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An accurate and fast regularization approach to thermodynamic topology optimization

D. R. Jantos, K. Hackl, P. Junker

International Journal for Numerical Methods in Engineering, 117, 991-1017, (2019)

DOI: 10.1002/nme.5988

Download: BibTEX

In a series of previous works, we established a novel approach to topology optimization for compliance minimization based on thermodynamic principles known from the field of material modeling. Hamilton's principle for dissipative processes directly yields a partial differential equation (referred to as the evolution equation) as an update scheme for the spatial distribution of density mass describing the topology. Consequently, no additional mathematical minimization algorithms are needed. In this article, we introduce a regularization scheme by penalization of the gradient of the spatial distribution of mass density. The parabolic evolution equation (owing to a similar structure to the transient heat-conduction equation) is solved most efficiently by an explicit time discretization. The Laplace operator is discretized via a Taylor series expansion yielding an operator matrix that is constant for the entire optimization process. This method shares some similarities to meshless methods and allows for an accurate application also on unstructured finite element meshes. The minimal size of the structure member can directly be controlled, a priori, by a numerical parameter introduced along with the regularization, similar to classical filter radii. © 2018 John Wiley & Sons, Ltd.

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{"type":"article", "name":"d.r.jantos20193", "author":"D. R. Jantos and K. Hackl and P. Junker", "title":"An accurate and fast regularization approach to thermodynamic topology optimization", "journal":"International Journal for Numerical Methods in Engineering", "volume":"117", "OPTnumber":"9", "OPTmonth":"3", "year":"2019", "OPTpages":"991-1017", "OPTnote":"", "OPTkey":"meshless Laplacian; parabolic PDE; regularization; thermodynamic topology optimization; unstructured meshes; variational material modeling", "DOI":"10.1002/nme.5988"}
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