13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- constants of grid structure excluding the cell size factor. In other words, they calculated the equivalent elastic constants, which only considering the cell microstructure and volume fraction ratio. In addition, some correlative research works have been done by Andrews [15], Yan and Cheng [16]. Wei[17] deduced the basic equation of elasticity of grid structure according to the principle of minimum potential energy and FEM, gave the elastic matrix based on the equivalent of virtual strain energy, and got the equivalent of density based on the equivalent of the kinetic energy. It is verified that the method has a good precision and is appropriate for such kind of analysis in the engineering field. The grid cylindrical structure is equivalent to an isotropic shell with homogeneous thickness through the equivalent of unit cell mechanics properties. The energy absorption capacity, deformation model of grid cylindrical structure and equivalent continuum cylindrical structure were studied under the impact load. Meanwhile, the influence of the relative density and relative thickness to equivalent accuracy of grid cylindrical structure were considered. 2. Calculation model and method Finite element models of grid cylindrical structure filled with stagger-arranged triangular cell and equivalent to continuum cylindrical structure with the same thickness were established as shown in figure 1. The dimensions of the two structures are: radius R1=100mm, length L1=272mm, and thickness T1. And the shape of cell is equilateral triangle with length L2=15.7mm, height H=13.6mm and thickness T2. The numbers of circumferential and axial cell are 40 and 20 respectively. For boundary conditions, all the nodes at upper and lower ends of cylindrical structure are constrained. Those two cylindrical structures are lateral impacted by rigid sphere with a certain speed, which radius R2=30mm, horizontal direction X1=100mm, vertical directionY1=L1/2. Grid structure Triangle Continuum structure Figure 1. Finite element models of cylindrical structure Cell-wall was modeled using Beam161 with Hughes-Liu element algorithm and rectangular cross section shape, and the material properties assumed to be perfect elastic. The number of the total elements is 24400 with each cell-wall divided into 10. In this numerical simulation, sphere was modeled using 3D Solid 164 , of which material property is plastic-kinematic, and yield stress is 76Mpa. All degree of sphere freedom was confined except lateral impact direction. The density of
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