BESHOP: A Program Package for Shape Optimization in 2-D Elasticity Problems

1992 ◽  
Author(s):  
Behrooz Farshi ◽  
Shapour Moradi
Keyword(s):  
Shape Optimization ◽  
Classical Case ◽  
Optimization Method ◽  
Program Package ◽  
Optimum Shape ◽  
Case Examples ◽  
Design Variables ◽  
Critical Boundary ◽  
Elasticity Problems ◽  
Number Of Cycles

Abstract In this paper a package is introduced which handles shape optimization in 2-dimensional elasticity problems where Boundary Element Method is used for the analysis phase affording a large reduction in the problem dimensionality together with a variant of the Method of Center Points for the optimization phase. This optimization method allows a high reduction in the number of constraints considered in each step, as well as low number of cycles, resulting in notable overall efficiency. Design variables in optimum shape determination consists of basic nodal coordinates for B-spline functions as the means to define smooth boundary curves. Maximum stress and/or displacements at critical boundary points are observed as constraints in each cycle of the procedure. Three classical case examples are solved successfully, and the results are compared with those of others, illustrating the superior capabilities of the program package.

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 Shape optimization of a blended-wing-body underwater glider using surrogate-based global optimization method IESGO-HSR

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042095014
Author(s):  
Pengcheng Ye ◽  
Guang Pan
Keyword(s):  
Global Optimization ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Hydrodynamic Performance ◽  
Optimum Shape ◽  
Underwater Glider ◽  
Global Optimization Method ◽  
Shape Optimization Problem ◽  
Blended Wing Body

As a novel flying-wing configuration underwater glider, the blended-wing-body underwater glider (BWBUG) has the satisfactory hydrodynamic performance in comparison to the conventional cylindrical autonomous underwater gliders (AUGs). The complicated shape optimization of BWBUG is significant for improving its hydrodynamic efficiency while it has to require huge computation time and efforts. A novel surrogate-based shape optimization (SBSO) framework is proposed to deal with the BWBUG shape optimization problem for improving the optimization efficiency and quality. During the optimization search, the parametric geometric model of the BWBUG is constructed depending on seven specific sectional airfoils, with the planar surface being unaltered. Moreover, an improved ensemble of surrogates based global optimization method using a hierarchical design space reduction strategy (IESGO-HSR) is used for optimizing the chosen sectional airfoils. The optimum shape of BWBUG can be obtained using all sectional airfoils which are successfully optimized. The maximum lift to drag ratio (LDR) of the optimal BWBUG is improved by 24.32% with acceptable computational resources. The optimization results show that the proposed SBSO framework is more superior and efficient in handling the BWBUG shape optimization problem.

A novel surrogate-based aerodynamic optimization method using field approximate model

2017 ◽  
Vol 233 (3) ◽  
pp. 883-895 ◽  
Author(s):  
Wenjie Wang ◽  
Zeping Wu ◽  
Donghui Wang ◽  
Weihua Zhang
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Optimization Method ◽  
Approximate Model ◽  
Dynamics Simulation ◽  
Aerodynamic Optimization ◽  
Optimal Point ◽  
Design Variables ◽  
Sampling Set ◽  
Optimization Efficiency

An efficient surrogate-based aerodynamic shape optimization method is developed to improve the optimization efficiency. In this method, the field approximate model is presented firstly to predict the flow field parameters of interest for specific aerodynamic optimization problems with respect to the design variables and sequentially updated. The differential evolution is used to locate the optimum of field approximate model coupled with the analytical post-processing to calculate the objective and constraints for aerodynamic optimization. This optimal point is calculated by time-consuming computational fluid dynamics simulation and the result is added to the sampling set to update the sampling points and field approximate model. The proposed method is compared with conventional sequential approximate optimization and shows great advantages in accuracy and efficiency. Two shape optimization test cases are provided to verify the efficacy and efficiency of the proposed method.

