Optimization of Support Locations of Beam and Plate Structures Under Self-Weight by Using a Sprung Structure Model

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Gang-Won Jang ◽  
Ho Seong Shim ◽  
Yoon Young Kim
Keyword(s):  
Objective Function ◽  
Optimization Method ◽  
Extensive Study ◽  
Plate Structures ◽  
Design Variables ◽  
Gradient Based ◽  
Elastically Supported ◽  
Structural Behaviors ◽  
Important Design

To find support locations minimizing uneven deformation is an important design issue in a large plate under self-weight. During the imprinting process of LCD panels, for instance, a large variation in the deflection of an LCD panel due to its self-weight deteriorates the quality of nanoscale imprinted lines. Motivated by this need, this research aims to develop an efficient gradient-based optimization method of finding optimal support locations of beam or plate structures under self-weight. To use a gradient-based algorithm, the support locating problem is formulated with continuous design variables. In this work, a beam or plate structure is assumed to be supported by a set of distributed springs, which are attached to all nodes of the discretized model of a given structure. The spring stiffness is made to vary continuously as a function of the design variable in which unsupported and supported states of a structure are represented with springs having limit stiffness values. Because elastically supported structures exhibit considerably different structural behaviors from structures without elastic supports, it is difficult to select an objective function fulfilling the design goal and ensuring convergence to distinct supported-unsupported states without ambiguous intermediate states. To address this issue, an extensive study is conducted and an appropriate objective function is then suggested. An optimization formulation using the objective function is presented and several numerical problems are considered to check the validity and usefulness of the developed formulation.

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.

The Effect of Different Optimization Methods on Robustness for Robust Optimization Design

2014 ◽  
Vol 721 ◽  
pp. 464-467
Author(s):  
Tao Fu ◽  
Qin Zhong Gong ◽  
Da Zhen Wang
Keyword(s):  
Robust Optimization ◽  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Parameters ◽  
Hybrid Particle Swarm Optimization ◽  
Design Variables ◽  
Robust Optimization Design

In view of robustness of objective function and constraints in robust design, the method of maximum variation analysis is adopted to improve the robust design. In this method, firstly, we analyses the effect of uncertain factors in design variables and design parameters on the objective function and constraints, then calculate maximum variations of objective function and constraints. A two-level optimum mathematical model is constructed by adding the maximum variations to the original constraints. Different solving methods are used to solve the model to study the influence to robustness. As a demonstration, we apply our robust optimization method to an engineering example, the design of a machine tool spindle. The results show that, compared with other methods, this method of HPSO(hybrid particle swarm optimization) algorithm is superior on solving efficiency and solving results, and the constraint robustness and the objective robustness completely satisfy the requirement, revealing that excellent solving method can improve robustness.

Optimization of Highly Loaded Fan Rotor Based on Throughflow Model

2007 ◽  
Author(s):  
Hong Wu ◽  
Qiushi Li ◽  
Sheng Zhou
Keyword(s):  
Mass Flow ◽  
Total Pressure ◽  
Pressure Ratio ◽  
Optimization Method ◽  
Design Variables ◽  
Adaptive Simulated Annealing ◽  
Throughflow Model ◽  
Important Design ◽  
Total Pressure Ratio ◽  
Highly Loaded

This paper presents an optimization method for fan/compressor which couples throughflow model solving axisymmetric Euler equations with adaptive simulated annealing (ASA) algorithm. One of the advantages of this optimization method is that it spends much less time than 3D optimization due to the rapid solving of throughflow model. In addition, the optimization space is quite extensive because more design variables can be adjusted in throughflow phase, such as swirl distribution, hub curve and sweep. To validate this optimization method, a highly loaded fan rotor with pressure ratio of 3.06 as a baseline is optimized. During the optimization process, the objective function is total pressure ratio, moreover, mass flow and efficiency are selected as the constraint conditions. Three important design variables including swirl distribution, hub curve and sweep are parameterized using Bezier curve, and then optimized in throughflow model independently, finally the optimum designs are validated using 3D viscous CFD solver. It is shown that pressure ratio and rotor loading can be improved further through optimizing swirl distribution, however, hub and sweep curves take more effects on mass flow and efficiency respectively. The optimization results demonstrate the advantage and feasibility of this optimization method.

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.

Metamodel-Based Optimum Design Examples of Structures

2014 ◽  
pp. 667-676
Author(s):  
Kwon-Hee Lee ◽  
Ji-In Heo
Keyword(s):  
Weight Reduction ◽  
Performance Enhancement ◽  
Fuel Efficiency ◽  
Optimization Methods ◽  
Optimization Method ◽  
The Other ◽  
True Response ◽  
Design Variables ◽  
Weight One ◽  
Gradient Based

In order to achieve greater fuel efficiency and energy conservation, the reduction of weight and enhancement of the performance of structures has been sought. In general, there are two approaches to reducing structural weight. One of which is to use materials that are lighter than steel and the other is to redesign the structure. However, conventional structural optimization methods using gradient-based algorithm directly have difficulties in defining complex shape design variables and preventing mesh distortions. To overcome these difficulties a metamodel-based optimization method is introduced in order to replace the true response by an approximate one. This research presents four case studies of structural design using a metamodel-based approximation model for weight reduction or performance enhancement.

