Non‐linear explicit dynamic analysis of shells using the BST rotation‐free triangle

The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.

[1]  M. Ortiz,et al.  Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis , 2000 .

[2]  C. R. Calladine,et al.  A simple class of finite elements for plate and shell problems. I - Elements for beams and thin flat plates. II - An element for thin shells, with only translational degrees of freedom , 1992 .

[3]  C. R. Calladine,et al.  A simple class of finite elements for plate and shell problems. II: An element for thin shells, with only translational degrees of freedom , 1992 .

[4]  Klaus-Jürgen Bathe,et al.  ANALYSIS OF PLATES IN BENDING USING LARGE FINITE ELEMENTS , 1970 .

[5]  Eugenio Oñate,et al.  Finite elements versus finite volumes. Is there really a choice , 1992 .

[6]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory , 1990 .

[7]  Barry Hilary Valentine Topping,et al.  Three node triangular bending elements with one degree of freedom per node , 1992 .

[8]  J. Z. Zhu,et al.  The finite element method , 1977 .

[9]  Ted Belytschko,et al.  A simple triangular curved shell element , 1984 .

[10]  M. A. Crisfield,et al.  Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics , 1997 .

[11]  S. BRODETSKY,et al.  Theory of Plates and Shells , 1941, Nature.

[12]  Klaus-Jürgen Bathe,et al.  A study of three‐node triangular plate bending elements , 1980 .

[13]  Dong-Yol Yang,et al.  Comparative investigation into implicit, explicit, and iterative implicit/explicit schemes for the simulation of sheet-metal forming processes , 1995 .

[14]  David Bushnell,et al.  Finite-difference energy method for nonlinear shell analysis , 1971 .

[15]  Emmett A. Witmer,et al.  THEORETICAL-EXPERIMENTAL CORRELATION OF LARGE DYNAMIC AND PERMANENT DEFORMATIOONS OF IMPULSIVELY-LOADED SIMPLE STRUCTURES , 1964 .

[16]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  Eugenio Oñate,et al.  Finite element analysis of sheet metal forming problems using a selective viscous bending/membrane formulation , 1990 .

[18]  Miguel Cervera,et al.  A finite volume format for structural mechanics , 1994 .

[19]  Z. Zhong.  Finite Element Procedures for Contact-Impact Problems , 1993 .

[20]  Ted Belytschko,et al.  A review of shell finite elements and corotational theories , 1995 .

[21]  K. Bathe,et al.  FINITE ELEMENT FORMULATIONS FOR LARGE DEFORMATION DYNAMIC ANALYSIS , 1975 .

[22]  Eugenio Oñate,et al.  Rotation-free triangular plate and shell elements , 2000 .

[23]  Miguel Cervera,et al.  Derivation of thin plate bending elements with one degree of freedom per node , 1993 .

[24]  Eugenio Oñate Ibáñez de Navarra,et al.  Analysis of beams and shells using a rotation – free Finite Element – Finite Volume formulation , 1999 .

[25]  Eugenio Oñate,et al.  Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems , 1998 .

[26]  Manolis Papadrakakis,et al.  Nonlinear dynamic analysis of shells with the triangular element TRIC , 2003 .

[27]  Eugenio Oñate,et al.  A basic thin shell triangle with only translational DOFs for large strain plasticity , 2001 .

[28]  A. Ugural.  Stresses in plates and shells , 1981 .

[29]  E. Oñate,et al.  Finite volumes and finite elements: Two ‘good friends’ , 1994 .

[30]  J. Dienes.  On the analysis of rotation and stress rate in deforming bodies , 1979 .

[31]  Eugenio Oñate,et al.  Application of explicit FE codes to simulation of sheet and bulk metal forming processes , 1998 .