The implicit corotational method and its use in the derivation of nonlinear structural models for beams and plates

[1]  Giovanni Garcea,et al.  Mixed formulation in Koiter analysis of thin-walled beams , 2001 .

[2]  L. E. Malvern Introduction to the mechanics of a continuous medium , 1969 .

[3]  Raffaele Casciaro,et al.  3D beam element based on Saint Venànt’s rod theory , 2004 .

[4]  Giuseppe A. Trunfio,et al.  Mixed formulation and locking in path-following nonlinear analysis , 1998 .

[5]  Dinar Camotim,et al.  GBT formulation to analyse the first-order and buckling behaviour of thin-walled members with arbitrary cross-sections , 2009 .

[6]  Raffaele Casciaro,et al.  PERTURBATION APPROACH TO ELASTIC POST-BUCKLING ANALYSIS , 1998 .

[7]  A. Nayfeh Introduction To Perturbation Techniques , 1981 .

[8]  Giuseppe A. Trunfio,et al.  Path‐following analysis of thin‐walled structures and comparison with asymptotic post‐critical solutions , 2002 .

[9]  J. C. Simo,et al.  A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .

[10]  T. Belytschko,et al.  Applications of higher order corotational stretch theories to nonlinear finite element analysis , 1979 .

[11]  Ginevra Salerno,et al.  Extrapolation locking and its sanitization in Koiter's asymptotic analysis , 1999 .

[12]  Raffaele Casciaro Computational asymptotic post-buckling analysis of slender elastic structures , 2005 .

[13]  Raffaele Casciaro,et al.  Asymptotic post-buckling FEM analysis using corotational formulation , 2009 .

[14]  M. Géradin,et al.  Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids Part 2: Anisotropic and advanced beam models , 1998 .

[15]  A. Nayfeh,et al.  Linear and Nonlinear Structural Mechanics , 2002 .

[16]  Raffaele Casciaro,et al.  Asymptotic post-buckling analysis of rectangular plates by HC finite elements , 1995 .

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

[18]  Mark A. Bradford,et al.  Nonlinear analysis of members curved in space with warping and Wagner effects , 2005 .

[19]  Peter Wriggers,et al.  Thin shells with finite rotations formulated in biot stresses : theory and finite element formulation , 1993 .

[20]  F. Auricchio,et al.  On the geometrically exact beam model: A consistent, effective and simple derivation from three-dimensional finite-elasticity , 2008 .

[21]  Robert L. Taylor,et al.  On the role of frame-invariance in structural mechanics models at finite rotations , 2002 .

[22]  Ali H. Nayfeh,et al.  A new method for the modeling of geometric nonlinearities in structures , 1994 .

[23]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[24]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model , 1990 .

[25]  Anthony N. Palazotto,et al.  POLAR DECOMPOSITION AND APPROPRIATE STRAINS AND STRESSES FOR NONLINEAR STRUCTURAL ANALYSES , 1998 .

[26]  E. Reissner On one-dimensional finite-strain beam theory: The plane problem , 1972 .

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

[28]  E. Cosserat,et al.  Théorie des Corps déformables , 1909, Nature.

[29]  Ginevra Salerno,et al.  A nonlinear beam finite element for the post-buckling analysis of plane frames by Koiter's perturbation approach , 1997 .

[30]  Kuo Mo Hsiao,et al.  Co-rotational finite element formulation for thin-walled beams with generic open section , 2006 .

[31]  Moon-Young Kim,et al.  Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. I: Stability formulation and closed-form solutions , 2005 .

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

[33]  S. Antman Nonlinear problems of elasticity , 1994 .

[34]  Raffaele Casciaro,et al.  Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method , 2012 .

[35]  Michel Géradin,et al.  Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids. Part 1: Beam concept and geometrically exact nonlinear formulation , 1998 .

[36]  Giovanni Garcea,et al.  KOITER'S ANALYSIS OF THIN-WALLED STRUCTURES BY A FINITE ELEMENT APPROACH , 1996 .

[37]  Raffaele Casciaro,et al.  A numerical analysis of infinitesimal mechanisms , 2005 .