Postbuckling performance of the TRIC natural mode triangular element for Isotropic and laminated composite shells

We present the computational performance and the achieved accuracy of the TRIC flat triangular shell element for nonlinear postbuckling analysis of arbitrary isotropic and composite shells. The element is based on the natural mode finite element method, which allows a convenient description of the current position of the structure. These natural modes are assigned to a convective coordinate system which follows the element during deformation within the framework of an Eulerian motion. With respect to this coordinate system the natural modes are additive. Numerical examples verify the accuracy, computational efficiency and the potential of the TRIC element in predicting the postbuckling behaviour of shells. Natural energy measures inform us about the energy allocation during nonlinear deformation and the interplay of the separate energy components.

[1]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[2]  W. Wagner A note on FEM buckling analysis , 1995 .

[3]  J. Argyris,et al.  TRIC: a simple but sophisticated 3-node triangular element based on 6 rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells , 1997 .

[4]  D. Owen,et al.  Finite element software for plates and shells , 1984 .

[5]  A. B. Sabir,et al.  The applications of finite elements to large deflection geometrically nonlinear behaviour of cylindrical shells , 1972 .

[6]  E. Riks An incremental approach to the solution of snapping and buckling problems , 1979 .

[7]  Lazarus Tenek,et al.  Computational aspects of the natural-mode finite element method , 1997 .

[8]  M. Crisfield A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[9]  Manolis Papadrakakis Solving Large-scale Problems in Mechanics , 1993 .

[10]  W. Wunderlich Nonlinear Finite Element Analysis in Structural Mechanics , 1981 .

[11]  Peter Wriggers,et al.  Consistent linearization for path following methods in nonlinear FE analysis , 1986 .

[12]  X. Peng,et al.  A consistent co‐rotational formulation for shells using the constant stress/constant moment triangle , 1992 .

[13]  Sergio Idelsohn,et al.  An effective automatic incremental/iterative method for static nonlinear structural analysis , 1989 .

[14]  Manolis Papadrakakis,et al.  A truncated Newton–Lanczos method for overcoming limit and bifurcation points , 1990 .

[15]  John Argyris,et al.  Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method , 1994 .

[16]  Carlos Alberto Brebbia,et al.  Variational Methods in Engineering , 1985 .

[17]  John Argyris,et al.  Natural Mode Method: A Practicable and Novel Approach to the Global Analysis of Laminated Composite Plates and Shells , 1996 .

[18]  Ekkehard Ramm,et al.  An assessment of assumed strain methods in finite rotation shell analysis , 1989 .

[19]  J. Argyris,et al.  An efficient and locking-free flat anisotropic plate and shell triangular element , 1994 .