## 3. Hinged Plate

The eigenfrequencies and eigenmodes of a thin flat isotropic plate with a hinge are calculated. The purpose of the analysis is to demonstrate and check the modelling of a hinge, by means of different patches and the LINC command. Mass matrices are calculated with the default B2000++ consistent mass configuration.

The plate has a total length of a = 1.0 [m], a width b = 0.4 [m] and a thickness t = 0.004 [m]. The material of the plate is linear isotropic with a modulus of elasticity E = 74.E9 [N/m2], a Poisson number ν = 0.3 and a density ρ = 2700 [kg/m3]. One of the short edges is clamped, while the others are free. The hinge is located halfway between the two smaller edges (at a = a/2). The input options are listed below.

Table 7. Input options

 htype Selects the hinge type: htype=1 adds a hinge, htype=2 means no hinge.

The results for the different element types for the plate with or without hinge are listed in the table below:

Table 8. Eigenfrequencies

 Element Hinge f1 f2 f3 f4 f5 Q4.S.MITC.E4 yes 3.46 17.84 21.56 56.76 60.77 Q4.S.MITC.E4 no 9.73 17.79 54.88 60.75 84.20