A novel minimum weight formulation of topology optimization implemented with reanalysis approach
Summary In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A high‐efficiency computational approach of topology optimization is implemented within the framework of approximate reanalysis. The key point...
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| Published in: | International journal for numerical methods in engineering Vol. 120; no. 5; pp. 567 - 579 |
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| Main Authors: | , , , , , , |
| Format: | Journal Article |
| Language: | English |
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Bognor Regis
Wiley Subscription Services, Inc
02.11.2019
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | Summary
In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A high‐efficiency computational approach of topology optimization is implemented within the framework of approximate reanalysis. The key point of the formulation is the introduction of the reciprocal‐type variables. The topology optimization seeking for minimum weight can be transformed as a sequence of quadratic program with separable and strictly positive definite Hessian matrix, thus can be solved by a sequential quadratic programming approach. A modified sensitivity filtering scheme is suggested to remove undesirable checkerboard patterns and mesh dependence. Several typical examples are provided to validate the presented approach. It is observed that the optimized structure can achieve lighter weight than those from the established method by the demonstrative numerical test. Considerable computational savings can be achieved without loss of accuracy of the final design for 3D structure. Moreover, the effects of multiple constraints and upper bound of the allowable compliance upon the optimized designs are investigated by numerical examples. |
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| AbstractList | Summary
In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A high‐efficiency computational approach of topology optimization is implemented within the framework of approximate reanalysis. The key point of the formulation is the introduction of the reciprocal‐type variables. The topology optimization seeking for minimum weight can be transformed as a sequence of quadratic program with separable and strictly positive definite Hessian matrix, thus can be solved by a sequential quadratic programming approach. A modified sensitivity filtering scheme is suggested to remove undesirable checkerboard patterns and mesh dependence. Several typical examples are provided to validate the presented approach. It is observed that the optimized structure can achieve lighter weight than those from the established method by the demonstrative numerical test. Considerable computational savings can be achieved without loss of accuracy of the final design for 3D structure. Moreover, the effects of multiple constraints and upper bound of the allowable compliance upon the optimized designs are investigated by numerical examples. In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A high‐efficiency computational approach of topology optimization is implemented within the framework of approximate reanalysis. The key point of the formulation is the introduction of the reciprocal‐type variables. The topology optimization seeking for minimum weight can be transformed as a sequence of quadratic program with separable and strictly positive definite Hessian matrix, thus can be solved by a sequential quadratic programming approach. A modified sensitivity filtering scheme is suggested to remove undesirable checkerboard patterns and mesh dependence. Several typical examples are provided to validate the presented approach. It is observed that the optimized structure can achieve lighter weight than those from the established method by the demonstrative numerical test. Considerable computational savings can be achieved without loss of accuracy of the final design for 3D structure. Moreover, the effects of multiple constraints and upper bound of the allowable compliance upon the optimized designs are investigated by numerical examples. |
| Author | Liu, Jie Du, Yixian Saeed, Nouman Chen, Zhuo Wang, Xuan Long, Kai Gu, Chunlu |
| Author_xml | – sequence: 1 givenname: Kai orcidid: 0000-0001-7921-0497 surname: Long fullname: Long, Kai email: longkai1978@163.com organization: North China Electric Power University – sequence: 2 givenname: Chunlu surname: Gu fullname: Gu, Chunlu organization: North China Electric Power University – sequence: 3 givenname: Xuan orcidid: 0000-0003-2485-7095 surname: Wang fullname: Wang, Xuan organization: Hefei University of Technology – sequence: 4 givenname: Jie surname: Liu fullname: Liu, Jie organization: Guangzhou University – sequence: 5 givenname: Yixian surname: Du fullname: Du, Yixian organization: China Three Gorges University – sequence: 6 givenname: Zhuo surname: Chen fullname: Chen, Zhuo organization: North China Electric Power University – sequence: 7 givenname: Nouman surname: Saeed fullname: Saeed, Nouman organization: North China Electric Power University |
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| Cites_doi | 10.1007/s00158-013-0978-6 10.1016/j.cma.2014.10.011 10.1002/nme.2536 10.1016/j.enganabound.2018.07.010 10.1016/S0020-7683(03)00417-7 10.1016/S0045-7825(01)00216-X 10.1007/s001580050141 10.1007/s00158-015-1381-2 10.1080/0305215X.2017.1417401 10.1080/0305215X.2018.1497613 10.1002/nme.2774 10.1002/nme.5432 10.1002/nme.3072 10.1007/s00158-010-0586-7 10.1002/nme.5575 10.1007/s00158-015-1309-x 10.1007/BF01214002 10.1016/j.cma.2018.08.028 10.1002/nme.2778 10.1007/s00158-017-1811-4 10.1007/BF01650949 10.1002/nme.1620240207 10.1038/nature23911 10.1007/s00158-009-0443-8 10.1007/s00158-009-0406-0 10.1007/s00158-013-0956-z 10.1016/j.cma.2012.07.008 10.1007/s00158-014-1098-7 10.1007/s00158-018-2048-6 10.1007/s00158-018-2159-0 10.1002/nme.5593 10.1016/j.cma.2017.05.009 10.1007/s00158-009-0463-4 10.1007/s00158-013-1015-5 10.1016/j.cma.2016.10.029 10.1002/nme.4344 10.1007/s00158-010-0610-y 10.1016/0045-7825(88)90086-2 10.1016/S0020-7683(99)00251-6 10.1016/j.ijsolstr.2003.11.027 |
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In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A... In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A... |
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| SubjectTerms | approximate reanalysis Dependence Design optimization Hessian matrices Matrix methods Minimum weight design multigrid preconditioned conjugate gradients Optimization preconditioned conjugate gradient Quadratic programming sequential quadratic programming Topology optimization Upper bounds Weight reduction |
| Title | A novel minimum weight formulation of topology optimization implemented with reanalysis approach |
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