DOI QR코드

DOI QR Code

Parametric 3D elastic solutions of beams involved in frame structures

  • Received : 2014.07.08
  • Accepted : 2014.10.20
  • Published : 2015.07.25

Abstract

Frame structures have been traditionally represented as an assembling of components, these last described within the beam theory framework. In the case of frames involving complex components in which classical beam theory could fail, 3D descriptions seem the only valid route for performing accurate enough analyses. In this work we propose a framework for frame structure analyses that proceeds by assembling the condensed parametric rigidity matrices associated with the elementary beams composing the beams involved in the frame structure. This approach allows a macroscopic analysis in which only the condensed degrees of freedom at the elementary beams interfaces are considered, while fine 3D parametric descriptions are retained for local analyses.

Keywords

References

  1. Ammar. A., Mokdad. B., Chinesta. F. and Keunings. R. (2006), "Anew family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids", J. Non-Newton. Fluid Mech., 139, 153-176. https://doi.org/10.1016/j.jnnfm.2006.07.007
  2. Ammar. A., Chinesta. F., Diez, P. and Huerta, A. (2010), "An estimator for separated representations of highly multidimensional models", Comput. Meth. Appl. Mech. Eng., 199, 1872-1880. https://doi.org/10.1016/j.cma.2010.02.012
  3. Ammar. A. Huerta, A., Chinesta, F., Cueto, E. and Leygue, A. (2014), "Parametric solutions involving geometry: a step towards efficient shape optimization", Comput. Meth. Appl. Mech. Eng., 268, 178-193. https://doi.org/10.1016/j.cma.2013.09.003
  4. Bognet, B., Leygue, A., Chinesta, F., Poitou, A. and Bordeu, F. (2012), "Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity", Comput. Meth. Appl. Mech. Eng., 201, 1-12.
  5. Bognet, B., Leygue, A. and Chinesta, F. (2014), "Separated representations of 3D elastic solutions in shell geometries", Adv. Model. Simul. Eng. Sci., 1(1), 1-34. https://doi.org/10.1186/2213-7467-1-1
  6. Carrera, E. (2002), "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Arch. Comput. Meth. Eng., 9(2), 87-140. https://doi.org/10.1007/BF02736649
  7. Carrera, E. (2003), "Historical review of Zig-Zag theories for multilayered plates and shells", Appl. Mech. Rev., 56(3), 287. https://doi.org/10.1115/1.1557614
  8. Carrera, E. (2003), "Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Meth. Eng., 10(3), 215-296. https://doi.org/10.1007/BF02736224
  9. Chinesta, F., Ammar, A. and Cueto, E. (2010), " Recent advances and new challenges in the use of the Proper Generalized Decomposition for solving multidimensional models", Arch. Comput. Meth. Eng., 17, 327-350. https://doi.org/10.1007/s11831-010-9049-y
  10. Chinesta, F., Ammar, A., Leygue, A. and Keunings, R. (2011), "An overview of the Proper Generalized Decomposition with applications in computational rheology", J. Non-Newton. Fluid Mech., 166, 578-592. https://doi.org/10.1016/j.jnnfm.2010.12.012
  11. Chinesta, F., Ladeveze, P. and Cueto, E. (2011), "A short review in model order reduction based on Proper Generalized Decomposition", Arch. Comput. Meth. Eng., 18, 395-404. https://doi.org/10.1007/s11831-011-9064-7
  12. Chinesta, F., Leygue, A., Bognet, B., Ghnatios, Ch., Poulhaon, F., Bordeu, F., Barasinski, A., Poitou, A., Chatel, S. and Maison-Le-Poec, S. (2012). "First steps towards an advanced simulation of composites manufacturing by automated tape placement", Int J. Mater. Form. 7(1), 81-92. https://doi.org/10.1007/s12289-012-1112-9
  13. Chinesta, F., Leygue, A., Bordeu, F., Aguado, J.V., Cueto, E., Gonzalez, D., Alfaro, I., Ammar, A. and Huerta, A. (2013), "Parametric PGD based computational vademecum for efficient design, optimization and control", Arch. Comput. Meth. Eng., 20, 31-59. https://doi.org/10.1007/s11831-013-9080-x
  14. Chinesta, F., Keunings, R., Leygue, A. (2014), The Proper Generalized Decomposition for Advanced Numerical Simulations, A Primer, Springerbriefs, Springer.
  15. Ghnatios, Ch., Chinesta, F. and Binetruy, Ch. (2015), "The squeeze flow of composite laminates", International Journal of Material Forming. (in Press)
  16. Hochard, Ch., Ladeveze, P. and Proslier L. (1993), "A simplified analysis of elastic structures", Eur. J. Mech. A/Solid., 12(4), 509-535.
