Details
| Original language | English |
|---|---|
| Article number | 114698 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 393 |
| Early online date | 23 Feb 2022 |
| Publication status | Published - 1 Apr 2022 |
Abstract
In our previous works, we established the method of thermodynamic topology optimization based on Hamilton's principle. With the use of a gradient-enhanced regularization and the formulation of the resulting differential equation in the strong form, it is necessary to calculate the Laplacian of the design function. Also, a Neumann boundary condition needs to be accounted for. As the values of the design function are only known in discrete points, both of these problems require a numerical approximation. Previous approaches fail depending on the type of the used finite element mesh. In this contribution, we show how the Taylor series can be combined with the weighted least square method to obtain approximations for these problems when the values of the design function are given in arbitrary point clouds. We show simulation results for common benchmark problems for various types of meshes proving the mesh independence, versatility and reliability of the novel method.
Keywords
- Finite element method, Meshless Laplacian, Taylor series, Thermodynamic topology optimization, Unstructured meshes
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 393, 114698, 01.04.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Application of Taylor series combined with the weighted least square method to thermodynamic topology optimization
AU - Blaszczyk, Mischa
AU - Jantos, Dustin Roman
AU - Junker, Philipp
PY - 2022/4/1
Y1 - 2022/4/1
N2 - In our previous works, we established the method of thermodynamic topology optimization based on Hamilton's principle. With the use of a gradient-enhanced regularization and the formulation of the resulting differential equation in the strong form, it is necessary to calculate the Laplacian of the design function. Also, a Neumann boundary condition needs to be accounted for. As the values of the design function are only known in discrete points, both of these problems require a numerical approximation. Previous approaches fail depending on the type of the used finite element mesh. In this contribution, we show how the Taylor series can be combined with the weighted least square method to obtain approximations for these problems when the values of the design function are given in arbitrary point clouds. We show simulation results for common benchmark problems for various types of meshes proving the mesh independence, versatility and reliability of the novel method.
AB - In our previous works, we established the method of thermodynamic topology optimization based on Hamilton's principle. With the use of a gradient-enhanced regularization and the formulation of the resulting differential equation in the strong form, it is necessary to calculate the Laplacian of the design function. Also, a Neumann boundary condition needs to be accounted for. As the values of the design function are only known in discrete points, both of these problems require a numerical approximation. Previous approaches fail depending on the type of the used finite element mesh. In this contribution, we show how the Taylor series can be combined with the weighted least square method to obtain approximations for these problems when the values of the design function are given in arbitrary point clouds. We show simulation results for common benchmark problems for various types of meshes proving the mesh independence, versatility and reliability of the novel method.
KW - Finite element method
KW - Meshless Laplacian
KW - Taylor series
KW - Thermodynamic topology optimization
KW - Unstructured meshes
UR - http://www.scopus.com/inward/record.url?scp=85125116682&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2022.114698
DO - 10.1016/j.cma.2022.114698
M3 - Article
AN - SCOPUS:85125116682
VL - 393
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 114698
ER -