A NON-GRADIENT APPROACH FOR THREE DIMENSIONAL TOPOLOGY OPTIMIZATION

Authors

  • Minh Ngoc Nguyen Ho Chi Minh city University of Technology - VNU-HCM
  • Nha Thanh Nguyen
  • Minh Tuan Tran

DOI:

https://doi.org/10.15625/2525-2518/59/3/14996

Abstract

The present work is devoted to the extension of the non-gradient approach, namely Proportional Topology Optimization (PTO), for compliance minimization of three-dimensional (3D) structures. Two schemes of material interpolation within the framework of the solid isotropic material with penalization (SIMP), i.e. the power function and the logistic function are analyzed. Through a comparative study, the efficiency of the logistic-type interpolation scheme is highlighted.  Since no sensitivity is involved in the approach, a density filter is applied instead of sensitivity filter to avoid checkerboard issue

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References

Sigmund O., A 99 line topology optimization code written in Matlab, Structural and Multidisciplinary Optimization, 21 (2001) 120-127.

Andreassen E., Clausen A., Schevenels M., Lazarov B. S. and Sigmund O., Efficient topology optimization in MATLAB using 88 lines of code, Structural and Multidisciplinary Optimization 43 (2011) 1-16.

Talischi C., Paulino G. H., Pereira A. and Menezes I. F. M., "PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes, Structural and Multidisciplinary Optimization 45 (2012) 329-357.

Wang M. Y., Wang X. and Guo D., A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering 192 (1-2) (2003) 227-246.

Challis V. J., A discrete level-set topology optimization code written in Matlab, Structural and Multidisciplinary Optimization 41 (3) (2009) 453-464.

Otomori M., Yamada T., Izui K. and Nishiwaki S., Matlab code for a level set-based topology optimization method using a reaction diffusion equation, Structural and Multidisciplinary Optimization 51 (5) (2015) 1159-1172.

A. Takezawa, Nishiwaki S. and Kitamura M., Shape and topology optimization based on the phase field method and sensitivity analysis, Journal of Computational Physics 229 (2010) 2697-2718.

Dede L., Borden M. J. and Hughes T. J. R., Isogeometric analysis for topology optimization with a phase field model, Archives of Computational Methods in Engineering 19 (3) (2012) 427-465.

Carraturo M., Rocca E., Bonetti E., Hömberg D., Reali A. and Auricchio F., Graded-material design based on phase-field and topology optimization, Computational Mechanics 64 (6) (2019) 1589-1600.

Chen Q., Zhang X. and Zhu B., A 213-line topology optimization code for geometrically nonlinear structures, Structural and Multidisciplinary Optimization 59 (5) (2019) 1863-1879.

Luo Y., Li M. and Kang Z., Topology optimization of hyperelastic structures with frictionless contact supports, International Journal of Solids and Structures 81 (2016) 373-382.

Chen F., Wang Y., Wang M. Y. and Zhang Y. F., Topology optimization of hyperelastic structures using a level set method, Journal of Computational Physics 351 (2017) 437-454.

Wallin M., Jönsson V. and Wingren E., Topology optimization based on finite strain plasticity, Structural and Multidisciplinary Optimization 54 (4) (2016) 783-793.

Amir O., Stress-constrained continuum topology optimization: a new approach based on elasto-plasticity, Structural and Multidisciplinary Optimization, 55 (5) (2017) 1797-1818.

Zhao T., Ramos A. S. Jr. and Paulino G. H., Material nonlinear topology optimization considering the von Mises criterion through an asymptotic approach: Max strain energy and max load factor formulations, International Journal for Numerical Methods in Engineering, 118 (13) (2019) 804-828.

Patel N. M., Tillotson D. and Renaud J. E., Comparative study of topology optimization techniques, AIAA Journal 46 (8) (2008) 1963-1975.

Yang R. and Du J., Microstructural topology optimization with respect to sound power radiation, Structural and Multidisciplinary Optimization 47 (2) (2013) 191-206.

Wu C.-Y. and Tseng K.-Y., Topology optimization of structures using modified binary differential evolution, Structural and Multidisciplinary Optimization 42 (6) (2010) 939-953.

Luh G.-C., Lin C.-Y. and Lin Y.-S., A binary particle swarm optimization for continuum structural topology optimization, Applied Soft Computing 11 (2011) 2833-2844.

Guirguis D. and Aly M. F., A derivative-free level-set method for topology optimization, Finite Elements in Analysis and Design 120 (2016) 41-56.

Sigmund O., On the usefulness of non-gradient approaches in topology optimization," Structural and Multidisciplinary Optimization 43 (2011) 589-596.

Biyikli E. and To A. C., Proportional topology optimization: a new non-sensitivity method for solving stress constrained and minimum compliance problems and its implementation in MATLAB, PLoS One 10 (12) (2015) e0145041.

Cui M., Zhang Y., Yang X. and Luo C. - Multi-material proportional topology optimization based on the modified interpolation scheme, Engineering with Computers 34 (2) (2018) 287-305.

Liu K. and Tovar A., An efficient 3D topology optimization code written in Matlab," Structural and Multidisciplinary Optimization 50 (6) (2014) 1175-1196.

Du Y., Yan S., Zhang Y., Xie H. and Tian Q., A modified interpolation approach for topology optimization, Acta Mechanica Solida Sinica 28 (4) (2015) 420-439.

Diaz A. and Sigmund O., Checkerboard patterns in layout optimization, Structural Optimization 10 (1995) 40-45.

Sigmund O. and Petersson J., Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Structural Optimization 16 (1998) 68-75.

Guest J. K., Asadpoure A. and Ha S.-H., Eliminating beta-continuation from Heaviside projection and density filter algorithms, Structural and Multidisciplinary Optimization 44 (2011) 443-453.

Sigmund O., Morphology-based black and white filters for topology optimization, Structural and Multidisciplinary Optimization 33 (2007) 401-425.

Xia L. and Breitkopf P., Design of materials using topology optimization and energy-based homogenization approach in Matlab, Structural and Multidisciplinary Optimization 52 (2015) 1229-1241.

Paris J., Navarrina F., Colominas I. and Casteleiro M., Stress constraints sensitivity analysis in structural topology optimization, Computer Methods in Applied Mechanics and Engineering 199 (33-36) (2010) 2110-2122.

Holmberg E., Torstenfelt B. and Klarbring A., Stress constrained topology optimization, Structural and Multidisciplinary Optimization 48 (2013) 33-47.

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Published

17-05-2021

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Section

Mechanical Engineering - Mechatronics