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. Gal, Erez; Levy, Robert: Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element (2006)
  2. Lagaros, Nikos D.; Papadopoulos, Vissarion: Optimum design of shell structures with random geometric, material and thickness imperfections (2006)
  3. Levy, R.; Gal, E.: The geometric stiffness of thick shell triangular finite elements for large rotations (2006)
  4. Papadopoulos, Vissarion; Papadrakakis, Manolis; Deodatis, George: Analysis of mean and mean square response of general linear stochastic finite element systems (2006)
  5. Charmpis, Dimos C.; Papadrakakis, Manolis: Improving the computational efficiency in finite element analysis of shells with uncertain properties (2005)
  6. Papadopoulos, Vissarion; Papadrakakis, Manolis: The effect of material and thickness variability on the buckling load of shells with random initial imperfections (2005)
  7. Corradi, L.; Panzeri, N.: A triangular finite element for sequential limit analysis of shells (2004)
  8. Fragakis, Yannis; Papadrakakis, Manolis: The mosaic of high-performance domain decomposition methods for structural mechanics. II: Formulation enhancements, multiple right-hand sides and implicit dynamics (2004)
  9. Stefanou, G.; Papadrakakis, M.: Stochastic finite element analysis of shells with combined random material and geometric properties. (2004)
  10. Argyris, John; Papadrakakis, Manolis; Mouroutis, Zacharias S.: Nonlinear dynamic analysis of shells with the triangular element TRIC. (2003)
  11. Corradi, Leone; Panzeri, Nicola: Post-collapse analysis of plates and shells based on a rigid-plastic version of the TRIC element. (2003)
  12. Fragakis, Yannis; Papadrakakis, Manolis: The mosaic of high performance domain decomposition methods for structural mechanics: formulation, interrelation and numerical efficiency of primal and dual methods. (2003)
  13. Argyris, J. H.; Papadrakakis, M.; Karapitta, L.: Elasto-plastic analysis of shells with the triangular element TRIC (2002)
  14. Argyris, John; Papadrakakis, Manolis; Stefanou, George: Stochastic finite element analysis of shells (2002)
  15. Eriksson, Anders; Pacoste, Costin: Element formulation and numerical techniques for stability problems in shells (2002)
  16. Corradi, Leone; Panzeri, Nicola; Poggi, Carlo: Post-critical behavior of moderately thick axisymmetric shells: a sequential limit analysis approach (2001)
  17. Papadrakakis, M.; Fragakis, Y.: An integrated geometric-algebraic method for solving semi-definite problems in structural mechanics. (2001)
  18. Argyris, J. H.; Papadrakakis, M.; Apostolopoulou, C.; Koutsourelakis, S.: The TRIC shell element: Theoretical and numerical investigation (2000)
  19. Mackerle, Jaroslav: Finite element linear and nonlinear, static and dynamic analysis of structural elements -- an addendum. A bibliography (1996--1999) (2000)
  20. Felippa, C. A.; Militello, C.: Construction of optimal 3-node plate bending triangles by templates (1999)