Numerical Methods for the Design of Meso-Structures: A Comparative Review

2015 ◽  
Author(s):  
Marcus Yoder ◽  
Zachary Satterfield ◽  
Mohammad Fazelpour ◽  
Joshua D. Summers ◽  
Georges Fadel
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Material Properties ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Future Research ◽  
Structured Materials ◽  
3 Dimensional ◽  
Comparative Review ◽  
Gradient Based

Over the past decade, there has been an increase in the intentional design of meso-structured materials that are optimized to target desired material properties. This paper reviews and critically compares common numerical methodologies and optimization techniques used to design these meso-structures by analyzing the methods themselves and published applications and results. Most of the reviewed research targets mechanical material properties, including effective stiffness and crushing energy absorption. The numerical methodologies reviewed include topology and size/shape optimization methods such as homogenization, Solid Isotropic Material with Penalization, and level sets. The optimization techniques reviewed include genetic algorithms (GAs), particle swarm optimization (PSO), gradient based, and exhaustive search methods. The research reviewed shows notable patterns. The literature reveals a push to apply topology optimization in an ever-growing number of 3-dimensional applications. Additionally, researchers are beginning to apply topology optimization and size/shape optimization to multiphysics problems. The research also shows notable gaps. Although PSOs are comparable evolutionary algorithms to GAs, the use of GAs dominates over PSOs. These patterns and gaps, along with others, are discussed in terms of possible future research in the design of meso-structured materials.

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.

Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

scholarly journals Pyrolysis modeling, sensitivity analysis, and optimization techniques for combustible materials: A review

2019 ◽  
Vol 37 (4-6) ◽  
pp. 377-433
Author(s):  
Tatenda Nyazika ◽  
Maude Jimenez ◽  
Fabienne Samyn ◽  
Serge Bourbigot
Keyword(s):  
Sensitivity Analysis ◽  
Material Properties ◽  
Input Parameter ◽  
Fire Behavior ◽  
Sensitivity Study ◽  
Optimization Techniques ◽  
Decomposition Reactions ◽  
Input Parameters ◽  
Gradient Based ◽  
Complete Set

Over the past years, pyrolysis models have moved from thermal models to comprehensive models with great flexibility including multi-step decomposition reactions. However, the downside is the need for a complete set of input data such as the material properties and the parameters related to the decomposition kinetics. Some of the parameters are not directly measurable or are difficult to determine and they carry a certain degree of uncertainty at high temperatures especially for materials that can melt, shrink, or swell. One can obtain input parameters by searching through the literature; however, certain materials may have the same nomenclature but the material properties may vary depending on the manufacturer, thereby inducing uncertainties in the model. Modelers have resorted to the use of optimization techniques such as gradient-based and direct search methods to estimate input parameters from experimental bench-scale data. As an integral part of the model, a sensitivity study allows to identify the role of each input parameter on the outputs. This work presents an overview of pyrolysis modeling, sensitivity analysis, and optimization techniques used to predict the fire behavior of combustible solids when exposed to an external heat flux.

Estimation of Thermal Boundary Conditions by Gradient Based and Genetic Algorythms

2012 ◽  
Vol 729 ◽  
pp. 144-149 ◽  
Author(s):  
Imre Felde
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Nsga Ii ◽  
Thermal Boundary Conditions ◽  
Treatment Processes ◽  
Gradient Based ◽  
Type Boundary

The prediction of third type boundary conditions occurring during heat treatment processes is an essential requirement for characterization of heat transfer phenomena. In this work, the performance of four optimization techniques is studied. These models are the Conjugate Gradient Method, the Levenberg-Marquardt Method, the Simplex method and the NSGA II algorithm. The models are used to estimate the heat transfer coefficient during transient heat transfer. The performance of the optimization methods is demonstrated using numerical techniques.

scholarly journals A Level Set Method in Shape and Topology Optimization for Variational Inequalities

2007 ◽  
Vol 17 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Piotr Fulmański ◽  
Antoine Laurain ◽  
Jean-Francois Scheid ◽  
Jan Sokołowski
Keyword(s):  
Topology Optimization ◽  
Variational Inequalities ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Energy Functional ◽  
Optimization Techniques ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Topological Derivatives

