Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification

Ou Disheng; Zheng Xuefen; Zhou Xiongxin

doi:doi:10.11648/j.ijmea.20221001.11

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Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification

Ou Disheng, Zheng Xuefen, Zhou Xiongxin

Published in International Journal of Mechanical Engineering and Applications (Volume 10, Issue 1)

Received: 16 January 2022 Accepted: 29 January 2022 Published: 16 February 2022

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Abstract

To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, taking pseudo density as design variables, mathematical model of the minimization mass with constraints of nodal displacements and element stresses is constructed. Secondly, according to essential extremum conditions of Dual objective function, iterative optimization direction and analytical step-size of constraint multipliers are derived. And, according to essential extremum conditions of Generalized Lagrange function, iterative optimization direction and analytical step-size of pseudo densities are derived. Analytical step-sizes are used to avoid one-dimensional optimization and then the calculation quantity of iterative optimization can be decreased. Thirdly, first-order partial derivatives of nodal displacement and element equivalent stress constraints with respect to pseudo densities are given. After that, by using self-compiled MATLAB program for continuum structure analysis, partial derivative calculation and optimization iteration, 4 optimization examples of different beam structures are used to show the changes of active nodal displacement and element equivalent stress constraints, and structural mass in the optimization iteration process, and to show the effectiveness of Ratio-Extremum algorithm in topology optimization of continuum structures.

Published in	International Journal of Mechanical Engineering and Applications (Volume 10, Issue 1)
DOI	10.11648/j.ijmea.20221001.11
Page(s)	1-6
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Continuum Structure, Topology Optimization, Ratio-Extremum Algorithm, Optimization Direction, Step-size, Active Constraint Identification

References

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APA Style

Ou Disheng, Zheng Xuefen, Zhou Xiongxin. (2022). Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification. International Journal of Mechanical Engineering and Applications, 10(1), 1-6. https://doi.org/10.11648/j.ijmea.20221001.11

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ACS Style

Ou Disheng; Zheng Xuefen; Zhou Xiongxin. Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification. Int. J. Mech. Eng. Appl. 2022, 10(1), 1-6. doi: 10.11648/j.ijmea.20221001.11

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AMA Style

Ou Disheng, Zheng Xuefen, Zhou Xiongxin. Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification. Int J Mech Eng Appl. 2022;10(1):1-6. doi: 10.11648/j.ijmea.20221001.11

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@article{10.11648/j.ijmea.20221001.11,
  author = {Ou Disheng and Zheng Xuefen and Zhou Xiongxin},
  title = {Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {10},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.ijmea.20221001.11},
  url = {https://doi.org/10.11648/j.ijmea.20221001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20221001.11},
  abstract = {To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, taking pseudo density as design variables, mathematical model of the minimization mass with constraints of nodal displacements and element stresses is constructed. Secondly, according to essential extremum conditions of Dual objective function, iterative optimization direction and analytical step-size of constraint multipliers are derived. And, according to essential extremum conditions of Generalized Lagrange function, iterative optimization direction and analytical step-size of pseudo densities are derived. Analytical step-sizes are used to avoid one-dimensional optimization and then the calculation quantity of iterative optimization can be decreased. Thirdly, first-order partial derivatives of nodal displacement and element equivalent stress constraints with respect to pseudo densities are given. After that, by using self-compiled MATLAB program for continuum structure analysis, partial derivative calculation and optimization iteration, 4 optimization examples of different beam structures are used to show the changes of active nodal displacement and element equivalent stress constraints, and structural mass in the optimization iteration process, and to show the effectiveness of Ratio-Extremum algorithm in topology optimization of continuum structures.},
 year = {2022}
}

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TY  - JOUR
T1  - Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification
AU  - Ou Disheng
AU  - Zheng Xuefen
AU  - Zhou Xiongxin
Y1  - 2022/02/16
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmea.20221001.11
DO  - 10.11648/j.ijmea.20221001.11
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20221001.11
AB  - To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, taking pseudo density as design variables, mathematical model of the minimization mass with constraints of nodal displacements and element stresses is constructed. Secondly, according to essential extremum conditions of Dual objective function, iterative optimization direction and analytical step-size of constraint multipliers are derived. And, according to essential extremum conditions of Generalized Lagrange function, iterative optimization direction and analytical step-size of pseudo densities are derived. Analytical step-sizes are used to avoid one-dimensional optimization and then the calculation quantity of iterative optimization can be decreased. Thirdly, first-order partial derivatives of nodal displacement and element equivalent stress constraints with respect to pseudo densities are given. After that, by using self-compiled MATLAB program for continuum structure analysis, partial derivative calculation and optimization iteration, 4 optimization examples of different beam structures are used to show the changes of active nodal displacement and element equivalent stress constraints, and structural mass in the optimization iteration process, and to show the effectiveness of Ratio-Extremum algorithm in topology optimization of continuum structures.
VL  - 10
IS  - 1
ER  -

