Multi-objective optimization of functionally graded thick shells for thermal loading

2007 ◽  
Vol 81 (3) ◽  
pp. 386-400 ◽  
Author(s):  
Senthil S. Vel ◽  
Jacob L. Pelletier
Keyword(s):  
Thermal Loading ◽  
Functionally Graded ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Thick Shells

Multi-objective optimization of a functionally graded sandwich panel under mechanical loading in the presence of stress constraint

2017 ◽  
Vol 26 (3-4) ◽  
pp. 79-93 ◽  
Author(s):  
Mohammad Ashjari ◽  
Mohammad Reza Khoshravan
Keyword(s):  
Mechanical Loading ◽  
Sandwich Panel ◽  
Functionally Graded ◽  
Solution Technique ◽  
Control Points ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Simply Supported ◽  
Volume Fractions ◽  
Multi Objective

AbstractA method was presented for multi-objective optimization of material distribution of simply supported functionally graded (FG) sandwich panel, and sensitivity analyses of optimal designs were also conducted based on design variables and objective functions. The material composition was assumed to vary only in the thickness direction. Piecewise cubic interpolation of volume fractions was used to calculate volume fractions of constituent material phases at a point; these fractions were defined at a limited number of evenly spaced control points. The effective material properties of the panel were obtained by applying the linear rule of mixtures. The behavior of FG sandwich panel was predicted by Reddy’s assumptions of third-order shear deformation theory. Exact solutions for deflections and stresses of simply supported sandwich panel were presented using the Navier-type solution technique. The volume fractions at control points, material, and thickness of the faces which were selected as decision variables were optimized by a multi-objective evolutionary algorithm known as the fast and elitist multi-objective genetic algorithm (NSGA-II). The mass and deflection of the model were considered the objective functions to be minimized with stress constraints. This model was optimized to verify the capability and efficiency of the proposed model under mechanical loading. The framework proposed for designing FG sandwich panel under pure mechanical conditions was furnished by the results.

Multi-objective Optimization of Geometric Dimensions and Material Composition of Functionally Graded Components

2008 ◽  
Author(s):  
Senthil S. Vel ◽  
Andrew J. Goupee ◽  
Glaucio H. Paulino ◽  
Marek-Jerzy Pindera ◽  
Robert H. Dodds ◽  
...  
Keyword(s):  
Functionally Graded ◽  
Material Composition ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Functionally Graded Components

Multi-Objective Optimization of Functionally Graded Hollow Cylinders

2011 ◽  
Author(s):  
M. Nabian ◽  
M. T. Ahmadian
Keyword(s):  
Natural Frequency ◽  
Volume Fraction ◽  
Optimization Method ◽  
Functionally Graded ◽  
Multi Objective Optimization ◽  
Algorithm Optimization ◽  
Multi Objective ◽  
Graded Material ◽  
Hollow Cylinders ◽  
Volume Fraction Function

In this study, two physical properties of simply supported hollow cylinders made of functionally graded materials are investigated. These two properties are mass and first natural frequency which is desirable to be minimized and maximized respectively in mechanical applications. The functionally graded material properties are assumed to vary continuously through the thickness of the cylinder. In this multi-objective optimization problem the first natural frequency of the FGM cylinders as well as its mass are formulated in terms of the volume fraction of the constituents, then by using Genetic algorithm optimization method the continuous volume fraction function of the constituents has been derived to minimize the mass and maximize the first natural frequency simultaneously.

Steam Turbine Exhaust Optimization Based on Gaussian Covariance Networks Using Transient CFD Simulations

2018 ◽  
Author(s):  
Kevin Cremanns ◽  
Dirk Roos ◽  
Andreas Penkner ◽  
Simon Hecker ◽  
Christian Musch
Keyword(s):  
Steam Turbine ◽  
Surrogate Model ◽  
Power Plants ◽  
Thermal Loading ◽  
High Efficiency ◽  
Cfd Simulation ◽  
Surrogate Models ◽  
Training Data ◽  
Multi Objective Optimization ◽  
Multi Objective

Renewable energies are increasingly contributing to the overall volume of the electricity grid and demand besides high efficiency, greater flexibility of the conventional fossil power plants. To optimize these objectives, extensive CFD calculations are required in most cases. For example, transient CFD calculations are only rarely combined with an optimizer because of their high demand on computational resources and time. Surrogate models, which are mathematical methods to learn and approximate the relationship between input and output parameters, are a common way to solve these problems. Once they are trained, they can perform the evaluations within seconds and replace the expensive simulation. Of course, real calculations are still needed to generate the training data. Therefore, it is useful to apply efficient and sequentially extensible design plans. This paper presents a new surrogate model method, based on a deep neural network learning the non-stationary hyperparameters of combined Gaussian process covariance matrices. It is used to approximate the complex and time consuming transient CFD simulation of a combined high-intermediate pressure steam turbine double shell outer casing. To minimize the exergy loss, the exhaust geometry is optimized in a single and multi-objective optimization on the surrogate models. The multi-objective optimization also includes the uniform velocity distribution of the steam in different areas of the casing, to predict the thermal loading of the steam turbine inner casing and to avoid an imbalanced thermal loading. A sequential sampling approach combined with a sensitivity analysis is used to find the minimum number of samples needed to train the surrogate models in order to gain sufficient prediction quality. Additionally, the paper describes the initial geometry, its numerical setup and the required control mechanisms to avoid noisy designs, which might complicate the surrogate model training. There is also a comparison of the initial and chosen optimal designs.

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