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Title
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The Generation of Inter-Element-Compatible Stiffness and Mass Matrices by the Use of Interpolation Formulas
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Description
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This paper presents a general method of subelement displacement states which makes it a relatively simple task to insure completely compatible displacement states. The method involves the use of Hermite interpolation formulas of various order. The total potential energy principle is used to generate stiffness matrices based on these displacement states. The approach is presented in general orthogonal curvilinear coordinates for shell type structures. Inter-element-compatible stiffness matrices are presented for a rectangular membrane, a rectangular plate with twelve degrees of freedom, and a rectangular plate with twenty four degrees of freedom. The corresponding consistent mass matrices are presented for both plate elements. Numerical examples of static deflection analysis are presented based on both of the plate subelements and the monotonic convergence of the discretization error is confirmed. Application of the simpler plate subelement to the determination of natural modes and frequencies is also illustrated with a numerical example. All of the examples are selected so that comparison with classical results can be made.
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Date
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1966
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Index Abstract
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Not Available
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Photo Quality
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Not Needed
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Report Number
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AFFDL-TR-66-80 p. 395-443
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Creator
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Bogner, F. K
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Fox, R. L.
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Schmit, L. A., Jr.
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Corporate Author
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Case Institute of Technology
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Laboratory
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Air Force Flight Dynamics Laboratory
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Extent
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49
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Access Rights
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Distribution of this document is unlimited.
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Distribution Classification
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1
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Contract
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Laboratory Research - No Contract
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DTIC Record Exists
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No
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Distribution Change Authority Correspondence
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None
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Distribution Conflict
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No
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Report Availability
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Full text available
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Date Issued
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1966-11
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Abstract
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This paper presents a general method of subelement displacement states which makes it a relatively simple task to insure completely compatible displacement states. The method involves the use of Hermite interpolation formulas of various order. The total potential energy principle is used to generate stiffness matrices based on these displacement states. The approach is presented in general orthogonal curvilinear coordinates for shell type structures. Inter-element-compatible stiffness matrices are presented for a rectangular membrane, a rectangular plate with twelve degrees of freedom, and a rectangular plate with twenty four degrees of freedom. The corresponding consistent mass matrices are presented for both plate elements. Numerical examples of static deflection analysis are presented based on both of the plate subelements and the monotonic convergence of the discretization error is confirmed. Application of the simpler plate subelement to the determination of natural modes and frequencies is also illustrated with a numerical example. All of the examples are selected so that comparison with classical results can be made.
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Identifier
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AD0646300
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Provenance
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Bombardier/Aero
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Type
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article
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Format
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1 online resource
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Is Referenced By
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Ummels, Raphael, & Castro, Saullo G. P. "Overlap-Stiffened Panels for Optimized Buckling Performance Under Minimum Steering Radius Constraints", Preprint DOI
10.31224/osf.io/xpvn4
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Mauricio F. Caliri, Jr., Antonio J.M. Ferreira, and Volnei Titac
A new C1 4-node flat laminated shell element based on a generalized plate formulation
v163 (2021): 107648
[Oxford] : Elsevier Applied Science
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Wang, Zhihua, José Humberto S. Almeida Jr., Aravind Ashok, Zhonglai Wang and Saullo G. P. Castro, "Lightweight design of variable-angle filament-wound cylinders combining Kriging-based metamodels with particle swarm optimization", May 12, 2021
https://engrxiv.org/3ym95/
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Ummels, R., & Castro, S. G. P. (2021). Overlap-stiffened panels for optimized buckling performance under
minimum steering radius constraints. Composites Part C: Open Access, 6, [100174].
https://doi.org/10.1016/j.jcomc.2021.100174
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Castro, S. G. P. & Jansen, E. L. (2022) Displacement-based multi-modal formulation of Koiter’s method applied to cylindrical shells. Preprint files.osf.io
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Castro, S. G. P. & Jansen, E. L. (2022) Displacement-based multi-modal formulation of Koiter’s method applied to cylindrical shells AIAA SCITECH 2022 Forum https://arc.aiaa.org/doi/10.2514/6.2022-0256
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Wang, Zhihua, José Humberto S. Almeida Jr., Aravind Ashok, Zhonglai Wang and Saullo G. P. Castro, "Lightweight design of variable-angle filament-wound cylinders combining Kriging-based metamodels with particle swarm optimization", Structural and Multidisciplinary Optimizaion, 65:140 (2022)
