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

Abstract

This paper presents a level set topology optimization method in combination with the reproducing kernel particle method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM allows for arbitrary particle placement in discretization and approximation of unknowns. This attractive property in combination with the implicit boundary representation given by the level set method provides an effective framework to handle the design-dependent loads by moving the particles on the pressure boundary without the need of remeshing or special numerical treatments. Moreover, the reproducing kernel (RK) smooth approximation allows for the Young's modulus to be interpolated using the RK shape functions. This is another advantage of the proposed method as it leads to a smooth Young's modulus distribution for smooth boundary sensitivity calculation which yields a better convergence. Numerical results show good agreement with those in the literature.

TOPress: a MATLAB implementation for topology optimization of structures subjected to design-dependent pressure loads

“…Including load sensitivities within the formulation may certainly affect the optimized shape and topology and thus, the final objective value. The shape of the former resembles one presented in Sigmund and Clausen (2007), whereas the shape of the latter resembles that reported in Picelli et al (2019); Neofytou et al (2020).…”

“…Herein TOPress is modified to solve the pressurized chamber design that was first presented by Hammer and Olhoff (2000). The problem is subsequently solved in Chen and Kikuchi (2001); Zhang et al (2008); Picelli et al (2015Picelli et al ( , 2019; Neofytou et al (2020); Huang et al (2022). The design domain with pressure and displacement boundary conditions is shown in Fig.…”

A Gradient-Free Topology Optimization Strategy for Continuum Structures with Design-Dependent Boundary Loads

“…The elemental relative density of the triangle element in the design domain is shown in Figure 13. As seen in Figure 12, the optimized topology for the cover-like structure is an arched structure, which is similar to the optimized solution obtained by Zhang [12] and Neofytou [23]. Therefore, it can be seen that the proposed method is effective in solving the topology optimization problem with design-dependent loads.…”

“…Besides, many researchers have made a lot of efforts to determine the loading surface using specific fluids or multi-physics models within density-based frameworks [13][14][15][16][17]. In addition, the evolutionary method [18] and the level-set method [19][20][21][22][23] have also been developed to deal with the topology optimization problems with design-dependent loads.…”

A Thermal-Solid–Fluid Method for Topology Optimization of Structures with Design-Dependent Pressure Load

“…The main challenge of such problems is how to accurately track pressure boundary during the design process. To solve this challenge, a direct idea is to use the boundarybased topology optimization methods, such as the level set method [4][5][6][7][8][9][10]. These kinds of methods provide an implicit description of material boundaries and also enable easier extraction of their geometric information (normal direction and curvature), and thus, are particularly suitable for structural boundary/interface-related design problems.…”