Displacement Welding Technique for Coupled Analysis of Independently Modeled Finite Element Substructures

In this work, a displacement welding technique is proposed to analyze the whole model which consists of independently modeled finite element substructures. In the proposed method, the incompatible displacement fields in the interfaces of independently modeled substructures are directly welded together through a blended function that is newly defined in the mismatching interface region. To construct the blended function, the moving least squares function, which does not require well-defined nodal connectivity, is utilized along with the original finite element shape function. The meshless character of the moving least squares function makes it possible to efficiently handle the mismatching interfaces of independently modeled finite element substructures. To prove the validity of the proposed method, the patch tests and convergence tests are carried out for various mismatching models. To assess the performance of the proposed welding technique, several numerical examples are worked out including beam type problem, plate with circular hole, and L-shaped beam type problem.

[1]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

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

[3]  Ted Belytschko,et al.  Numerical integration of the Galerkin weak form in meshfree methods , 1999 .

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

[5]  Mohammad Aminpour,et al.  Improved interface modeling technology , 2001 .

[6]  Tzi-Kang Chen,et al.  A coupled finite element and meshless local Petrov–Galerkin method for two-dimensional potential problems , 2003 .

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

[8]  Hyun Gyu Kim.  Interface element method (IEM) for a partitioned system with non-matching interfaces , 2002 .

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

[10]  Hyun Gyu Kim,et al.  Analysis of thin beams, using the meshless local Petrov–Galerkin method, with generalized moving least squares interpolations , 1999 .

[11]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

[12]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[13]  Susan L. Mccleary,et al.  A new interface element for connecting independently modeled substructures , 1993 .

[14]  I. Raju,et al.  Coupling Finite Element and Meshless Petrov-Galerkin Methods for Two-Dimensional Potential Problems , 2002 .

[15]  Mohammad A. Aminpour,et al.  A coupled analysis method for structures with independently modelled finite element subdomains , 1995 .