scholarly journals Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations

2020 ◽  
Author(s):  
Idriss Mazari ◽  
Antoine Henrot ◽  
Yannick Privat
Keyword(s):  
Shape Optimization ◽  
Optimization Problem ◽  
Elliptic Partial Differential Equations ◽  
Volume Constraint ◽  
Standard Problem ◽  
Semilinear Elliptic ◽  
Dirichlet Type ◽  
Optimal Shapes ◽  
Linear Version ◽  
The Stability

Minimizing the so-called “Dirichlet energy” with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the problem, where one aims at mini- mizing a Dirichlet-type energy involving the solution to a semilinear elliptic PDE with respect to the domain, under a volume constraint. One of the main differences with the standard version of this problem rests upon the fact that the criterion to minimize does not write as the minimum of an energy, and thus most of the usual tools to analyze this problem cannot be used. By using a relaxed version of this problem, we first prove the existence of optimal shapes under several assumptions on the problem parameters. We then analyze the stability of the ball, expected to be a good candidate for solving the shape optimization problem, when the coefficients of the involved PDE are radially symmetric.

Shape Optimization Design of Brackets Connecting Girders of an Internal Bulkhead and Pressure Hull Under External Pressure

2017 ◽  
Author(s):  
Chengtao Jiang ◽  
Yuansheng Cheng ◽  
Wei Xiao ◽  
Qijian He ◽  
Shangdi Gao
Keyword(s):  
Shape Optimization ◽  
Optimization Design ◽  
Optimization Problem ◽  
Maximum Stress ◽  
High Stress ◽  
External Pressure ◽  
Coarse Mesh ◽  
Optimal Shapes ◽  
Design Variables ◽  
Hull Structure

In order to decrease the local high stress in the brackets which connect to the horizontal and vertical girders of an internal bulkhead and submersible pressure shell, the mathematical models for the shape optimization of the brackets are proposed. In the study, stress analysis of the pressure hull structure including an internal bulkhead and brackets with coarse mesh is firstly conducted, then the submodeling technique is further employed to analyze the refinement stress distribution of the brackets with refined mesh. The boundary shapes of the brackets are assumed as the design variables while the maximum stress of the bracket is treated as objective function to be minimized in the shape optimization problem. The proposed mathematical model is solved by using analysis code Hyperworks/Optistruct and optimal shapes of the brackets are obtained. Results of the shape optimization show that the optimized bracket types can effectively reduce the level of stress. Therefore, the proposed method can be referred to similar structure designs.

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.

scholarly journals Latency-Optimal Computational Offloading Strategy for Sensitive Tasks in Smart Homes

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2347
Author(s):  
Yanyan Wang ◽  
Lin Wang ◽  
Ruijuan Zheng ◽  
Xuhui Zhao ◽  
Muhua Liu
Keyword(s):  
Queue Length ◽  
Optimization Problem ◽  
Time Slot ◽  
Smart Homes ◽  
Back Pressure ◽  
Smart Devices ◽  
Smart Device ◽  
Simulation Results ◽  
Computational Offloading ◽  
The Stability

In smart homes, the computational offloading technology of edge cloud computing (ECC) can effectively deal with the large amount of computation generated by smart devices. In this paper, we propose a computational offloading strategy for minimizing delay based on the back-pressure algorithm (BMDCO) to get the offloading decision and the number of tasks that can be offloaded. Specifically, we first construct a system with multiple local smart device task queues and multiple edge processor task queues. Then, we formulate an offloading strategy to minimize the queue length of tasks in each time slot by minimizing the Lyapunov drift optimization problem, so as to realize the stability of queues and improve the offloading performance. In addition, we give a theoretical analysis on the stability of the BMDCO algorithm by deducing the upper bound of all queues in this system. The simulation results show the stability of the proposed algorithm, and demonstrate that the BMDCO algorithm is superior to other alternatives. Compared with other algorithms, this algorithm can effectively reduce the computation delay.

scholarly journals Optimal Location and Design of TCSC controller For Improvement of Stability

2011 ◽  
pp. 210-215
Author(s):  
Swathi Kommamuri ◽  
P. Sureshbabu
Keyword(s):  
Power System ◽  
Optimization Problem ◽  
Low Frequency ◽  
System Stability ◽  
Simulation Environment ◽  
Swarm Optimization ◽  
Stability Performance ◽  
Low Frequency Oscillations ◽  
Simulation Results ◽  
The Stability

Power system stability improvement by a coordinate Design ofThyristor Controlled Series Compensator (TCSC) controller is addressed in this paper.Particle Swarm Optimization (PSO) technique is employed for optimization of the parameterconstrained nonlinear optimization problem implemented in a simulation environment. The proposed controllers are tested on a weakly connected power system. The non-linear simulation results are presented. The eigenvalue analysis and simulation results show the effectiveness and robustness of proposed controllers to improve the stability performance of power system by efficient damping of low frequency oscillations under various disturbances.

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