Rectangular Plate Under In-Plane Loading

In the experimental analysis of the undamaged plate, the input voltage for  the piezo stack  actuator   equals

4。5 V resulting in a stroke of 27 μm。 This is equivalent to a force amplitude of 95 N。 The measurements for the undamaged plate were conducted on a mesh of 45 × 39 points in x- and y-direction, respectively。 The distance between the points equals 1。3 mm so that an area of

56。3 mm × 49。2 mm is covered by the mesh in the centre of the plate。

Fig。 7 Positioning imprecisions for different mesh densities

Displacements The measured displacements in the x-, y- and z-direction are depicted in Fig。 9。 The displace- ments ux and uy are very uniform and the region of zero displacement in x-direction is in the centre of a measurement area。 This indicates a satisfactory align- ment of the specimen in the x-y plane。 However, the out-of-plane displacement indicates that the specimen is subjected rigid body motion and a slight amount of bending。 The bending strain falls far below 0。1% of the strain in y-direction and is therefore neglected in the following discussion。

Strains The strains in a rectangular plate under uni- axial loading are theoretically constant。 Due to noise in the measured data this is not true for the experi- mentally derived data。 The standard deviation of the experimentally derived strain field strongly depends on the width m of the SG filter。 The estimated strain εyy for m = 4 equals (205。5 ± 8。1) × 10−6 and for m = 12 one has (205。8 ± 2。5) × 10−6。 The strain field εyy for three different values of m is illustrated in Fig。 10。

The material parameters for the isotropic acrylic plate were derived from the strains derived with m  =

12。 With the principle stresses in the plate σxx = 0 and σyy = F/A, where F = 95 N is the load of the piezo actuator and A = 184 mm2 is the cross sectional area of the plate, the Young’s modulus and the Pois- son ratio yield E = 2510 MPa and ν = 0。37, respec- tively。 Published values for the Young’s modulus and Poisson’s ratio [19, 20] vary greatly ranging from be- tween E = 2300 − 3700 MPa and ν = 0。35 − 0。40。 Sep- arate extensional testing on the specimens found the Young’s modulus to vary considerably between E = 2900 ± 400 MPa。

Rectangular Plate with Circular Hole Under In-Plane Loading

The displacements for the rectangular plate with a cir- cular hole were conducted on a radially arranged mesh with 21 × 90 points in r- and ϕ-direction, as illustrated

Fig。 8 Variance coefficient of the strain in terms of   the mesh size and the smoothing parameter m

Fig。 9 Displacements ux, uy and uz measured on the undamaged plate

in Fig。 5(b)。 Similar to the experiments with the un- damaged plate, the amplitude of the input voltage for the piezo stack equals 4。5 V。 Due to the lower stiffness of the plate with the hole, this results in a lower force amplitude of 91 N。

The mesh covers an annulus with the  inner  and outer radius of 10。3 mm and 27。6  mm, respectively。 The 0。3 mm gap between the  boundary  of  the  hole and the mesh is left because the lasers can not measure directly on the edges of a structure。 A schematic of the specimen and the mesh is given in Fig。 5(b)。

Fig。 10 Strain εyy for various filter strengths m

Displacements The experimental and numerical re- sults for the displacements are compared in Fig。 11。 The results coincide well, however a slight misalignment can be observed for ux。 The misalignment breaks the symmetry of the problem and slightly different values for the amplification factor of the strain at the edge of the hole are expected。