TRIC is a simple but sophisticated 3-node shear-deformable isotropic and composite flat shell element suitable for large-scale linear and nonlinear engineering computations of thin and thick anisotropic plate and complex shell structures. Its stiffness matrix is based on 12 straining modes but essentially requires the computation of a sparse 9 by 9 matrix. The element formulation departs from conventional Cartesian mechanics as well as previously adopted physical lumping procedures and contains a completely new implementation of the transverse shear deformation; it naturally circumvents all previously imposed constraints. The methodology is based on physical inspirations of the natural-mode finite element method formalized through appropriate geometrical, trigonometrical and enigneering mathematical relations and it involves only exact integrations; its stiffness, mass and geometrical matrices are all explicitly derived. The kinematics of the element are hierarchically decomposed into 6 rigid-body and 12 straining modes of deformation. A simple congruent matrix operation transforms the elemental natural stiffness matrix to the local and global Cartesian coordinates. The modes show explicitly how the element deforms in axial straining, symmetrical and antisymmetrical bending as well as in transverse shearing; the latter has only become clear in the formulation presented here and has brought about a completion of the understanding of natural modes as they apply to the triangular shell element. A wide range of numerical examples substantiate the conception and purpose of the element TRIC; fast convergence is observed in many examples.

References in zbMATH (referenced in 47 articles , 1 standard article )

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  1. He, P. Q.; Sun, Q.; Liang, K.: Generalized modal element method. I: Theory and its application to eight-node asymmetric and symmetric solid elements in linear analysis (2019)
  2. Huang, Wei; Huang, Qun; Liu, Yin; Yang, Jie; Hu, Heng; Trochu, François; Causse, Philippe: A Fourier based reduced model for wrinkling analysis of circular membranes (2019)
  3. Levyakov, Stanislav V.: Development of invariant-based triangular element for nonlinear thermoelastic analysis of laminated shells (2019)
  4. Papadopoulos, V.; Soimiris, G.; Giovanis, D. G.; Papadrakakis, M.: A neural network-based surrogate model for carbon nanotubes with geometric nonlinearities (2018)
  5. Li, Z. X.; Zheng, T.; Vu-Quoc, L.; Izzuddin, B. A.: A 4-node co-rotational quadrilateral composite shell element (2016)
  6. Martins, Ricardo Rodrigues; Zouain, Nestor; Borges, Lavinia; de Souza Neto, Eduardo A.: A continuum-based mixed shell element for shakedown analysis (2014)
  7. Levyakov, S. V.; Kuznetsov, Viktor Vasilevich: Complete system of two-dimensional invariants for formulation of triangular finite element of composite shells (2012)
  8. Levyakov, S. V.; Kuznetsov, V. V.: Application of triangular element invariants for geometrically nonlinear analysis of functionally graded shells (2011)
  9. Li, Z. X.; Liu, Y. F.; Izzuddin, B. A.; Vu-Quoc, L.: A stabilized co-rotational curved quadrilateral composite shell element (2011)
  10. Chasanis, Paris; Brass, Manuel; Kenig, Eugeny Y.: Investigation of multicomponent mass transfer in liquid-liquid extraction systems at microscale (2010)
  11. Schillinger, Dominik; Papadopoulos, Vissarion; Bischoff, Manfred; Papadrakakis, Manolis: Buckling analysis of imperfect I-section beam-columns with stochastic shell finite elements (2010)
  12. Kuznetsov, V. V.; Levyakov, S. V.: Phenomenological invariants and their application to geometrically nonlinear formulation of triangular finite elements of shear deformable shells (2009)
  13. Papadopoulos, Vissarion; Stefanou, George; Papadrakakis, Manolis: Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties (2009)
  14. Kadioglu, Fethi; Pidaparti, Ramana M.: Finite element design analysis of composite rebar shapes for use in concrete structures (2008)
  15. Yang, Y. B.; Lin, S. P.; Chen, C. S.: Letter to the editor: Closure to discussion on the article “Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation” by Y.B. Yang, S.P. Lin, C.S. Chen [Comput. Methods Appl. Mech. Engrg. 196 (2007) 1178-1192] (2008)
  16. Kuznetsov, V. V.; Levyakov, S. V.: Phenomenological invariant-based finite-element model for geometrically nonlinear analysis of thin shells (2007)
  17. Papadopoulos, Vissarion; Iglesis, Pavlos: The effect of non-uniformity of axial loading on the buckling behaviour of shells with random imperfections (2007)
  18. Yang, Y. B.; Lin, S. P.; Chen, C. S.: Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation (2007)
  19. Battini, Jean-Marc; Pacoste, Costin: On the choice of the linear element for corotational triangular shells (2006)
  20. Corradi, Leone; Luzzi, Lelio; Vena, Pasquale: Finite element limit analysis of anisotropic structures (2006)

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