Sandwich plates of minimal compliance
The subject of the paper is an optimal choice of material parameters characterizing the core layer of sandwich plates within the framework of the conventional plate theory in which the core layer is treated as soft in the in-plane direction. The mathematical description is similar to the Hencky–Reis...
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| Published in | Computer methods in applied mechanics and engineering Vol. 197; no. 51; pp. 4866 - 4881 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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15.10.2008
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| Abstract | The subject of the paper is an optimal choice of material parameters characterizing the core layer of sandwich plates within the framework of the conventional plate theory in which the core layer is treated as soft in the in-plane direction. The mathematical description is similar to the Hencky–Reissner model of plates with transverse shear deformation. Here, however, the bending stiffnesses and the transverse shear stiffnesses can be designed independently. The present paper deals only with optimal design of the core layer to make the plate compliance minimal. Two core materials are at our disposal, which leads to the ill-posed problem. To consider it one should relax this problem by admitting composite domains and characterize their overall properties by the homogenization formulae. The numerical approach is based on this relaxed formulation thus making it mesh-independent. The equilibrium problem is solved by the DSG3 finite element method. The optimization results are found with using the convergent updating schemes of the COC method. |
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| AbstractList | The subject of the paper is an optimal choice of material parameters characterizing the core layer of sandwich plates within the framework of the conventional plate theory in which the core layer is treated as soft in the in-plane direction. The mathematical description is similar to the Hencky–Reissner model of plates with transverse shear deformation. Here, however, the bending stiffnesses and the transverse shear stiffnesses can be designed independently. The present paper deals only with optimal design of the core layer to make the plate compliance minimal. Two core materials are at our disposal, which leads to the ill-posed problem. To consider it one should relax this problem by admitting composite domains and characterize their overall properties by the homogenization formulae. The numerical approach is based on this relaxed formulation thus making it mesh-independent. The equilibrium problem is solved by the DSG3 finite element method. The optimization results are found with using the convergent updating schemes of the COC method. |
| Author | Czarnecki, S. Kursa, M. Lewiński, T. |
| Author_xml | – sequence: 1 givenname: S. surname: Czarnecki fullname: Czarnecki, S. organization: Institute of Structural Mechanics, Warsaw University of Technology, Al. Armii Ludowej 16, 00-637 Warsaw, Poland – sequence: 2 givenname: M. surname: Kursa fullname: Kursa, M. organization: Institute of Fundamental Technological Research, Polish Academy of Sciences, Ul. Świe¸tokrzyska 21, 00-049 Warsaw, Poland – sequence: 3 givenname: T. surname: Lewiński fullname: Lewiński, T. email: T.Lewinski@il.pw.edu.pl organization: Institute of Structural Mechanics, Warsaw University of Technology, Al. Armii Ludowej 16, 00-637 Warsaw, Poland |
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| Cites_doi | 10.1016/S0263-8223(99)00074-4 10.1016/0020-7683(94)00202-8 10.1016/S0045-7825(01)00216-X 10.1016/0020-7683(92)90202-5 10.1016/S0045-7949(99)00140-6 10.1007/s002110050253 10.1007/BF01213995 10.1016/S0263-8223(02)00246-5 10.1016/S0167-6636(97)00056-2 10.1007/BF01198376 10.1007/s004190050248 10.1007/BF00380913 10.1016/S1359-8368(03)00063-5 10.1016/0045-7825(94)00777-K 10.1007/BF02193100 10.1016/0045-7825(91)90080-P 10.1090/qam/20440 10.1007/BF00044332 |
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| Issue | 51 |
| Keywords | Topology optimization Sandwich plates Minimum compliance problem Interfacial layer Geometrical shape Sandwich structure Homogenization Reissner model Material selection Topology Modeling Optimization Optimal design Plate Finite element method Ill posed problem Hencky model Effective medium model Transverse shear |
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| SubjectTerms | Computational techniques Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical methods in physics Minimum compliance problem Physics Sandwich plates Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Topology optimization |
| Title | Sandwich plates of minimal compliance |
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