A Strategy for Multi-Point Shape Optimization of Turbine Stages in Three-Dimensional Flow

2009 ◽  
Author(s):  
Mohammad Arabnia ◽  
Wahid Ghaly
Keyword(s):  
Shape Optimization ◽  
Three Dimensional ◽  
Optimization Method ◽  
Secondary Flows ◽  
Optimization Strategy ◽  
Streamwise Vorticity ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Design Variables ◽  
The Individual

This paper presents an effective and practical shape optimization strategy for turbine stages so as to minimize the adverse effects of three-dimensional flow features on the turbine performance. The optimization method combines a genetic algorithm (GA), with a Response Surface Approximation (RSA) of the Artificial Neural Network (ANN) type. During the optimization process, the individual objectives and constraints are approximated using ANN that is trained and tested using a few three-dimensional CFD flow simulations; the latter are obtained using the commercial package Fluent. The optimization objective is a weighted sum of individual objectives such as isentropic efficiency, streamwise vorticity and is penalized with a number of constraints. To minimize three-dimensional effects, the stator and rotor stacking curves are taken as the design variable. They are parametrically represented using a quadratic rational Bezier curve (QRBC) whose parameters are related to the blade lean, sweep and bow, which are used as the design variables. The described strategy was applied to single and multipoint optimization of the E/TU-3 turbine stage. This optimization strategy proved to be successful, flexible and practical, and resulted in an improvement of around 1% in stage efficiency over the turbine operating range with as low as 5 design variables. This improvement is attributed to the reduction in secondary flows, in stator hub choking, and in the transonic region and the associated flow separation.

Shape Optimization of Clutch Cushion Disc Using Differential Evolution Method

2015 ◽  
Author(s):  
N. Kaya ◽  
S. Kartal ◽  
T. Çakmak ◽  
F. Karpat ◽  
A. Karaduman
Keyword(s):  
Shape Optimization ◽  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Optimization Method ◽  
Elastic Stiffness ◽  
Optimum Shape ◽  
Shape Parameters ◽  
Engine Torque ◽  
Pressure Plate ◽  
Finite Element Software

The clutch is an element which makes a temporary connection between gear box and vehicle engine. It transmits not only engine torque, but also ensures comfort and drivability during slippage. One of the main functions of clutch disc is to transmit the engine torque while absorbing vibrations. It allows a soft gradual reengagement of torque transmission. The cushion disc which is located between two clutch facings has wavy surface, thus it behaves like a spring during engagement and disengagement. The axial elastic stiffness of the clutch disc is obtained by a cushion disc. The load-deflection curve is obtained by compressing clutch disc between two plates, representing pressure plate and flywheel. The wavy shape of the cushion disc provides progressive stiffness curve of the clutch disc. The cushion disc participates in drivers comfort during engagement of the clutch. The comfort depends on the limits of the progressive stiffness curve. Outside the limits of this cushion function, the clutch engagement would be harsh and uncomfortable for the driver. Besides, engine torque may not be transmitted during the later service lifetime and the life of the clutch might be decreased. In the case cushion disc has no cushioning function, then the engine might be stopped. Additionally, improper cushioning function causes heat and deform of the pressure plate and it also decreases the transmitted engine torque. Therefore, cushion disc has to have certain cushioning characteristics in order to overcome these problems. In this study, the optimum shape design of cushion disc was performed using an evolutionary optimization algorithm. Differential evolution algorithm was selected as the optimization method because it guarantees the global optimum. Design of experiment method has been employed to construct the response surface that approximates the behavior of the objective function inside a certain design space. Three shape parameters of cushion disc have been selected. The objective of the shape optimization is to find the optimum shape parameters that provide the target stiffness curve. After solving the optimization problem with differential evolution method, optimum shape parameters of cushion disc have been found for two case studies. A Pascal code based differential evolution optimization code was developed for shape optimization and Ansys finite element software was used for calculating stiffness curve of cushion disc.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

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.

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.

Structural Optimization of Composite Panel with Lamination Parameters and Equivalent Stiffness Laminate Method

2014 ◽  
Vol 496-500 ◽  
pp. 429-435
Author(s):  
Xiao Ping Zhong ◽  
Peng Jin
Keyword(s):  
Genetic Algorithm ◽  
Structural Optimization ◽  
Composite Structure ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Composite Panel ◽  
Analysis Tool ◽  
Equivalent Stiffness ◽  
Lamination Parameters ◽  
Design Variables

Firstly, a two-level optimization procedure for composite structure is investigated with lamination parameters as design variables and MSC.Nastran as analysis tool. The details using lamination parameters as MSC.Nastran input parameters are presented. Secondly, with a proper equivalent stiffness laminate built to substitute for the lamination parameters, a two-level optimization method based on the equivalent stiffness laminate is proposed. Compared with the lamination parameters-based method, the layer thicknesses of the equivalent stiffness laminate are adopted as continuous design variables at the first level. The corresponding lamination parameters are calculated from the optimal layer thicknesses. At the second level, genetic algorithm (GA) is applied to identify an optimal laminate configuration to target the lamination parameters obtained. The numerical example shows that the proposed method without considering constraints of lamination parameters can obtain better optimal results.

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