A new boundary search scheme for topology optimization of continuum structures with design-dependent loads

Zhang, Hui; Zhang, Xiong; Liu, Shutian

doi:10.1007/s00158-007-0221-4

Cited by 41 publications

(24 citation statements)

References 19 publications

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“…Fuchs and Shemesh [14] proposed a method wherein the evolving pressure loading boundary Γ p b is predefined using an additional set of variables, which are also optimized along with the design variables. Zhang et al [22] proposed an element-based search method to locate the load surface. They used the actual boundary of the finite elements (FEs) to construct the load surface and thereafter, transferred pressure to corresponding element nodes directly.…”

Section: Introductionmentioning

confidence: 99%

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

Kumar

Frouws

Langelaar

2020

Struct Multidisc Optim

101

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In various applications, design problems involving structures and compliant mechanisms experience fluidic pressure loads. During topology optimization of such design problems, these loads adapt their direction and location with the evolution of the design, which poses various challenges. A new density-based topology optimization approach using Darcy's law in conjunction with a drainage term is presented to provide a continuous and consistent treatment of design-dependent fluidic pressure loads. The porosity of each finite element and its drainage term are related to its density variable using a Heaviside function, yielding a smooth transition between the solid and void phases. A design-dependent pressure field is established using Darcy's law and the associated PDE is solved using the finite element method. Further, the obtained pressure field is used to determine the consistent nodal loads. The approach provides a computationally inexpensive evaluation of load sensitivities using the adjoint-variable method. To show the efficacy and robustness of the proposed method, numerical examples related to fluidic pressure loaded stiff structures and small-deformation compliant mechanisms are solved. For the structures, compliance is minimized, whereas for the mechanisms a multi-criteria objective is minimized with given resource constraints.

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Section: Introductionmentioning

confidence: 99%

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

Kumar

Frouws

Langelaar

2020

Struct Multidisc Optim

101

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“…For example, Bézier curves are adopted in the works of Hammer and Olhoff and Fuchs and Shemesh, a fictitious thermal loading is applied in the work of Chen and Kikuchi, isolines (iso‐density line to define the boundary) are used by Du and Olhoff and Lee and Martins a pseudo potential function is introduced in the work of Zheng et al, and strategies of considering the void phase as an incompressible hydrostatic fluid transferring thus pressure loads are employed by Sigmund and Clausen and Bruggi and Cinquini . Some works use algorithm searching schemes (based on decision criterion) in the background grid to identify the load surfaces (see, for instance, the work of Zhang et al). There are also papers mixing methods to recover the loading surface at each step of the minimization process.…”

Section: Introductionmentioning

confidence: 99%

Level set topology optimization for design‐dependent pressure load problems

Emmendoerfer

Fancello

Silva

2018

Numerical Meth Engineering

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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.

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“…In [11], the aeroelastic optimization of a membrane micro air vehicle wing was designed through TO. For pressure-loaded problems, many studies have been conducted with using an explicit boundary between the fluid and structure [12][13][14][15][16]. In [17,18], mixed formulation was employed for pressure-loaded problems.…”

Section: Introductionmentioning

confidence: 99%

Stress-based topology optimization method for steady-state fluid–structure interaction problems

Yoon

2014

Computer Methods in Applied Mechanics and Engineering

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A new boundary search scheme for topology optimization of continuum structures with design-dependent loads

Cited by 41 publications

References 19 publications

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

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

Level set topology optimization for design‐dependent pressure load problems

Stress-based topology optimization method for steady-state fluid–structure interaction problems

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