Shape Optimization Using a Variable Number of Conic Patches

1993 ◽  
Author(s):  
James M. Widmann ◽  
Sheri D. Sheppard
Keyword(s):  
Shape Optimization ◽  
Design Space ◽  
Variable Number ◽  
Optimization Process ◽  
Optimized Design ◽  
Two Dimensional ◽  
Geometric Description ◽  
Design Representation ◽  
Design Variables ◽  
Dimensional Shape

Abstract Shape Optimization is a branch of structural optimization in which the boundaries of geometry are varied. The shape of the boundary is determined by optimizing a set of design variables that form the geometric description of the shape. This paper presents a method of two dimensional shape optimization in which the number of design variables is allowed to change during the optimization process. First an initial design representation is chosen and optimized. Next a new mathematical description of the optimized design is created with an increased number of design variables. This new design is subsequently optimized. This allows the optimization process to work within a larger design space that includes a greater variety of shapes. The process of adding design variables is repeated until no additional improvements in the design are made. Several design examples are solved with this procedure and presented.

Application of a Decomposition Technique for Treating a Shape Optimization Problem

1989 ◽  
Author(s):  
M. Bremicker ◽  
H. Eschenauer
Keyword(s):  
Sensitivity Analysis ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Optimization Methods ◽  
Objective Functions ◽  
Shape Optimization Problem ◽  
Boundary State ◽  
Design Variables ◽  
Dimensional Shape ◽  
Suitable Approximation

Abstract The range of application of structural optimization methods can be considerably enlarged by using decomposition techniques. In this paper a novel procedure is introduced to deal with such problems more efficiently. The mechanical structure resp. system is divided into several subsystems splitting up the design variables, objective functions, and constraints accordingly. The boundary state quantities of the subsystems and the global (i.e. subsystem overlapping) functions are approximated by a sensitivity analysis of the entire system using suitable approximation concepts. It is thus possible to optimize the subsystems independently. Variables, objective functions and constraints can be chosen arbitrarily; all coupling information is obtained from the sensitivity analysis by means of global information. The application of this technique is demonstrated by a two-dimensional shape optimization problem.

Optimization Framework Using Surrogate Model for Aerodynamically Improved 3D Turbine Blade Design

2014 ◽  
Author(s):  
Sanga Lee ◽  
Saeil Lee ◽  
Kyu-Hong Kim ◽  
Dong-Ho Lee ◽  
Young-Seok Kang ◽  
...  
Keyword(s):  
Surrogate Model ◽  
Design Space ◽  
Computational Cost ◽  
Three Dimensional ◽  
Experimental Point ◽  
Optimized Design ◽  
Kriging Method ◽  
Baseline Design ◽  
Design Variables ◽  
Nonlinear Design

In simple optimization problem, direct searching methods are most accurate and practical enough. However, for more complicated problem which contains many design variables and demands high computational costs, surrogate model methods are recommendable instead of direct searching methods. In this case, surrogate models should have reliability for not only accuracy of the optimum value but also globalness of the solution. In this paper, the Kriging method was used to construct surrogate model for finding aerodynamically improved three dimensional single stage turbine. At first, nozzle was optimized coupled with base rotor blade. And then rotor was optimized with the optimized nozzle vane in order. Kriging method is well known for its good describability of nonlinear design space. For this reason, Kriging method is appropriate for describing the turbine design space, which has complicated physical phenomena and demands many design variables for finding optimum three dimensional blade shapes. To construct airfoil shape, Prichard topology was used. The blade was divided into 3 sections and each section has 9 design variables. Considering computational cost, some design variables were picked up by using sensitivity analysis. For selecting experimental point, D-optimal method, which scatters each experimental points to have maximum dispersion, was used. Model validation was done by comparing estimated values of random points by Kriging model with evaluated values by computation. The constructed surrogate model was refined repeatedly until it reaches convergence criteria, by supplying additional experimental points. When the surrogate model satisfies the reliability condition and developed enough, finding optimum point and its validation was followed by. If any variable was located on the boundary of design space, the design space was shifted in order to avoid the boundary of the design space. This process was also repeated until finding appropriate design space. As a result, the optimized design has more complicated blade shapes than that of the baseline design but has higher aerodynamic efficiency than the baseline turbine stage.

scholarly journals Two-Dimensional Shape Optimization with Nearly Conformal Transformations

2018 ◽  
Vol 40 (6) ◽  
pp. A3807-A3830 ◽  
Author(s):  
José A. Iglesias ◽  
Kevin Sturm ◽  
Florian Wechsung
Keyword(s):  
Shape Optimization ◽  
Conformal Transformations ◽  
Two Dimensional ◽  
Dimensional Shape

A Design Optimization Process Based on an Energy Finite Element Formulation

1999 ◽  
Author(s):  
George Borlase ◽  
Nickolas Vlahopoulos ◽  
Luis Octavio Garza-Rios
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Numerical Models ◽  
Optimization Process ◽  
Element Formulation ◽  
Optimized Design ◽  
Element Analysis ◽  
Fishing Boat ◽  
Design Variables ◽  
Energy Finite Element Analysis

Abstract The Energy Finite Element Analysis (EFEA) offers an alternative solution to the established Statistical Energy Analysis (SEA) for simulating the vibration of large scale structures. A brief theoretical overview and comparison of the two methods is presented first. Numerical models for a fishing boat are utilized for a comparison between the two formulations. In order to demonstrate the powerful capabilities of EFEA in the area of simulation based design, an optimization routine is integrated with an EFEA solver. The optimized distribution of damping over the hull of a vessel is computed. The formulation of the optimization process is presented. The definition of the design variables, the objective function, and the constraints is discussed. The flow chart of the optimization process, and a comparison between the initial and the optimized design are presented.

Multi-Objective Shape Optimization of Convective Wavy Channels

2005 ◽  
Author(s):  
Enrico Nobile ◽  
Francesco Pinto ◽  
Gino Rizzetto
Keyword(s):  
Shape Optimization ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Design Variables ◽  
Wavy Channels ◽  
Steady Laminar ◽  
Objective Shape

In this paper we describe a procedure for the multi-objective shape optimization of periodic wavy channels, representative of the repeating module of an ample variety of heat exchangers. The two objectives considered are the maximization of heat transfer rate and minimization of friction factor. Since there is no a single optimum to be found, we use a Multi-Objective Genetic Algorithm and the so-called Pareto’s dominance concept. The optimization of the periodic channel is obtained, by means of an unstructured Finite Element solver, for a fluid of Prandtl number Pr = 0.7, assuming fully developed velocity and temperature fields, and steady laminar conditions. For the two-dimensional case, the geometry is parameterized either by means of linear-piecewise profiles, or NURBS, and their control points represent the design variables. The three-dimensional channels are obtained by simple extrusion of the two-dimensional geometries. The results obtained are very encouraging, and the procedure described can be applied, in principle, to even more complex problems.

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