TRIC - A SIMPLE BUT SOPHISTICATED 3-NODE TRIANGULAR ELEMENT BASED ON 6 RIGID-BODY AND 12 STRAINING MODES FOR FAST COMPUTATIONAL SIMULATIONSOF ARBITRARY ISOTROPIC AND LAMINATED COMPOSITE SHELLS

TRIC is a simple but sophisticated 3-node shear-deformable isotropic a nd composite flat shell element suitable for large-scale linear and no nlinear engineering computations of thin and thick anisotropic plate a nd complex shell structures. Its stiffness matrix is based on 12 strai ning modes but essentially requires the computation of a sparse 9 by 9 matrix. The element formulation departs from conventional Cartesian m echanics as well as previously adopted physical lumping procedures and contains a completely new implementation of the transverse shear defo rmation; it naturally circumvents all previously imposed constraints. The methodology is based on physical inspirations of the Natural-Mode finite element method (NM-FEM) formalized through appropriate geometri cal, trigonometrical and engineering mathematical relations and it inv olves only exact integrations; its stiffness, mass and geometrical mat rices are all explicitly derived. The kinematics of the element are hi erarchically decomposed into 6 rigid-body and 12 straining modes of de formation. A simple congruent matrix operation transforms the elementa l natural stiffness matrix to the local and global Cartesian coordinat es. The modes show explicitly how the element deforms in axial straini ng, symmetrical and antisymmetrical bending as well as in transverse s hearing; the latter has only become clear in the formulation presented here and has brought about a completion of the understanding of natur al modes as they apply to the triangular shell element. A wide range o f numerical examples substantiate the conception and purpose of the el ement TRIC; fast convergence is observed in many examples.