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Author Information

Ou Disheng

School of Innovation and Entrepreneurship, Center of Engineering Practice and Innovation Education, Guangxi University of Science and Technology, Liuzhou, China
Zheng Xuefen

School of Mechanical and Automotive Engineering, Guangxi University of Science and Technology, Liuzhou, China
Zhou Xiongxin

School of Innovation and Entrepreneurship, Center of Engineering Practice and Innovation Education, Guangxi University of Science and Technology, Liuzhou, China

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Plain Text BibTeX RIS

APA Style

Ou Disheng, Zheng Xuefen, Zhou Xiongxin. (2022). Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification. International Journal of Mechanical Engineering and Applications, 10(1), 1-6. https://doi.org/10.11648/j.ijmea.20221001.11

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ACS Style

Ou Disheng; Zheng Xuefen; Zhou Xiongxin. Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification. Int. J. Mech. Eng. Appl. 2022, 10(1), 1-6. doi: 10.11648/j.ijmea.20221001.11

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AMA Style

Ou Disheng, Zheng Xuefen, Zhou Xiongxin. Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification. Int J Mech Eng Appl. 2022;10(1):1-6. doi: 10.11648/j.ijmea.20221001.11

Copy | Download

@article{10.11648/j.ijmea.20221001.11,
  author = {Ou Disheng and Zheng Xuefen and Zhou Xiongxin},
  title = {Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {10},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.ijmea.20221001.11},
  url = {https://doi.org/10.11648/j.ijmea.20221001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20221001.11},
  abstract = {To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, taking pseudo density as design variables, mathematical model of the minimization mass with constraints of nodal displacements and element stresses is constructed. Secondly, according to essential extremum conditions of Dual objective function, iterative optimization direction and analytical step-size of constraint multipliers are derived. And, according to essential extremum conditions of Generalized Lagrange function, iterative optimization direction and analytical step-size of pseudo densities are derived. Analytical step-sizes are used to avoid one-dimensional optimization and then the calculation quantity of iterative optimization can be decreased. Thirdly, first-order partial derivatives of nodal displacement and element equivalent stress constraints with respect to pseudo densities are given. After that, by using self-compiled MATLAB program for continuum structure analysis, partial derivative calculation and optimization iteration, 4 optimization examples of different beam structures are used to show the changes of active nodal displacement and element equivalent stress constraints, and structural mass in the optimization iteration process, and to show the effectiveness of Ratio-Extremum algorithm in topology optimization of continuum structures.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification
AU  - Ou Disheng
AU  - Zheng Xuefen
AU  - Zhou Xiongxin
Y1  - 2022/02/16
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmea.20221001.11
DO  - 10.11648/j.ijmea.20221001.11
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20221001.11
AB  - To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, taking pseudo density as design variables, mathematical model of the minimization mass with constraints of nodal displacements and element stresses is constructed. Secondly, according to essential extremum conditions of Dual objective function, iterative optimization direction and analytical step-size of constraint multipliers are derived. And, according to essential extremum conditions of Generalized Lagrange function, iterative optimization direction and analytical step-size of pseudo densities are derived. Analytical step-sizes are used to avoid one-dimensional optimization and then the calculation quantity of iterative optimization can be decreased. Thirdly, first-order partial derivatives of nodal displacement and element equivalent stress constraints with respect to pseudo densities are given. After that, by using self-compiled MATLAB program for continuum structure analysis, partial derivative calculation and optimization iteration, 4 optimization examples of different beam structures are used to show the changes of active nodal displacement and element equivalent stress constraints, and structural mass in the optimization iteration process, and to show the effectiveness of Ratio-Extremum algorithm in topology optimization of continuum structures.
VL  - 10
IS  - 1
ER  -

Copy | Download