h-adaptive topology optimization considering variations of material properties and energy error density recovery
ISSN: 0264-4401
Article publication date: 7 May 2020
Issue publication date: 28 October 2020
Abstract
Purpose
The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.
Design/methodology/approach
The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.
Findings
Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.
Originality/value
This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.
Keywords
Acknowledgements
The authors thank the Post-Graduate Program in Mechanical Engineering (PGMec) of the Federal University of Paraná (UFPR) for providing the necessary infrastructure and environment for research, the Federal University of Technology of Paraná (UTFPR) and the Coordination for the Improvement of Higher Level Personnel (CAPES) for the financial support.
Citation
da Silva, J., Pereira, J.T. and Torres, D.A.F. (2020), "h-adaptive topology optimization considering variations of material properties and energy error density recovery", Engineering Computations, Vol. 37 No. 9, pp. 3209-3241. https://doi.org/10.1108/EC-10-2019-0464
Publisher
:Emerald Publishing Limited
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