PSI - Issue 14

K. Shrivastava et al. / Procedia Structural Integrity 14 (2019) 556–563

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K.Shrivastava et al. / Structural Integrity Procedia 00 (2018) 000–000

Table 1. Dynamic Properties of Stiffened sample obtained though Experimental Setup Mode Experiment ω n (Hz) 1 488 2 - 3 928 4 1098 5 1393

3. Numerical Modeling The next step in analyzing the stiffened plate for modal parameters was carried out by establishing a simple numerical model. The preliminary numerical model of the Stiffened Plate was created by coupling the Plate and Beam Finite Element model through Longitudinal and Torsional 1-D springs. The schematic model of the system is depicted in Fig. 2.

Fig. 2. Schematic Diagram of the Setup

The plate was modelled using Mindlin plate theory formulated by Mindlin et al. (1956). The energy expression forming the basis of FE model for plate element is given by eq. 3. The terms in the energy expression are contribution from bending and shear.

2 1







U

dV  

dV





 

(3)

Plate

b b

s s

2

V

V

where, σ b and ε b are bending stress and strain respectively, τ s and γ s are transverse sheer stress and strain respectively, and the α is sheer correction factor and is taken as α =0.833.

The plate was discretised using bilinear four-noded quadrilateral (Q4) element as illustrated by Ferreira (2009) and Cook et al. (2003). Each node has three DOF, u = z 0 v = x θ z w = y θ z , where, u is the translational whereas v and w are rotational (bending) DOF of the plate.