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

Abstract

A few level-set topology optimization (LSTO) methods have been proposed to address complex fluid-structure interaction. Most of them did not explore benchmark fluid pressure loading problems and some of their solutions are inconsistent with those obtained via density-based and binary topology optimization methods. This paper presents a LSTO strategy for designdependent pressure. It employs a fluid field governed by Laplace's equation to compute hydrostatic fluid pressure fields that are loading linear elastic structures. Compliance minimization of these structures is carried out considering the designdependency of the pressure load with moving boundaries. The Ersatz material approach with fixed grid is applied together with work equivalent load integration. Shape sensitivities are used. Numerical results show smooth convergence and good agreement with the solutions obtained by other topology optimization methods.

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.…”

“…The solution obtained by RKPM in Fig. 10b is much similar with the ones obtained by Picelli et al (2019) in which the level set method with equivalent nodal loads is used, and Picelli et al (2015) using the BESO method. The main difference between the different approaches is in the number of internal structural members appearing.…”

“…10a. The authors have considered this example using SIMP by Sigmund and Clausen (2007) and Lee and Martins (2012), BESO by Picelli et al (2015), and the level set method by Xia et al (2015), Emmendoerfer et al (2018), and Picelli et al (2019). Roller boundary condition is applied on the sides and the center point is fixed (Fig.…”

“…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. A similar approach has recently been employed by Picelli et al (2019) where a discretized fluid domain was used to explore benchmarking examples with purely hydrostatic pressure loading.…”

Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method

“…They used the zero level contour of an LSF to represent the loading boundary but did not regard load sensitivities. Recently, Picelli et al [27] proposed a method wherein Laplace's equation is employed to compute hydrostatic fluid pressure fields, in combination with interface tracking based on a flood fill procedure. Shape sensitivities in conjunction with Ersatz material interpolation approach are used within their approach.…”