Issue 47

A. Chouiter et alii, Frattura ed Integrità Strutturale, 47 (2019) 30-38; DOI: 10.3221/IGF-ESIS.47.03 32 M ODELING o model the bellows, we used the finite element ANSYS code. Due to symmetry, the design of the joint includes a two-dimensional axisymmetric half U-shape. The dimensions of the structure are the inner radius and the thickness. For meshing the structure, we used 8 nodes quadrilateral axisymmetric elements. These elements have compatible displacement shape, and are well suited for modeling curved boundaries. The meshing in finite element models is the very important step in during analysis because it affects the accuracy and the economy of the solid model. The mesh used in 2D has 10802 elements and 22607 nodes (Fig. 2). For the boundary conditions, we respected the symmetry conditions and those of the experiment. Consequently, the following boundary conditions are used (Fig. 3): (i) the smaller diameter end (right side) is unrestrained axially and restrained in the radial direction, (ii) the large diameter end (left side) is restrained in the axial direction and unrestrained in the radial direction, (iii) the body is subjected to uniform pressure in shell side and displacement in axial direction . Figure 2 : Meshing of the expansion bellows. Figure 3 : Boundary and loading conditions. Using ANSYS finite element software, a subroutine has been developed and implemented in the main code for the determination of the most stressed area (M *) at the curved boundaries (see Fig. 2) in which cracks can be developed. The behavior of the critical point (M *) where the equivalent stress σ* is maximal is obtained with the code ANSYS ® and implanted in the post-processor using (Lemaitre and Doghri, [13]) damage model based on Newton iterative method. In continuum damage mechanics, a surface density of microcracks Lemaitre and Chaboche [14] defines the damage variable: D S D S    (1) T