13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- where ij s and p denote the deviatoric stresses and hydrostatic pressure, respectively. qrepresents the bulk viscosity, ijδdenotes the Kronecker delta (if i = j; otherwise ijδ=0), and ijε denotes the strain rate tensor. The proportion of hourglass energy has a crucial effect on energy conservation. Hughes-Liu integral was used in Beam element calculation, and full integral was adopted in the process of homogenization equivalent for continuous shell element. The relationship of internal energy and hourglass energy of grid cylindrical structure and equivalent continuum cylindrical structure are shown in figure 3(c-continuum cylindrical structure, g-grid cylindrical structure). It can be seen that the hourglass energy proportion is far less than 5%, which is required in simulation calculation. If the hourglass energy having a good control, we believe that energy is conservative, and calculation accuracy is high in the whole impact process. 012345678910 0 20 40 60 80 100 120 140 Energy/J Time/ms g-internal energy g-hourglass energy 012345678910 0 20 40 60 80 100 120 140 Energy/J Time/ms c-internal energy c-hourglass energy Figure 3. The relationship of internal energy and hourglass energy 4.1 The effect of the impact velocity There are two main influence factors to impact resistant ability of cylindrical structure: structure deformation and energy absorption. When the sphere impacts to two kinds of structure at the velocity of 30 m/s, the displacement variation of structure is acquired before the sphere reflected back as shown in figure 4 (c-continuum cylindrical structure, g- grid cylindrical structure). It is obvious that the deformation of structure is basically identical before 3.1ms. With the increase of impact, the deformation error of structure is gradually increase. And the deformation of continuum cylindrical structure is larger about 6% than that of grid cylindrical structure at this stage. This is because that the energy is absorbed through global deformation of the structure in the initial stage of impact. At this time, the difference of the two kinds of structure is not obvious and the deformations are approximately the same. With the proceeding of impact, the local deformation of structure becomes gradually obvious and concentrates to the impacted area. The influence of grid performance and arrangement mode to the impact resistance properties of structure is gradually reflected. Some energy is additionally absorbed by distortion of grid. Therefore, deformation of the continuum cylindrical structure is larger than that of grid cylindrical structure at this stage.
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