  17. Kratzig, W.B. and Jun, D. (2002), "Multi-layer multi-director concepts for D-adaptivity in shell theory", Comput. Struct., 80(9), 719-734. https://doi.org/10.1016/S0045-7949(02)00043-3
  18. Ladeveze, P. (1999), "Nonlinear Computational Structural Mechanics - New Approaches and Non-IncrementalMethods of Clculation, Springer, Berlin.
  19. Ladeveze, P., Arnaud, L., Rouch, P. and Blanz, C. (2001), "The variational theory of complex rays for the calculation of medium-frequency vibrations", Eng. Comput., 18(1-2), 193-221. https://doi.org/10.1108/02644400110365879
  20. Leygue, A., Chinesta, F., Beringhier, M., Nguyen, T.L., Grandidier, J.C., Pasavento, F. and Schrefler, B. (2013), "Towards a framework for non-linear thermal models in shell domains", lnt. J. Numer: Meth. Heat Fluid Flow, 23, 55-73. https://doi.org/10.1108/09615531311289105
  21. Naceur, H., Shiri, S., Coutellier, D. and Batoz, J.L. (2013), "On the modeling and design of composite multilayered structures using solid-shell finite element model", Finite Elem. Anal. Des., 70, 1-14.
  22. Nazeer, M., Bordeu, F., Leygue, A. and F. Chinesta, F. (2014), "Arlequin based PGD domain decomposition", Comput. Mech., 54(5), 1175-1190. https://doi.org/10.1007/s00466-014-1048-7
  23. Niroomandi, S., Gonzalez, D., Alfaro, I., Bordeu, F., Leygue, A., Cueto, E. and Chinesta, F. (2013), "Real time simulation of biological soft tissues : A PGD approach", lnt. J. Numer. Meth. Biomed. Eng., 29(5), 586-600. https://doi.org/10.1002/cnm.2544
  24. Qatu, M.S. (2012), "Review of recent literature on static analyses of composite shells: 2000-2010", Open J. Compos. Mater., 2(3), 61-86. https://doi.org/10.4236/ojcm.2012.23009
  25. Reddy, J.N. and Arciniega, R.A. (2004), "Shear deformation plate and shell theories: from Stavsky to present", Mech. Adv. Mater. Struct., 11(6), 535-582. https://doi.org/10.1080/15376490490452777
  26. Sedira, L., Ayad, R., Sabhi, H., Hecini, M. and Sakami, S. (2012), "An enhanced discrete Mindlin finite element model using a zigzag function", Euro. J. Comput. Mech., 21(1-2), 122-140.
  27. Timoshenko, S.P. (1955), Strength of Materials, Van Nostrand.
  28. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill.
  29. Timoshenko, S.P. and Young, D.H. (1982), Theory of Structures, McGraw-Hill.
  30. Trinh, V.D., Abed-Meraim, F. and Combescure, A. (2011), "A new assurned strain solid-shell formulation "SHB6" for the six-node prismatic finite element", J. Mech. Sci. Tech., 25(9), 2345-2364. https://doi.org/10.1007/s12206-011-0710-7
  31. Vidal, P., Gallimard, L. and Polit, O. (2013), "Proper generalized decomposition and layer-wise approach for the modeling of composite plate structures", lnt. J. Solid. Struct., 50(14-15), 2239-2250. https://doi.org/10.1016/j.ijsolstr.2013.03.034
  32. Viola, E., Tornabene, F. and Fantuzzi, N. (2013), "Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories", Compos. Struct., 101, 59-93. https://doi.org/10.1016/j.compstruct.2013.01.002
  33. Zhang, Y.X. and Yang, C.H. (2009), "Recent developments in finite element analysis for laminated composite plates", Compos. Struct., 88(1), 147-157. https://doi.org/10.1016/j.compstruct.2008.02.014

Cited by

  1. Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data pp.1886-1784, 2020, https://doi.org/10.1007/s11831-018-9301-4
  2. Tape surface characterization and classification in automated tape placement processability: Modeling and numerical analysis vol.5, pp.5, 2018, https://doi.org/10.3934/matersci.2018.5.870
  3. Non-intrusive proper generalized decomposition involving space and parameters: application to the mechanical modeling of 3D woven fabrics vol.6, pp.1, 2015, https://doi.org/10.1186/s40323-019-0137-8
  4. A non-local void dynamics modeling and simulation using the Proper Generalized Decomposition vol.13, pp.4, 2015, https://doi.org/10.1007/s12289-019-01490-7
  5. Non-Intrusive In-Plane-Out-of-Plane Separated Representation in 3D Parametric Elastodynamics vol.8, pp.3, 2015, https://doi.org/10.3390/computation8030078
  6. Spurious-free interpolations for non-intrusive PGD-based parametric solutions: Application to composites forming processes vol.14, pp.1, 2015, https://doi.org/10.1007/s12289-020-01561-0
  7. Seismic vulnerability assessment of buried pipelines: A 3D parametric study vol.143, pp.None, 2015, https://doi.org/10.1016/j.soildyn.2021.106627