Static and dynamic analysis of 2D and 3D elastic solids using the modified FGFEM

In this paper, a modification on the fixed grid finite element method (FGFEM) is presented and used for the static and dynamic analysis of 2D and 3D elastic solids. In this study, fixed non-boundary-fitted meshes are used to solve elasticity problems. A new approach for computing stiffness matrix of boundary intersecting elements is presented. Natural boundary conditions applied via numerical integration of traction forces and essential boundary conditions applied using a technique based on penalty function on the non-conforming boundaries. The proposed method is applied to some 2D and 3D problems in linear elasticity and the results show good agreement with analytic solutions. This method is also used for the natural frequency analysis of elastic solids and the results show good agreement with those obtained using the finite element method.

[1]  D. C. Barton,et al.  Extension of the fixed grid finite element method to eigenvalue problems , 2007, Adv. Eng. Softw..

[2]  Yi Min Xie,et al.  Introduction of fixed grid in evolutionary structural optimisation , 2000 .

[3]  Oscar E. Ruiz,et al.  FIXED GRID FINITE ELEMENT ANALYSIS FOR 3D STRUCTURAL PROBLEMS , 2005 .

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

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

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

[7]  B. Clark,et al.  The penalty boundary method , 2003 .

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

[9]  Grant P. Steven.  Internally discontinuous finite elements for moving interface problems , 1982 .

[10]  J. Reddy.  An introduction to the finite element method , 1989 .

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

[12]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[13]  Grant P. Steven,et al.  Fixed grid finite elements in elasticity problems , 1999 .

[14]  Ted Belytschko,et al.  Structured extended finite element methods for solids defined by implicit surfaces , 2002 .

[15]  W. X. Wang,et al.  Isoparametric finite point method in computational mechanics , 2003 .

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

[17]  Qing Li,et al.  A strength-based multiple cutout optimization in composite plates using fixed grid finite element method , 2006 .

[18]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[19]  T. Liszka,et al.  The finite difference method at arbitrary irregular grids and its application in applied mechanics , 1980 .

[20]  M. J. Garcia,et al.  Shape optimisation of continuum structures via evolution strategies and fixed grid finite element analysis , 2004 .