A Quadratic Boundary Implementation for Solving 2D Problems of Elasticity by Topology Optimization

Abstract:

The main goal of this work relies on implementing discontinuous quadratic elements on a previous existent optimization code. The existent code refers to problems of topology optimization using a standard Boundary Element Method (BEM) formulation. A Topological Derivative (D_T) is used for determining the domains sensitivity. The implicit cost function used for D_T derivation is based on the total potential energy. A fixed amount of material with less efficiency is progressively removed during the optimization process. It is expected that the quadratic elements implementation increases the accuracy of the final solution, since the previous code were implemented by using linear elements. Despite of this code is still under development the final topology presents a good agreement when compared with those presented in the literature.

• Periodical: Applied Mechanics and Materials (Volume 394)
• Pages: 554-559
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.394.554
• Online since: September 2013
• Authors: Kaio L. Teotônio, Carla T.M. Anflor, Éder Lima de Albuquerque
• Keywords: 2D, Boundary Element Method (BEM), Elasticity, Optimization, Topological Derivative

References

[1] A. H. D., Cheng and Cheng, D T. Heritage and early history of the boundary element method, Engineering Analysis with Boundary Elements, Elsevier (2005).

DOI: 10.1016/j.enganabound.2004.12.001

[2] T. W. Ulrich, F. A. Moslehy, A boundary element method for stress reduction by optimal auxiliary holes, Engineering Analysis with Boundary Elements, 15, 219-223 (1995).

DOI: 10.1016/0955-7997(95)00025-j

[3] A R Meric, Differential and integral sensitivity formulations and shape optimization by BEM, Engineering Analysis with Boundary Elements, 15, 181-188 (1995).

DOI: 10.1016/0955-7997(95)00016-h

[4] E. Kita, H. Tanie, Shape optimization of continuum structures by genetic algorithm and boundary element method, Engineering Analysis with Boundary Elements, 19, 129-136 (1997).

DOI: 10.1016/s0955-7997(97)00014-3

[5] Cerrolaza, M, Annicchiarico, W, Martinez, M, Optimization of 2D boundary element models using β-splines and genetic algorithms, Engineering Analysis with Boundary Elements, 24, 427-440 (2000).

DOI: 10.1016/s0955-7997(00)00006-0

[6] Marczak, R. Topology optimization and boundary elements - a preliminary implementation for linear heat transfer. Engineering Analysis with Boundary Elements, 31, 793-802, (2007).

DOI: 10.1016/j.enganabound.2007.01.005

[7] Anflor C T M, R. Marczak, A boundary element approach for topology design in diffusive problems containing heat sources, International Journal of Heat and Mass Transfer, 52, 4604–4611, (2009).

DOI: 10.1016/j.ijheatmasstransfer.2009.02.048

[8] Neches, L C, A P Cisilino, Topology optimization of 2D elastic structures using boundary elements, Engineering Analysis with Boundary Elements32, 533–544, (2008).

DOI: 10.1016/j.enganabound.2007.10.003

[9] Marczak, R J, Optimization of elastic structures using boundary elements and a topological-shape sensitivity formulation, Latin American Journal of Solids and Structures 5 99-117 (2008).

[10] Katsikadelis, J, Boundary Elements Theory and Applications, Elsevier(2002).

[11] Kane, J.H. Boundary Element Analysis in Engineering Continuum Mechanics, Prentice Hall, EnglewoodClis (1994).

[12] Novotny, A. A. Análise de Sensibilidade Topológica, LNCC/MCT, D. Sc., Modelagem Computacional, (2003).

[13] Anflor C T M, R. Marczak, Topological Optimization of Anisotropic Heat Conducting Devices using Bezier-Smoothed Boundary Representation, Computer Modeling in Engineering & Sciences, 78, 151-168 (2011).