Level set-fitted polytopal meshes with application to structural topology optimization

TL;DR

This paper introduces a novel level set-fitted polygonal mesh method combined with Discontinuous Galerkin approximation, enabling accurate modeling of complex geometries and optimized structural layouts without mesh post-processing.

Contribution

It extends standard body-fitted strategies to arbitrary polygonal tessellations and integrates with topology optimization for improved structural design.

Findings

Effective in modeling complex geometries with heterogeneous materials

Produces optimized layouts with clear boundaries and strong mechanical performance

Validated through extensive numerical experiments

Abstract

We propose a method to modify a polygonal mesh in order to fit the zero-isoline of a level set function by extending a standard body-fitted strategy to a tessellation with arbitrarily-shaped elements. The novel level set-fitted approach, in combination with a Discontinuous Galerkin finite element approximation, provides an ideal setting to model physical problems characterized by embedded or evolving complex geometries, since it allows skipping any mesh post-processing in terms of grid quality. The proposed methodology is firstly assessed on the linear elasticity equation, by verifying the approximation capability of the level set-fitted approach when dealing with configurations with heterogeneous material properties. Successively, we combine the level set-fitted methodology with a minimum compliance topology optimization technique, in order to deliver optimized layouts exhibiting crisp boundaries and reliable mechanical performances. An extensive numerical test campaign confirms the effectiveness of the proposed method.