Finite Volume and Boundary Element Analyses on an edge-notched Beam

In this paper two numerical techniques of Boundary Element Method (BEM) and Finite Volume Method (FVM) are used to study the deformations and stresses in a cantilever Timoshenko edge-notched beam. The beam is end loaded and the plane strain status is assumed. Computer codes were written for each method Using MATLAB package. First-order polynomials are employed for interpolation of the field and the physical variables. To do this, the linear elements in BEM and the constant strain triangles in FVM are used to discretize the beam. The effect of mesh refinement or numbers of nodes upon the accuracy of the results is studied by means of the evaluation of the displacements or energy norm. Finite element modeling of the problem has also been carried out using the commercial software of ANSYS. The results show that the BEM is more accurate than the FVM for computational purposes on the boundary nodes. Also, the FVM is less mesh-sensitive compared to the BEM.

Keywords:

: Boundary Element Method , Finite Volume Method , Energy Norm , Eedge notch