Level set topology optimization for design‐dependent pressure load problems

Abstract

Summary This work presents a level set framework to solve the compliance topology optimization problem considering design‐dependent pressure loads. One of the major technical difficulties related to this class of problem is the adequate association between the moving boundary and the pressure acting on it. This difficulty is easily overcome by the level set method that allows for a clear tracking of the boundary along the optimization process. In the present approach, a reaction‐diffusion equation substitutes the classical Hamilton‐Jacobi equation to control the level set evolution. This choice has the advantages of allowing the nucleation of holes inside the domain and the elimination of the undesirable reinitialization steps. Moreover, the proposed algorithm allows merging pressurized (wet) boundaries with traction‐free boundaries during level set movements. This last property, allied to the simplicity of the level set representation and successful combination with the reaction‐diffusion based evolution applied to a design‐dependent pressure load problem, represents the main contribution of this paper. Numerical examples provide successful results, many of which comparable with others found in the literature and solved with different techniques.

Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method

“…The arch-like optimum solution in Fig. 7 b agrees well with those obtained by previous works that considered this example (Sigmund and Clausen 2007; Picelli et al 2015;Picelli et al 2019;Xia et al 2015;Emmendoerfer et al 2018). These solutions are shown in Fig.…”

“…Shu et al (2014) also used a Dirac delta function to minimize sound pressure in an acoustic-structural system. More recently, Emmendoerfer et al (2018) proposed a level set topology optimization in which the surface loads acting on the moving boundary are transformed into work-equivalent nodal forces to solve pressure loading problems with level set topology optimization and a fixed grid. In this work, the ersatz material was also used for the elements cut by the boundary and a virtual fluid flooding process was used to track the pressure surface.…”

Topology optimization for design-dependent hydrostatic pressure loading via the level-set method

“…5 is considered for optimization. To the best of the authors' knowledge, this problem was first explored by Bourdin and Chambolle (2003) and later used by several other works for a range of different methods (Sigmund and Clausen 2007;Lee and Martins 2012;Picelli et al 2015b;Emmendoerfer et al 2018). This schematic problem is explored here to verify the topology solution offered by our proposed method.…”

“…Pressure loads are applied on the structure with work equivalent integrals. The work equivalent loads were first used in a level-set method with the Ersatz material interpolation by Emmendoerfer et al (2018) and they are employed here due to its simplicity. Emmendoerfer et al (2018) also used fluid flooding, but no actual fluid pressure is solved in their work.…”

“…The work equivalent loads were first used in a level-set method with the Ersatz material interpolation by Emmendoerfer et al (2018) and they are employed here due to its simplicity. Emmendoerfer et al (2018) also used fluid flooding, but no actual fluid pressure is solved in their work. The addition of a fluid pressure field governed by Poisson's equation and the use of shape sensitivities are explored in this paper, as well as the application of the LSTO method previously used to address stress-based problems Picelli et al (2018a, b).…”