Topology Optimization of 2D and 3D Elastic Structures Using Boundary Elements

ADRIÁN P. CISILINO; CHRISTINE BERTSCH; LUIS CARRETERO NECHES; NÉSTOR CALVO

Rio de Janeiro, Brazil

Congreso; EngOpt 2008 - International Conference on Engineering Optimization; 2008

Brazilian Society of Mechanical Sciences and Engineering - EURO Working Group on Continuous Optimization - International Society for Structural and Multidisciplinary Optimization - Mathematical Programming Society

Topology Optimization of 2D and 3D Elastic Structures Using Boundary Elements Adrián P. Cisilino División Soldadura y Fractomecánica INTEMA, Facultad de Ingeniería – CONICET. Universidad Nacional de Mar del Plata, Av. Juan B. Justo 4302, (7600) Mar del Plata, Argentina. Email: cisilino@fi.mdp.edu.ar Christine Bertsch Institut für Festkörpermechanik, Technische Universität Braunschweig, Schleinitzstr. 20, D-38106 Braunschweig, Germany. Email: c.bertsch@tu-braunschweig.de Luis Carretero Neches Grupo de Elasticidad y Resistencia de Materiales, Departamento de Mecánica del Continuo, Escuela de Ingenieros Industriales, Universidad de Sevilla. Avda. de los Descubrimientos s/n, E-41092, Sevilla, Spain Néstor Calvo Centro Internacional de Métodos Computacionales en Ingeniería - CONICET Güemes 3450, 3000 Santa Fe, Argentina. Email: nestor.calvo@yahoo.com.ar 1. Abstract Topological Optimization provides a powerful framework to obtain the optimal domain topology for several engineering problems. The topological derivative is a function which characterizes the sensitivity of a given problem to the change of its topology, like opening a small hole in a continuum or changing the connectivity of rods in a truss. A numerical approach for the topological optimization of 2D and 3D linear elastic problems using Boundary Elements is presented in this work. The topological derivative is computed from strain and stress results which are solved by means of a standard Boundary Element analysis. Models are discretized using linear or constant elements and a periodic distribution of internal points over the domain. The total potential energy is selected as cost function. The evaluation of the topological derivative is performed as a post-processing procedure. Afterwards, material is removed from the model by deleting the internal points and boundary nodes with the lowest values of the topological derivate. The new geometry is then remeshed using algorithms capable of detecting “holes” at those positions where internal points and boundary points have been removed. The procedure is repeated until a given stopping criterion is satisfied. The proposed strategy proved to be flexible and robust. A number of examples are solved and results are compared to those available in the literature. 2. Keywords: topology optimization, topological derivative, boundary elements.topology optimization, topological derivative, boundary elements.