A natural neighbour meshless method with a 3D shell-like approach in the dynamic analysis of thin 3D structures

This work presents the dynamic analysis of three-dimensional plate and shell structures based on an improved meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM) using a shell-like formulation. In the NNRPIM, the nodal connectivity is imposed using the natural neighbours concept. An integration background mesh is constructed, totally node-dependent, and used in the numerical integration of the NNRPIM interpolation functions, which possess the delta Kronecker property. Several dynamic plate and shell problems are studied to demonstrate the effectiveness of the method.

[1]  S. Atluri,et al.  A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics , 1998 .

[2]  R. L. Hardy.  Theory and applications of the multiquadric-biharmonic method : 20 years of discovery 1968-1988 , 1990 .

[3]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[4]  L. Traversoni.  Natural Neighbour Finite Elements , 1970 .

[5]  J. M. Deb Nath,et al.  Dynamics of rectangular curved plates , 1969 .

[6]  D. J. Dawe,et al.  Rayleigh-Ritz vibration analysis of Mindlin plates , 1980 .

[7]  K. Wong,et al.  High-precision finite element analysis of cylindrical shells , 1987 .

[8]  Miguel Ángel Martínez,et al.  Overview and recent advances in natural neighbour galerkin methods , 2003 .

[9]  S. J. Lee,et al.  Free vibration analysis of plates by using a four-node finite element formulated with assumed natural transverse shear strain , 2004 .

[10]  K. Bathe.  Finite Element Procedures , 1995 .

[11]  Georges Voronoi.  Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .

[12]  B. Moran,et al.  Natural neighbour Galerkin methods , 2001 .

[13]  Gen Yamada,et al.  Natural Frequencies of Mindlin Circular Plates , 1980 .

[14]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[15]  T. Belytschko,et al.  THE NATURAL ELEMENT METHOD IN SOLID MECHANICS , 1998 .

[16]  Guirong Liu,et al.  A point interpolation meshless method based on radial basis functions , 2002 .

[17]  Guirong Liu.  Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition , 2009 .

[18]  S. Durvasula,et al.  Vibration of skew plates , 1973 .

[19]  Guirong Liu,et al.  A point interpolation method for two-dimensional solids , 2001 .

[20]  Sunil Saigal,et al.  Advances of thin shell finite elements and some applications—version I , 1990 .

[21]  B. Nayroles,et al.  Generalizing the finite element method: Diffuse approximation and diffuse elements , 1992 .

[22]  Y. K. Cheung,et al.  Free vibration and stability analysis of shells by the isoparametric spline finite strip method , 1996 .

[23]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[24]  R. M. Natal Jorge,et al.  Analysis of plates and laminates using the natural neighbour radial point interpolation method. , 2008 .

[25]  Marc Duflot,et al.  Meshless methods: A review and computer implementation aspects , 2008, Math. Comput. Simul..

[26]  R. Jorge,et al.  Analysis of 3D solids using the natural neighbour radial point interpolation method , 2007 .

[27]  Gui-Rong Liu,et al.  A point assembly method for stress analysis for two-dimensional solids , 2002 .

[28]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[29]  YuanTong Gu,et al.  Assessment and applications of point interpolation methods for computational mechanics , 2004 .

[30]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .