PSI - Issue 13

Kota Kishi et al. / Procedia Structural Integrity 13 (2018) 1111–1116 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1113

3

2.2. Mesh superposition method for dynamic crack analysis When dynamic crack analysis is made, velocity and acceleration should be considered. By discretization of each velocity and acceleration field in addition to displacement field, and principle of virtual work for dynamic problems, the following equation is obtained, [ G GL GL T L ] { G̈ L̈ } + [ G GL GL T L ] { G L } = { G L } (3) G and L are mass matrices for the global mesh and local mesh respectively and GL is a mass matrix representing the relationship between the global mesh and the local mesh. G̈ and L̈ are acceleration in both areas. 3. Static crack 3.1. The steel plate model In this study, an infinite steel plate which contains crack is assumed. As shown in Fig. 2, the global mesh and local mesh are covered the crack tip. Considering symmetry, upper half of the model is analysis object.

s ∞

㼏㼞㼍㼏㼗㻌

㻳㼘㼛㼎㼍㼘㻌㼙㼑㼟㼔

2

2 a

1

1

0.5

1

㻸㼛㼏㼍㼘㻌㼙㼑㼟㼔

s ∞

Fig. 2 Whole model of static crack analysis

3.2. Boundary conditions Boundary conditions are set up as shown in Fig. 3. In the global area, , exact solution of the displacement, is given at the boundary between the global mesh and the infinite steel plate to model remote tensile stress. Moreover, to model crack, right half of the bottom boundary is fixed while left half is free. In the local area, the displacement is zero at the edge of the local area to ensure continuity. Boundary conditions of the bottom are given as the global mesh.

(a) Global mesh boundary condition

(b) Local mesh boundary condition

Fig. 3 Boundary conditions

3.3. Results 3.3.1 Accuracy of displacement

Experiments are performed in the steel plate model and boundary conditions. As evaluation index of the accuracy of displacement, relative 2 norm, a variable to evaluate displacement field, is adopted. Relative 2 norm is shown as Eq. (4).