Optimum Design of Axial Flow Gas Turbine Stage—Part II: Solution of the Optimization Problem and Numerical Results

1980 ◽  
Vol 102 (4) ◽  
pp. 790-797 ◽  
Author(s):  
S. S. Rao ◽  
R. S. Gupta
Keyword(s):  
Gas Turbines ◽  
Optimization Problem ◽  
Interpolation Method ◽  
Axial Flow ◽  
Unconstrained Minimization ◽  
Problem Formulation ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Variable Metric ◽  
Minimization Technique

The problem of stage design of axial flow gas turbines has been formulated as a nonlinear mathematical programming problem with the objective of minimizing aerodynamic losses and mass of the stage. The aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem is presented in Part I of this paper. The optimization problem is solved by using the interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique with cubic interpolation method of one dimensional minimization is employed. Problems involving the optimization of efficiency and/or mass of the stage have been solved numerically in Part II of the paper. The results of sensitivity analysis conducted about the optimum point have also been reported.

Optimum Design of Axial Flow Gas Turbine Stage—Part I: Formulation and Analysis of Optimization Problem

1980 ◽  
Vol 102 (4) ◽  
pp. 782-789 ◽  
Author(s):  
S. S. Rao ◽  
R. S. Gupta
Keyword(s):  
Gas Turbines ◽  
Optimization Problem ◽  
Interpolation Method ◽  
Axial Flow ◽  
Unconstrained Minimization ◽  
Problem Formulation ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Variable Metric ◽  
Minimization Technique

The problem of stage design of axial flow gas turbines has been formulated as a nonlinear mathematical programming problem with the objective of minimizing aerodynamic losses and mass of the stage. The aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem is presented in Part I of this paper. The optimization problem is solved by using the interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique with cubic interpolation method of one-dimensional minimization is employed. Problems involving the optimization of efficiency and/or mass of the stage have been solved numerically in Part II of the paper. The results of a sensitivity analysis conducted about the optimum point have also been reported.

Axial Flow Compressor Design Optimization: Part I—Pitchline Analysis and Multivariable Objective Function Influence

1990 ◽  
Vol 112 (3) ◽  
pp. 399-404 ◽  
Author(s):  
A. Massardo ◽  
A. Satta
Keyword(s):  
Objective Function ◽  
Axial Flow ◽  
Problem Formulation ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Stall Margin ◽  
Variable Metric ◽  
Axial Flow Compressor ◽  
Minimization Technique ◽  
Flow Compressor

The design of an axial flow compressor stage has been formulated as a nonlinear mathematical programming problem with the objective of minimizing the aerodynamic losses and the weight of the stage, while maximizing the compressor stall margin. Aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem with a pitchline analysis is presented. The optimization problem is solved by using the penalty function method in which the Davidon-Fletcher-Powell variable metric minimization technique is employed. Designs involving the optimization of efficiency, weight of the stage, and stall margin are presented and the results discussed with particular reference to a multivariable objective function.

scholarly journals Axial Flow Compressor Design Optimization: Part I — Pitchline Analysis and Multivariate Objective Function Influence

1989 ◽  
Author(s):  
Aristide Massardo ◽  
Antonio Satta
Keyword(s):  
Objective Function ◽  
Axial Flow ◽  
Problem Formulation ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Stall Margin ◽  
Variable Metric ◽  
Axial Flow Compressor ◽  
Minimization Technique ◽  
Flow Compressor

The design of an axial flow compressor stage has been formulated as a nonlinear mathematical programming problem with the objective of minimizing the aerodynamic losses, and the weight of the stage while, maximizing the compressor stall margin. Aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem with a pitchline analysis is presented. The optimization problem is solved by using the penalty function method in which the Davidon-Fletcher-Powell variable metric minimization technique is employed. Designs involving the optimization of efficiency, weight of the stage, and stall margin are presented and the results discussed with particular reference to a multivariable objective function.

Reliability Based Optimization of Submarine Pressure Hulls With Inelastic Interstiffener Buckling Failure

2006 ◽  
Author(s):  
P. Radha ◽  
K. Rajagopalan
Keyword(s):  
Unconstrained Minimization ◽  
Computer Code ◽  
Correction Method ◽  
Penalty Function Method ◽  
Simulation Design ◽  
Design Variables ◽  
Minimization Technique ◽  
Buckling Failure ◽  
Optimal Values ◽  
Reliability Based Optimization

Uncertainties that exist in modelling and simulation, design variables and parameters, manufacturing processes etc., may lead to large variations in the performance characteristics of the system. Optimized deterministic designs determined without considering uncertainties can be unreliable and may lead to catastrophic failure of the structure being designed. Reliability based optimization (RBO) is a methodology that addresses these problems. In this paper the reliability based optimization of submarine pressure hulls in which the failure gets governed by inelastic interstiffener buckling has been described. The problem has been formulated to minimize the ratio of weight of shell-stiffener geometry to the weight of liquid displaced, subjected to reliability based inelastic interstiffener buckling constraint. Since the methods of analysis of inelastic buckling failure of submarine pressure hulls are inadequate, in the present study the Johnson-Ostenfeld inelastic correction method has been adopted for formulating the constraint. By considering spacing of the stiffener, thickness of the plating and depth of the stiffener as the design variables, Sequential Unconstrained Minimization Technique (SUMT) has been used to solve the design problem. RBO has been carried out to get the optimal values of these design variables for a target reliability index using Interior Penalty Function Method for which an efficient computer code in C++ has been developed.

