. It employs sensitivity analysis extensively during optimization. A new option allows the user to create, access, and plot sensitivity information for any prescribed design that can be processed by SHAPE. This feature of the program is described herein, and is illustrated by means of numerical examples.

Tracing the Envelope of the Objective-Space in Multi-Objective Topology Optimization

2011 ◽  
Author(s):  
Inna Turevsky ◽  
Krishnan Suresh
Keyword(s):  
Topology Optimization ◽  
Eigenvalue Problems ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Topological Sensitivity ◽  
Numerical Examples ◽  
Multi Objective ◽  
Objective Space

In multi-objective problems, one is often interested in generating the envelope of the objective-space, where the envelope is, in general, a superset of pareto-optimal solutions. In this paper, we propose a method for tracing the envelope of multi-objective topology optimization problems, and generating the corresponding topologies. The proposed method exploits the concept of topological sensitivity, and is applied to bi-objective optimization, namely eigenvalue-volume, eigenvalue-eigenvalue and compliance-eigenvalue problems. The robustness and efficiency of the method is illustrated through numerical examples.

scholarly journals A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

2021 ◽  
Vol 26 (2) ◽  
pp. 34
Author(s):  
Isaac Gibert Martínez ◽  
Frederico Afonso ◽  
Simão Rodrigues ◽  
Fernando Lau
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Volume Fraction ◽  
Optimization Techniques ◽  
Free Form ◽  
Aerodynamic Shape Optimization ◽  
Sequential Approach ◽  
Airfoil Surface ◽  
Aerodynamic Shape ◽  
Design Variables

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

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