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Application of topology optimization to thighbone and thighbone/implant structure modelling

Kutylowski Ryszard, Szwechlowicz Marek

Archives of Civil and Mechanical Engineering

2019

Vol. 19, no. 4

1006--1019

This paper presents an application of topology optimization in bioengineering. The varia- tional approach to the topology optimization is applied. Using an original numerical algorithm and a programme developed in Matlab, the structure of the thighbone was modelled by FEM. The numerical results of the mass distribution in modelled bone are provided. Obtained topologies are similar to the density distribution in real bone tissue including the case when the implant is imposed into the human body.

Special kind of multimaterial topology optimization

Kutyłowski R., Szwechłowicz M.

Archives of Civil and Mechanical Engineering

2013

Vol. 13, no. 3

334--344

Topology optimization provides an answer to the question how to distribute the available material in a design domain. The optimization process (usually aided by postprocessing) results in a material-void distribution, also called (in terms of relative density) a 0/1 distribution, which is graphically represented as a black-and-white distribution. Assuming that the optimum solution is such for which the energy accumulated in the construction is minimum, an optimum construction topology was arrived at. In this solution the material is in the same areas in which it would be for a 0/1 solution, however the relative density in the design domain is not only equal to zero or one, but also assumes values between zero and one (the values are closer to one than to zero). In this way a construction whose material properties vary from point to point in a way directly dependent on the effort of the material, i.e. adequately to the needs arising from the necessity of carrying the load by the construction, was obtained. Thus through the use of a proper optimization approach and the proposed algorithm a construction built from a material with graded mechanical properties was obtained.

Incremental method of Young modulus updating procedure in topology optimization

Kutylowski R., Rasiak B.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2012

Vol. 60, nr 2

159-164

This paper presents a new Young modulus updating procedure as an extension to the SIMP method used for topology optimization. In essence, the modified Young modulus updating procedure consists in taking into account in a given optimization step not only the material density from the preceding step, but also the increment in density in the two preceding steps. Thanks to this, it is possible to obtain a solution in cases in which the classic SIMP method failed. The variational approach was adopted and the structure’s strain energy was minimized under constraints imposed on body mass. FEM was used to solve numerical examples. The numerical analysis confirmed the effectiveness of the proposed method, particularly for structures with relatively long spans.