scholarly journals Critical Investigation of the Combined Compliance Average and Spreading Measures in the Robust Topology Optimization with Uncertain Loading Magnitude and Direction

2020 ◽  
Author(s):  
Anikó Csébfalvi
Keyword(s):  
Topology Optimization ◽  
Robust Design ◽  
Response Variable ◽  
Robust Solution ◽  
Robust Approach ◽  
Robust Topology Optimization ◽  
Design Variables ◽  
Bridge Problem ◽  
Creative Contribution

The paper critically investigates the role of the combined compliance average and spreading measures in the volume-constrained continuous robust topology optimization with uncertain loading magnitude and direction. In the robust topology optimization the generally expected and most popular robustness measure is the expected compliance, In the expectancy oriented approach, the compliance increment which is needed to get the robust design is an implicitly defined response variable. In order to open the possibility of the creative contribution of the designer to the best robust design searching process, this measure is sometimes combined with a spreading-oriented measure, which may be the variance or standard deviation. The best weighting schema can be done by a try-and-error-like algorithm in which the weights are design variables and the compliance-increment remains an implicitly defined response variable. In this paper, it will be shown that all of the compliance oriented approaches which are based on a single or combined statistical measure can be replaced by a new compliance-function-shape-oriented robust approach in which the allowed-compliance-increment will be an explicitly defined design variable and for a given increment value the robust solution will be the theoretically best one. A popular volume-constrained symmetric bridge problem with uncertain loading magnitude and direction will be presented to demonstrate the viability and efficiency of the proposed robust approach.

Extended Objective-Oriented Sequential Sampling Method for Robust Design of Complex Systems Against Design Uncertainty

2012 ◽  
Author(s):  
Siliang Zhang ◽  
Ping Zhu ◽  
Paul D. Arendt ◽  
Wei Chen
Keyword(s):  
Complex Systems ◽  
Robust Design ◽  
Sampling Method ◽  
Sequential Sampling ◽  
Robust Solution ◽  
Design Variables ◽  
Crashworthiness Design ◽  
The One ◽  
Uncertainty In Design ◽  
Sequential Strategy

In robust design of complex systems, metamodeling techniques are commonly used to replace expensive computer simulations. To improve the sampling efficiency, efforts have been made towards developing objective-oriented sequential sampling methods for deterministic problems. In this paper, an extended objective-oriented sequential sampling method is proposed for robust design, with an emphasis on those problems with uncertainty in design variables. The method involves quantitative assessment of the effects of metamodeling uncertainty on the robust responses, as well as a sequential strategy of choosing samples to adaptively improve the predicted robust response. To validate the benefits of the sequential strategy, two mathematical examples are illustrated first. This is followed by an automotive crashworthiness design example, a highly expensive and non-linear problem. Results show that the proposed method can mitigate the effect of both metamodeling uncertainty and design uncertainty, and more efficiently identify the robust solution compared to the one-stage sampling approach that is commonly used in practice.

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.

A robust topology optimization for enlarging working bandwidth of acoustic devices

2021 ◽  
Author(s):  
Jincheng Qin ◽  
Hiroshi Isakari ◽  
Kouichi Taji ◽  
Toru Takahashi ◽  
Toshiro Matsumoto
Keyword(s):  
Topology Optimization ◽  
Robust Topology Optimization

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.

Numerical Experiments in Using Voronoi Cell Finite Elements for Topology Optimization

2009 ◽  
Author(s):  
James M. Gibert ◽  
Georges M. Fadel
Keyword(s):  
Topology Optimization ◽  
Isotropic Material ◽  
Numerical Experiments ◽  
Voronoi Cell ◽  
Material Model ◽  
Topological Optimization ◽  
Advantages And Disadvantages ◽  
Compliance Minimization ◽  
Design Variables ◽  
Standard Linear

This paper provides two separate methodologies for implementing the Voronoi Cell Finite Element Method (VCFEM) in topological optimization. Both exploit two characteristics of VCFEM. The first approach utilizes the property that a hole or inclusion can be placed in the element: the design variables for the topology optimization are sizes of the hole. In the second approach, we note that VCFEM may mesh the design domain as n sided polygons. We restrict our attention to hexagonal meshes of the domain while applying Solid Isotropic Material Penalization (SIMP) material model. Researchers have shown that hexagonal meshes are not subject to the checker boarding problem commonly associated with standard linear quad and triangle elements. We present several examples to illustrate the efficacy of the methods in compliance minimization as well as discuss the advantages and disadvantages of each method.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

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