Separated representations of 3D elastic solutions in shell geometries

Springer Science and Business Media LLC - 2014
Brice Bognet1, Adrien Leygue1, Francisco Chinesta1
1GeM UMR CNRS-Centrale, Nantes 1 rue de la Noe, F-44300, Nantes, France

Tóm tắt

Abstract Background The solution of 3D models in degenerated geometries in which some characteristic dimensions are much lower than the other ones -e.g. beams, plates, shells,...- is a tricky issue when using standard mesh-based discretization techniques. Methods Separated representations allow decoupling the meshes used for approximating the solution along each coordinate. Thus, in plate or shell geometries 3D solutions can be obtained from a sequence of 2D and 1D problems allowing fine and accurate representation of the solution evolution along the thickness coordinate while keeping the computational complexity characteristic of 2D simulations. In a former work this technique was considered for addressing the 3D solution of thermoelastic problems defined in plate geometries. In this work, the technique is extended for addressing the solution of 3D elastic problems defined in shell geometries. Results The capabilities of the proposed approach are illustrated by considering some numerical examples involving different degrees of complexity, from simple shells to composite laminates involving stiffeners. Conclusions The analyzed examples prove the potentiality and efficiency of the proposed strategy, where the computational complexity was found evolving as reported in our former works, proving that 3D solutions can be computed at a 2D cost.

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Tài liệu tham khảo

Timoshenko SP, Woinowsky-Krieger S: Theory of plates and shells. New York,: McGraw-Hill classic textbook reissue; 1959. second edition second edition

Qatu MS: Review of recent literature on static analyses of composite shells: 2000–2010. Open J Composite Mater 2012,2(3):61–86. 10.4236/ojcm.2012.23009

Zhang YX, Yang CH: Recent developments in finite element analysis for laminated composite plates. Composite Struct 2009,88(1):147–157. 10.1016/j.compstruct.2008.02.014

Reddy JN, Arciniega RA: Shear deformation plate and shell theories: from Stavsky to present. Mech Adv Mater Struct 2004,11(6):535–582. 10.1080/15376490490452777

Viola E, Tornabene F, Fantuzzi N: Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories. Composite Struct 2013, 101: 59–93.

Carrera E: Historical review of Zig-Zag theories for multilayered plates and shells. Appl Mech Rev 2003,56(3):287. 10.1115/1.1557614

Sedira L, Ayad R, Sabhi H, Hecini M, Sakami S: An enhanced discrete Mindlin finite element model using a zigzag function. Eur J Comput Mech 2012,21(1–2):122–140.

Carrera E: Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Methods Eng 2002,9(2):87–140. 10.1007/BF02736649

Carrera E: Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Eng 2003,10(3):215–296. 10.1007/BF02736224

Kratzig WB, Jun D: Multi-layer multi-director concepts for D-adaptivity in shell theory. Comput Struct 2002,80(9):719–734.

Naceur H, Shiri S, Coutellier D, Batoz JL: On the modeling and design of composite multilayered structures using solid-shell finite element model. Finite Elem Anal Design 2013, 70: 1–14.

Trinh V-D, Abed-Meraim F, Combescure A: A new assumed strain solid-shell formulation “SHB6” for the six-node prismatic finite element. J Mech Sci Technol 2011,25(9):2345–2364. 10.1007/s12206-011-0710-7

Quatmann M, Aswini N, Reimerdes HG, Gupta NK: Superelements for a computationally efficient structural analysis of elliptical fuselage sections. Aerosp Sci Technol 2013,27(1):76–83. 10.1016/j.ast.2012.06.009

Wisnom MR, Gigliotti M, Ersoy N, Campbell M, Potter KD: Mechanisms generating residual stresses and distortion during manufacture of polymer-matrix composite structures. Composites Part A: Appl Sci Manuf 2006,37(4):522–529. 10.1016/j.compositesa.2005.05.019

Hochard Ch, Ladeveze P, Proslier L: A simplified analysis of elastic structures. Eur J Mech A/Solids 1993,12(4):509–535.

Ladeveze P, Arnaud L, Rouch P, Blanz C: The variational theory of complex rays for the calculation of medium-frequency vibrations. Eng Comput 2001,18(1–2):193–221.

Ladeveze P: Nonlinear computational structural mechanics. New York: Springer; 1999.

Ammar A, Mokdad B, Chinesta F, Keunings R: A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newtonian Fluid Mech 2006, 139: 153–176. 10.1016/j.jnnfm.2006.07.007

Chinesta F, Ammar A, Cueto E: Recent advances and new challenges in the use of the Proper Generalized Decomposition for solving multidimensional models. Arch Comput Methods Eng 2010, 17: 327–350. 10.1007/s11831-010-9049-y

Chinesta F, Ammar A, Leygue A, Keunings R: An overview of the Proper Generalized Decomposition with applications in computational rheology. J Non-Newtonian Fluid Mech 2011, 166: 578–592. 10.1016/j.jnnfm.2010.12.012

Chinesta F, Ladeveze P, Cueto E: A short review in model order reduction based on Proper Generalized Decomposition. Arch Comput Methods Eng 2011, 18: 395–404. 10.1007/s11831-011-9064-7

Chinesta F, Leygue A, Bordeu F, Aguado JV, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A: Parametric PGD based computational vademecum for efficient design, optimization and control. Arch Comput Methods Eng 2013, 20: 31–59. 10.1007/s11831-013-9080-x

Leygue A, Chinesta F, Beringhier M, Nguyen TL, Grandidier JC, Pasavento F, Schrefler B: Towards a framework for non-linear thermal models in shell domains. Int J Numerical Methods Heat Fluid Flow 2013,23(1):55–73. 10.1108/09615531311289105

Bognet B, Leygue A, Chinesta F, Poitou A, Bordeu F: Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity. Comput Methods Appl Mechanics Eng 2012, 201: 1–12.

Chinesta F, Leygue A, Bognet B, Ghnatios Ch, Poulhaon F, Bordeu F, Barasinski A, Poitou A, Chatel S: First steps towards an advanced simulation of composites manufacturing by automated tape placement. Int J Mater Forming 2014. http://www.springerlink.com/index/10.1007/s12289-012-1112-9

Vidal P, Gallimard L, Polit O: Proper Generalized Decomposition and layer-wise approach for the modeling of composite plate structures. Int J Solids Struct 2013,50(14–15):2239–2250.

Macneal RH, Harder RL: A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Design 1985, 1: 3–20. 10.1016/0168-874X(85)90003-4

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