New stiffened plate elements based on the absolute nodal coordinate formulation

In this study, several new stiffened plate element models are proposed based on the absolute nodal coordinate formulation. The stiffened plate elements with different geometrical continuity conditions and performances are developed by a full parametrized plate element and three different beam elements of absolute nodal coordinate formulation. The effect of stiffener is incorporated by internally constraining the stiffener displacement fields to the relevant plate displacement fields. The displacement compatible conditions of plate and stiffener are investigated to obtain the transformation matrix of nodal coordinates. The mass and stiffness of a stiffener is reflected at all the nodes of the plate element in which it is placed. Accordingly, the stiffener can be positioned anywhere within the plate element along lines of local coordinates and need not necessarily be placed on nodal lines, which gives a great flexibility in the choice of mesh size. The stiffened plate elements also achieve a better continuity condition with the slope constraint equations. Static, dynamic, and free vibration analyses are conducted to validate the proposed elements and to study the performance of the stiffeners. The results show that the new elements can be applied to describe mechanical behaviors of stiffened structures in both static and dynamic situations. The effects of the dimension of cross section and the number of stiffeners are also numerically investigated for both linear and nonlinear deformation problems.

[1]  A. Mikkola,et al.  Two Simple Triangular Plate Elements Based on the Absolute Nodal Coordinate Formulation , 2008 .

[2]  Yang Xiang,et al.  VIBRATION OF CIRCULAR AND ANNULAR MINDLIN PLATES WITH INTERNAL RING STIFFENERS , 1996 .

[3]  Haidong Yu,et al.  Dynamic model and behavior of viscoelastic beam based on the absolute nodal coordinate formulation , 2015 .

[4]  Ahmed A. Shabana,et al.  Analysis of Thin Plate Structures Using the Absolute Nodal Coordinate Formulation , 2005 .

[5]  A. Deb,et al.  Finite element models for stiffened plates under transverse loading , 1988 .

[6]  Edward A. Sadek,et al.  A finite element model for the analysis of stiffened laminated plates , 2000 .

[7]  Hiroyuki Sugiyama,et al.  Use of Plasticity Theory in Flexible Multibody System Dynamics , 2003 .

[8]  Aki Mikkola,et al.  Beam Elements with Trapezoidal Cross Section Deformation Modes Based on the Absolute Nodal Coordinate Formulation , 2010 .

[9]  K. C. Biswal,et al.  Finite element analysis for stiffened laminated plates using higher order shear deformation theory , 1994 .

[10]  Mohamed A. Omar,et al.  A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMS , 2001 .

[11]  Gengkai Hu,et al.  A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation , 2014 .

[12]  Johannes Gerstmayr,et al.  Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation , 2006 .

[13]  Aki Mikkola,et al.  Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity , 2017 .

[14]  Hung Nguyen-Xuan,et al.  Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements , 2013 .

[15]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory , 2001 .

[16]  M. Mukhopadhyay.  Vibration and stability analysis of stiffened plates by semi-analytic finite difference method, part II: Consideration of bending and axial displacements , 1989 .

[17]  M. Mukhopadhyay.  Vibration and stability analysis of stiffened plates by semi-analytic finite difference method, Part I: Consideration of bending displacements only , 1989 .

[18]  A. Shabana,et al.  Three-dimensional absolute nodal co-ordinate formulation: Plate problem , 1997 .

[19]  K. M. Liew,et al.  Free vibration analysis of rectangular plates using orthogonal plate function , 1990 .

[20]  A. Shabana,et al.  Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations , 2008 .

[21]  Ahmed A. Shabana,et al.  Flexible Multibody Dynamics: Review of Past and Recent Developments , 1997 .

[22]  Mark P. Rossow,et al.  Constraint method analysis of stiffened plates , 1978 .

[23]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[24]  Oleg Dmitrochenko,et al.  Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation , 2003 .

[25]  Aki Mikkola,et al.  Development of elastic forces for a large deformation plate element based on the absolute nodal coordinate formulation , 2006 .

[26]  A. Mikkola,et al.  Description of Elastic Forces in Absolute Nodal Coordinate Formulation , 2003 .

[27]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[28]  Ahmed A. Shabana,et al.  Use of general nonlinear material models in beam problems: Application to belts and rubber chains , 2009 .

[29]  Aki Mikkola,et al.  A Non-Incremental Finite Element Procedure for the Analysis of Large Deformation of Plates and Shells in Mechanical System Applications , 2003 .

[30]  K. Liew,et al.  Formulation of Mindlin-Engesser model for stiffened plate vibration , 1995 .