Jaya algorithm based optimum design of reinforced concrete retaining walls under dynamic loads

2021 ◽  
Vol 7 (2) ◽  
pp. 64
Author(s):  
Nur Eroğlu ◽  
Sena Aral ◽  
Sinan Melih Nigdeli ◽  
Gebrail Bekdaş
Keyword(s):  
Reinforced Concrete ◽  
Objective Function ◽  
Retaining Wall ◽  
Unit Length ◽  
Optimization Method ◽  
Dynamic Loads ◽  
Jaya Algorithm ◽  
Design Variables ◽  
Projection Length ◽  
Static Conditions

In this study, the optimum dimensioning of a reinforced concrete retaining wall that meets the safety conditions under static and dynamic loads in terms of cost has been performed using Jaya algorithm, which is one of the metaheuristic algorithms. In the optimization process, reinforced concrete design rules and ground stress, sliding and overturn tests have been determined as design constraints for the safe design of the retaining wall. While 5 cross-section dimensions of the retaining wall are defined as the design variable, the objective function is targeted as the total cost per unit length of the retaining wall. In the study, optimum results are also presented by examining the changes of the toe projection length of the retaining wall, which is one of the design variables, narrowing between 0.2-10 m. The design variables minimizing the objective function were found via Jaya algorithm that have single-phase. In addition to achieving optimum dimensioning results in terms of safety and cost with the optimization method used as a result of the reinforced concrete design made by applying the rules of the regulation on buildings to be constructed in earthquake zones, the change in cost in seismic and static conditions was examined.

Optimization, design and testing for morphing leading edge

2020 ◽  
pp. 095440622094188
Author(s):  
Yu Yang ◽  
Zhigang Wang ◽  
Binwen Wang ◽  
Shuaishuai Lyu
Keyword(s):  
Optimization Design ◽  
Design Method ◽  
Leading Edge ◽  
Optimization Method ◽  
Collaborative Optimization ◽  
Noise Abatement ◽  
Deformation Control ◽  
Design Variables ◽  
Weight Penalty

Wing's morphing leading edge, drooping in a seamless way, has significant potential for noise abatement and drag reduction. Innovative design methods for compliant skin and internal actuating mechanism, respectively, are proposed and validated through a mockup in this paper. For the skin, a collaborative optimization method is presented, which takes all design variables, continuous and discrete, into account simultaneously. Moreover, to overcome the drawback of conventional algorithm, which is insufficient for deformation control in critical regime, weight penalty is imposed on present objective function. On the other hand, an internal kinematic actuating mechanism is designed from an improved concept, of which positions of level-rod hinges are optimized in a larger zone to fit the deflection requirement. The test of mockup validates the above methods, and excellent morphing quality of the compliant skin proves the advancement of the collaborative optimization method. However, the design method of internal actuating mechanism needs further improvement, and the error induced deteriorates the final morphing quality of the mockup.

Parameter Optimization of a Static Micro-Mixer Using a Sequential Approximate Optimization Method

2006 ◽  
Vol 306-308 ◽  
pp. 471-476
Author(s):  
Seok Yoon Han ◽  
J.S. Maeng ◽  
S.H. Kim ◽  
J.Y. Park
Keyword(s):  
Objective Function ◽  
Cantilever Beam ◽  
Parameter Optimization ◽  
Optimization Method ◽  
Sequential Approximate Optimization ◽  
Mixing Efficiency ◽  
Approximate Optimization ◽  
Design Variables ◽  
Anova Table ◽  
Micro Mixer

Parameter optimization of a static micro-mixer with a cantilever beam was accomplished for maximizing mixing efficiency using a sequential approximate optimization method. The objective function and design variables were chosen as mixing index, and the length and the angle measured from the horizontal of the cantilever beam, respectively. The Optimization problem of the mixer was considered as a series of sub-problems. Approximation to solve the sub-problems was performed by response surface methodology. To verify the reliability and the accuracy of the approximated objective function, ANOVA table and variable selection method were implemented, respectively. It was verified that the sequential approximate optimization method worked very well, and the mixing efficiency was significantly improved compared with the initial design.

scholarly journals On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization—Part II: Viscous Flows

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 106
Author(s):  
Farzad Mohebbi ◽  
Ben Evans ◽  
Mathieu Sellier
Keyword(s):  
Shape Optimization ◽  
Viscous Flows ◽  
Optimization Method ◽  
Step Length ◽  
Aerodynamic Shape Optimization ◽  
Ansys Fluent ◽  
Transonic Flows ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Gradient Based

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

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.

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