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Layout Optimization : A Mathematical Programming Approach
Duysinx, Pierre
1997
 

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Keywords :
Sequential Convex Programming; Topology optimization; Convex Approximations; Dual methods; Permieter Method
Abstract :
[en] This paper presents applications of specially tailored methods of the mathematical programming approach for solving topology design problems formulated as an optimal material distribution, providing a way to enlarge the scope of potential applications of topology optimization. The first feature of the methodology is to resort to dual maximization to solve optimization problems with a huge number of design variables, using the concept of Sequential Convex Programming (SCP). Here a central theme is the choice of convex approximations suited to the problems. First order approximations are firstly considered and compared. However, to increase the performances of the procedures (for example, to reduce the number of steps to arrive to a stationary design), a new approach to build un-expensive second approximation schemes, especially relevant for large scale problems, have been developed and validated. To illustrate the efficiency of the mathematical programming approach, the final part of the paper deals with an efficient treatment of perimeter constraints. Such constraints are essential to regularize material distribution with non optimal microstructures, but perimeter constraints are very difficult to handle in a numerical procedure for practical designs. The paper presents a solution to this problem that has been implemented and validated on a wide range of applications.
Disciplines :
Mechanical engineering
Aerospace & aeronautics engineering
Author, co-author :
Duysinx, Pierre  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres
Language :
English
Title :
Layout Optimization : A Mathematical Programming Approach
Publication date :
March 1997
Report number :
540
Number of pages :
31
Collection name :
Danish Centre for Applied Mathematics and Mechanics
Funders :
Danish Research Council
Available on ORBi :
since 10 September 2009

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