Plastic buckling and collapse of thin shell structures, using layered plastic modeling and co-rotational ANDES finite elements

This study reveals an analysis of plastic buckling and collapse of thin shell structures. For this purpose, the co-rotational and layered plastic model as well as ANDES (Assumed Natural Deviatoric Strain) finite element formulations are used. The co-rotational kinematics formulation splits the translational and rotational deformations in a small deformation analysis. The ANDES finite element is modified to elastoplastic ANDES finite element by the introduction of the von Mises yield criterion elastoplastic formulation on its original deformation model. In order to accommodate the plasticity formulation, the Gauss point layered integration is inserted through of thickness of the element to produce the internal force vector and material stiffness matrix. Special effort is devoted to maintain the consistency of the internal forces and tangent stiffness as well as to enhance the robustness of element level computations. The arc-length method is used to follow the postbuckling equilibrium path. Results are presented for several benchmark elastoplastic shell problems available in the present literature, which are generally in agreement with the present work.

[1]  G. Saxcé,et al.  Plastic Limit Analysis of Plates, Shells and Disks , 2011 .

[2]  Carlos A. Felippa,et al.  Membrane triangles with corner drilling freedoms III: implementation and performance evaluation , 1992 .

[3]  J. Argyris.  An excursion into large rotations , 1982 .

[4]  Jean-Marc Battini,et al.  On the choice of the linear element for corotational triangular shells , 2006 .

[5]  Carlos A. Felippa,et al.  Membrane triangles with corner drilling freedoms II: the ANDES element , 1992 .

[6]  A. Ibrahimbegovic.  Stress Resultant Geometrically Exact Shell Theory for Finite Rotations and Its Finite Element Implementation , 1997 .

[7]  Boštjan Brank,et al.  On large deformations of thin elasto-plastic shells: Implementation of a finite rotation model for quadrilateral shell element , 1997 .

[8]  B. D. Veubeke,et al.  The dynamics of flexible bodies , 1976 .

[9]  C. Felippa.  Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the free formulation , 1989 .

[10]  C. Rankin,et al.  An element independent corotational procedure for the treatment of large rotations , 1986 .

[11]  Gerald Wempner,et al.  Finite elements, finite rotations and small strains of flexible shells , 1969 .

[12]  P. Bergan,et al.  Finite elements with increased freedom in choosing shape functions , 1984 .

[13]  Y. B. Yang,et al.  Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation , 2007 .

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

[15]  Wai-Fah Chen,et al.  Structural Plasticity: Theory, Problems, and CAE Software , 1991 .

[16]  Jean-Marc Battini,et al.  A modified corotational framework for triangular shell elements , 2007 .

[17]  B. J. Hsieh,et al.  Non-Linear Transient Finite Element Analysis with Convected Co--ordinates , 1973 .

[18]  Agustí Pérez-Foguet,et al.  On the formulation of closest‐point projection algorithms in elastoplasticity—part I: The variational structure , 2002 .

[19]  C. Rankin,et al.  Finite rotation analysis and consistent linearization using projectors , 1991 .

[20]  C. Rankin,et al.  THE USE OF PROJECTORS TO IMPROVE FINITE ELEMENT PERFORMANCE , 1988 .

[21]  Carlos A. Felippa,et al.  The first ANDES elements: 9-dof plate bending triangles , 1991 .

[22]  Bjørn Skallerud,et al.  Collapse of thin shell structures—stress resultant plasticity modelling within a co-rotated ANDES finite element formulation , 1999 .

[23]  Carlos A. Felippa,et al.  From the individual element test to finite element templates: Evolution of the patch test , 1995 .

[24]  Agustí Pérez Foguet,et al.  On the formulation of closest‐point projection algorithms in elastoplasticity—part II: Globally convergent schemes , 2000 .

[25]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part V: Nonlinear plasticity: formulation and integration algorithms , 1992 .

[26]  Carlos A. Felippa,et al.  A unified formulation of small-strain corotational finite elements: I. Theory , 2005 .

[27]  C. Felippa.  Parametrized multifield variational principles in elasticity: I. Mixed functionals , 1989 .

[28]  Carlos A. Felippa,et al.  A survey of parametrized variational principles and applications to computational mechanics , 1994 .