13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- beams and plates with different kinds of cores [12-14] subjected to underwater blast loading and air blast loading. The objective of this study is to numerically and analytically investigate the optimal design of dynamic response of corrugated metal sandwich plates with sinusoidal plate core. This paper is organized as follows. Firstly, the problem is stated and the topology of sandwich plate with sinusoidal plate core is introduced in Section 2. The analytical solutions to predict the dynamic response of asymmetric sandwich plates are presented in Section 3. In Sections 4 and 5, the analytical solutions of the dynamic response of the sandwich plates under impulsive loading are compared with the finite element results. Furthermore, the study of weight optimization is carried out, such as relative core density, core height, the ratio of core height to half-length of the unit, and the thickness ratio of top and bottom face sheets. Finally, concluding remarks are presented in Section 6. 2. Statement of the problem Here, we consider a metal sinusoidal plate core sandwich plate with infinite length in x direction under impulsive loading I , as shown in Figs. 1 and 2(a). Clamped conditions are imposed along the two sides in z direction. The top and bottom face sheets with thicknesses ht and hb are perfectly bonded to the sinusoidal plate core with the height of the core Hc, as shown in Fig. 2(b). The half-width of the sandwich plate and half-length of the unit cell are L and l, and the thickness of the core web is ch . The relative core density c s ρ ρ ρ = with cρ and sρ being the density of the core and core web material, respectively, can be calculated as 2 tan c s c h l H ρ φ = ⋅ ⋅ [15], where sl is the arc length of the core web in the half unit cell and tan cH l φ= . Figure 1. Sketch of a fully clamped sandwich plate subject to impulsive loading
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