Dyfyniad

Andreas Neofytou A, Renato Picelli R, Tsung-Hui Huang T-H, et al. (2020). Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method. Cardiff University. http://doi.org/10.17035/d.2020.0102035847

Manylion y Set Ddata

Disgrifiad

**All relevant data are available via the links in the description below.**

Design-dependent surface or boundary loads can be found in many engineering structures. Pressure vessels, civil structures subjected to wind and snow loading and underwater structures subjected to external fluid pressure are typical examples. The main challenge in topology optimization with design dependent loads lies in determining the surface on which the load will act.

To address this challenge, the level set topology optimization method is used in combination with the meshfree reproducing kernel particle method (RKPM). 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 topology optimization method (LSTO), 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.

The c++ level set code which is exactly the one used in the paper for the level set optimization part is available on github: https://github.com/M2DOLab/OpenLSTO.

User manuals for this OpenLSTO (v0.1) version can be found in http://m2do.ucsd.edu/software/.

The detailed methodology for the RKPM is available at https://link.springer.com/article/10.1007/s40571-019-00272-x along with an open-source matlab implementation: http://jschen.eng.ucsd.edu/open-source-rkpm-code.

__Implementation Details__

* Convergence of the objective is checked during 5 consecutive iterations and the tolerance is 0.001.

The reproducing kernel particle method was implemented using the following specifications:

*Cubic splines kernel function and linear basis were used for the construction of the shape function.

*Gauss integration as the domain integration method. 4x4 Quadrature points within each integration cell.

*The Lagrange multiplier technique is selected for the imposition of the essential boundary conditions.

*Support domain for all particles is set to 1.5 times the size of a background cell. (unit size)

*At each iteration particles are placed at the nodal positions of the background mesh and on the boundary points, i.e at the intersections of the zero level set with the element edges of the level set mesh.

*Young's modulus is set to 1 for the solid region and 0.0001 for the void region. Poisson's ratio is 0.5.

The approach was applied for 3 benchmarking examples in topology optimization with design dependent pressure loads. The results obtained by RKPM are in good agreement with the literature. The main benefit of our approach compared to previous methods, is the ability to add particles at the boundary which allows for direct imposition of the loads at the interface. This eliminates the need of load transformations and numerical treatments required by other methods. Furthermore, a direct comparison between RKPM and the most commonly used method in the literature, i.e transforming the surface loads into equivalent nodal loads, is included in the paper. It is observed that RKPM converges much faster due to its higher accuracy reducing significantly the number of optimization iterations.

Related research results are published at https://doi.org/10.1007/s00158-020-02549-9

Allweddeiriau

Level set topology optimization, Reproducing kernel particle method

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