Optimum Design of I. C. Engine Pistons

1984 ◽  
Vol 106 (2) ◽  
pp. 209-213 ◽  
Author(s):  
S. S. Rao ◽  
S. S. Srinivasa Rao
Keyword(s):  
Function Method ◽  
Optimization Problems ◽  
Interpolation Method ◽  
Unconstrained Minimization ◽  
Penalty Function Method ◽  
Minimum Volume ◽  
Constrained Optimization Problems ◽  
One Dimensional ◽  
Design Variables ◽  
Powell Method

The minimum volume design of I. C. engine pistons is considered with constraints on temperature and stresses developed in the piston. The interior penalty function method, coupled with the Davidon-Fletcher-Powell method of unconstrained minimization and the cubic interpolation method of one-dimensional search, is used for solving the constrained optimization problems. The temperature and stresses developed in the piston are determined by using the classic as well as the finite element methods of analysis. A sensitivity analysis is conducted to find the influence of changes in design variables on the objective function and the response parameters.

Rolling direction prediction of tensegrity robot on the slope based on FEM and GA

2020 ◽  
Vol 234 (19) ◽  
pp. 3846-3858
Author(s):  
Kaikai Zhao ◽  
Jian Chang ◽  
Bin Li ◽  
Wenjuan Du
Keyword(s):  
Genetic Algorithm ◽  
Finite Element Method ◽  
Finite Element ◽  
Unconstrained Optimization ◽  
Optimization Problem ◽  
Rolling Direction ◽  
Unconstrained Minimization ◽  
Unconstrained Optimization Problem ◽  
Minimization Technique ◽  
Element Method

Six-strut tensegrity robot is a new mobile robot whose outer surface is an icosahedron containing 8 regular triangles and 12 isosceles triangles, and the robot performs rolling locomotion along the edges of the triangle. On the slope, it has lots of poses depending on the slope’s angles and positions of robot, which is difficult to control the rolling directions in the real world. This paper proposed a new method based on finite element method and a genetic algorithm to predict the rolling directions of the robot. The balanced forces equations of robot nodes are established using finite element method, which is a constrained optimization problem. The equations are transformed into an unconstrained optimization problem by the thinking of sequential unconstrained minimization technique. Finally, the unconstrained optimization problem is calculated by genetic algorithm, and the relations between the actuators and the rolling directions are obtained through the dot product of gravitational torque and the edge vector of bottom triangle. This method is verified by simulation and experiment results.

Optimization of Constrained Dynamic Systems Using the Sequential Unconstrained Minimization Technique

1972 ◽  
Vol 94 (4) ◽  
pp. 319-322 ◽  
Author(s):  
B. N. Murali ◽  
L. R. Ebbesen ◽  
H. R. Sebesta
Keyword(s):  
Nonlinear Programming ◽  
Dynamic Systems ◽  
Optimization Problem ◽  
State Constraints ◽  
Unconstrained Minimization ◽  
Terminal State ◽  
Analysis Tool ◽  
Minimization Technique ◽  
Algebraic Optimization ◽  
Nonlinear Programming Method

The development of a computer program for the optimization of dynamic systems subject to parameter and terminal state constraints is presented in this paper. The problem is handled by converting it to an equivalent algebraic optimization problem. The resulting problem is then solved by a modified version (D YS UMT) of the nonlinear programming method S UMT (Sequential Unconstrained Minimization Technique). The available program provides an efficient and convenient analysis tool to aid engineers in the modeling and designing of dynamic systems.

THE l1 PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS

2010 ◽  
Vol 27 (05) ◽  
pp. 559-576 ◽  
Author(s):  
TADEUSZ ANTCZAK
Keyword(s):  
Penalty Function ◽  
Function Method ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Exact Penalty Function ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Exact Penalty ◽  
Penalized Optimization

In this paper, some new results on the l1 exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via the l1 exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable r-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with the l1 exact penalty function is also established.

scholarly journals Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

2021 ◽  
Author(s):  
Johanna Schultes ◽  
Michael Stiglmayr ◽  
Kathrin Klamroth ◽  
Camilla Hahn
Keyword(s):  
Shape Optimization ◽  
Optimization Problem ◽  
Mechanical Stability ◽  
Adjoint Equation ◽  
Tensile Load ◽  
Problem Formulation ◽  
State Equation ◽  
Efficient Solutions ◽  
Volume Stability ◽  
Shape Optimization Problem

AbstractIn engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, its weight and its cost. We consider a biobjective shape optimization problem maximizing the mechanical stability of a ceramic component under tensile load while minimizing its volume. Stability is thereby modeled using a Weibull-type formulation of the probability of failure under external loads. The PDE formulation of the mechanical state equation is discretized by a finite element method on a regular grid. To solve the discretized biobjective shape optimization problem we suggest a hypervolume scalarization, with which also unsupported efficient solutions can be determined without adding constraints to the problem formulation. FurthIn this section, general properties of the hypervolumeermore, maximizing the dominated hypervolume supports the decision maker in identifying compromise solutions. We investigate the relation of the hypervolume scalarization to the weighted sum scalarization and to direct multiobjective descent methods. Since gradient information can be efficiently obtained by solving the adjoint equation, the scalarized problem can be solved by a gradient ascent algorithm. We evaluate our approach on a 2 D test case representing a straight joint under tensile load.

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