A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

A methodology to consider local material properties in structural optimization

2016 ◽  
Vol 231 (15) ◽  
pp. 2822-2834 ◽  
Author(s):  
Riccardo Cenni ◽  
Matteo Cova ◽  
Giacomo Bertuzzi
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Cast Iron ◽  
Shape Optimization ◽  
Material Properties ◽  
Simulation Software ◽  
Optimization Techniques ◽  
Local Material ◽  
Local Strength ◽  
Local Material Properties

We propose a finite element methodology to consider local material properties for large cast iron components in shape optimization. We found that considering local strength instead of uniform strength within shape optimization brings to different results in terms of safety-cost balance for the same component. It is well known that local mechanical properties of large cast iron components are defined by their microstructure and defects, which locally affect the strength of the components. Considering or not local mechanical properties can dramatically change a component reliability evaluation during its design. Since a typical industrial aim for shape optimization is trying to get the optimal solution in terms of component quality and cost, considering local material properties is even more important than in traditional design process where no optimization techniques are used. We compute solidification process parameters via finite element solidification analysis, and then we exploit experimental correlation between these parameters and ultimate tensile strength to evaluate the local reliability of the finished component under its static loading conditions. We believe that this methodology represents an opportunity to better design casting components when mechanical properties are deeply affected by their production process as described in the provided examples. In these examples, we wanted to minimize casting cost constrained by a target reliability and we get component cost reduction by considering local material properties. Future research will address the problem of using dedicated casting simulation software instead of general purpose finite element analysis software to compute solidification analysis and then introducing fatigue analysis and correlation between fatigue material properties and casting process output variables.

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.

scholarly journals Coupled topology and shape optimization using an embedding domain discretization method

2021 ◽  
Vol 64 (4) ◽  
pp. 2687-2707
Author(s):  
Gabriel Stankiewicz ◽  
Chaitanya Dev ◽  
Paul Steinmann
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Optimization Methods ◽  
Density Field ◽  
Discretization Method ◽  
Topological Features ◽  
Topology And Shape Optimization ◽  
Discretization Technique ◽  
Domain Discretization

AbstractDensity-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.

scholarly journals Applications of Topology Optimization Techniques in Seismic Design of Structure

2012 ◽  
pp. 232-268 ◽  
Author(s):  
Kazem Ghabraie
Keyword(s):  
Topology Optimization ◽  
Seismic Design ◽  
Earthquake Engineering ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Periodic Loading ◽  
Wide Range ◽  
Numerical Instabilities ◽  
Passive Dampers ◽  
Seismic Design Of Structures

During the last two decades, topology optimization techniques have been successfully applied to a wide range of problems including seismic design of structures. This chapter aims to provide an introduction to the topology optimization methods and a review of the applications of these methods in earthquake engineering. Two well-established topology optimization techniques are introduced. Several problems including eigenfrequency control of structures, compliance minimization under periodic loading, and maximizing energy absorption of passive dampers will be addressed. Numerical instabilities and approaches to overcome them will be discussed. The application of the presented approaches and methods will be illustrated using numerical examples. It will be shown that in seismic design of structures, topology optimization methods can be useful in providing conceptual design for structural systems as well as detailed design of structural members.

scholarly journals Some applications of a novel desirability function in simultaneous optimization of multiple responses

2021 ◽  
Vol 49 (3) ◽  
pp. 534-548
Author(s):  
Velibor Marinković
Keyword(s):  
Comparative Analysis ◽  
Desirability Function ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
The Other ◽  
Simultaneous Optimization ◽  
Desirability Functions ◽  
Gradient Based ◽  
Response Optimization ◽  
Optimization Methodology

In the framework of multi-response optimization techniques, the optimization methodology based on the desirability function is one of the most popular and most frequently used methodologies by researchers and practitioners in engineering, chemistry, technology and many other fields of science and technique. Numerous desirability functions have been introduced to improve the performance of this optimization methodology. Recently, a novel desirability function for multi-response optimization is proposed, which is smooth, nonlinear, and differentiable, and thus more suitable for applying some of the more efficient gradient-based optimization methods. This paper evaluates the performance of the proposed method through six real examples. After a comparative analysis of the results, it is shown that the proposed method in a certain measure outperforms the other competitive optimization methods.

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