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.

scholarly journals A 2-dimensional shape optimization problem for tree branches

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Alberto Bressan ◽  
◽  
Sondre Tesdal Galtung ◽  
Keyword(s):  
Shape Optimization ◽  
Optimization Problem ◽  
Shape Optimization Problem ◽  
Dimensional Shape

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 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.

scholarly journals An Analytical Study in Multi-physics and Multi-criteria Shape Optimization

2021 ◽  
Author(s):  
Hanno Gottschalk ◽  
Marco Reese
Keyword(s):  
Shape Optimization ◽  
Physical System ◽  
Pareto Front ◽  
Optimization Problem ◽  
Analytical Study ◽  
Static Pressure ◽  
Hausdorff Metric ◽  
Objective Functions ◽  
Hölder Continuous ◽  
Turbine Vane

AbstractA simple multi-physical system for the potential flow of a fluid through a shroud, in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi-criteria shape optimization problem, where the shape of the component is allowed to vary under a certain set of second-order Hölder continuous differentiable transformations of a baseline shape with boundary of the same continuity class. As objective functions, we consider a simple loss model for the fluid dynamical efficiency and the probability of failure of the component due to repeated application of loads that stem from the fluid’s static pressure. For this multi-physical system, it is shown that, under certain conditions, the Pareto front is maximal in the sense that the Pareto front of the feasible set coincides with the Pareto front of its closure. We also show that the set of all optimal forms with respect to scalarization techniques deforms continuously (in the Hausdorff metric) with respect to preference parameters.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

Optimal design of a parallel robotic gripper using enhanced multi-objective ant lion optimizer with a sensitivity analysis approach

2020 ◽  
Vol 40 (5) ◽  
pp. 703-721
Author(s):  
Golak Bihari Mahanta ◽  
Deepak BBVL ◽  
Bibhuti B. Biswal ◽  
Amruta Rout
Keyword(s):  
Sensitivity Analysis ◽  
Distribution Function ◽  
Design Parameters ◽  
Objective Functions ◽  
Content Type ◽  
Multi Objective ◽  
The Past ◽  
Design Variables ◽  
Pick And Place ◽  
Ant Lion

Purpose From the past few decades, parallel grippers are used successfully in the automation industries for performing various pick and place jobs due to their simple design, reliable nature and its economic feasibility. So, the purpose of this paperis to design a suitable gripper with appropriate design parameters for better performance in the robotic production systems. Design/methodology/approach In this paper, an enhanced multi-objective ant lion algorithm is introduced to find the optimal geometric and design variables of a parallel gripper. The considered robotic gripper systems are evaluated by considering three objective functions while satisfying eight constraint equations. The beta distribution function is introduced for generating the initial random number at the initialization phase of the proposed algorithm as a replacement of uniform distribution function. A local search algorithm, namely, achievement scalarizing function with multi-criteria decision-making technique and beta distribution are used to enhance the existing optimizer to evaluate the optimal gripper design problem. In this study, the newly proposed enhanced optimizer to obtain the optimum design condition of the design variables is called enhanced multi-objective ant lion optimizer. Findings This study aims to obtain optimal design parameters of the parallel gripper with the help of the developed algorithms. The acquired results are investigated with the past research paper conducted in that field for comparison. It is observed that the suggested method to get the best gripper arrangement and variables of the parallel gripper mechanism outperform its counterparts. The effects of the design variables are needed to be studied for a better design approach concerning the objective functions, which is achieved by sensitivity analysis. Practical implications The developed gripper is feasible to use in the assembly operation, as well as in other pick and place operations in different industries. Originality/value In this study, the problem to find the optimum design parameter (i.e. geometric parameters such as length of the link and parallel gripper joint angles) is addressed as a multi-objective optimization. The obtained results from the execution of the algorithm are evaluated using the performance indicator algorithm and a sensitivity analysis is introduced to validate the effects of the design variables. The obtained optimal parameters are used to develop a gripper prototype, which will be used for the assembly process.

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